The Soliton Wake: Identifying the Runaway Object RBH-1 as a Gravitational Soliton

1. Introduction: The RBH-1 Anomaly

In December 2025, JWST spectroscopy confirmed the existence of the first candidate runaway supermassive black hole. Designated RBH-1, this object has an inferred mass of approximately $10^7 M_\odot$ and a proper motion of $v_{\bullet} = 954^{+110}_{-126}$ km/s, leaving behind a 62 kpc linear feature of active star formation. The discovery is consistent with theoretical predictions that supermassive black holes can be ejected from their host galaxies via gravitational wave recoil following a black hole merger (van Dokkum et al. 2025; Campanelli et al. 2007).

At $z \approx 0.96$, RBH-1 appears as a luminous streak extending from the galaxy RCP 28 in the constellation Sextans. A bow-shaped interaction region marks its leading edge, while the wake exhibits active star formation along its entire extent.

The Observational Puzzle

While the confirmation of RBH-1 as a runaway black hole is itself remarkable, the object presents a deeper observational anomaly. It appears as a linear streak of light extending 62 kpc ($\sim$200,000 light-years) from a distant galaxy ($z\approx 0.96$). At its tip lies a bright, bow-shaped interaction region where JWST spectroscopy reveals a sharp kinematic discontinuity: a line-of-sight velocity change of order $\sim 600$–$650$ km/s across $\sim$1 kpc (van Dokkum et al. 2023; van Dokkum et al. 2025).

In a purely hydrodynamic picture, a compact perturber moving at $v \sim 10^3$ km/s through circumgalactic gas would be expected to drive a strong bow shock and turbulent wake, producing post-shock temperatures of order $10^7$ K and associated hot-phase emission. RBH-1 instead exhibits a narrow, structurally coherent wake whose line diagnostics are consistent with gas cool enough to support ongoing star formation. This creates a fundamental quantitative tension.

Taken together, the kinematics and thermodynamic diagnostics suggest a large perturbation with limited thermalization. The following sections frame this tension through two related problems: the Temperature Paradox and the Geometry Problem.

The Cooling Bottleneck

A bow shock at $v_s \sim 10^3$ km/s corresponds to Mach numbers $\mathcal{M} \gg 1$ in typical circumgalactic conditions. Standard Rankine–Hugoniot jump conditions mandate substantial conversion of bulk kinetic energy into thermal energy. For $v_s \approx 1000$ km/s, the characteristic post-shock temperature is:

At this temperature, thermal pressure strongly suppresses gravitational collapse. Since the Jeans mass scales as $M_J \propto T^{3/2}$, raising the temperature from $100$ K to $10^7$ K increases the characteristic collapse mass scale by a factor of $10^{7.5}$ ($\sim 3\times 10^7$), making in-situ star formation in recently shocked gas difficult without highly efficient cooling.

The Cooling Bottleneck ($t_{\mathrm{cool}} \gg t_{\mathrm{dyn}}$)

The standard resolution invokes rapid radiative cooling, potentially aided by turbulent mixing or thermal instabilities (e.g., Gronke & Oh 2018). However, the viability of this mechanism is quantitatively constrained by the cooling physics. The following calculation demonstrates that under fiducial CGM conditions and standard optically thin cooling, the thermal model faces a fundamental timescale crisis.

Bremsstrahlung Cooling Time

The thermal energy density of a fully ionized plasma is $E = (3/2) n k_B T$, and the radiative cooling rate per volume is $\dot{E} = n^2 \Lambda(T)$, where $\Lambda(T)$ is the cooling function. At $T \sim 10^7$ K, cooling is dominated by free-free (Bremsstrahlung) emission with contributions from metal-line cooling, yielding $\Lambda(T) \approx 2.5 \times 10^{-23}$ erg cm$^3$ s$^{-1}$ for solar metallicity (Sutherland & Dopita 1993). The cooling time is:

Substituting the post-shock temperature $T = 1.4 \times 10^7$ K and a post-shock density $n = 0.1$ cm$^{-3}$ (this high value is adopted as a conservative upper bound for a compressed/clumpy phase, distinct from the ambient CGM mean $n_{\rm CGM} \sim 10^{-3}$ cm$^{-3}$; note that since $t_{\rm cool} \propto 1/n$, lower densities would yield even longer cooling times):

Dynamical Timescale

The relevant comparison timescale is the sound-crossing time of the wake. The post-shock sound speed for a fully ionized plasma ($\gamma = 5/3$, mean molecular weight $\mu = 0.6$) at $T = 1.4 \times 10^7$ K is:

For the observed wake radius $w \approx 0.7$ kpc (van Dokkum et al. 2025), the dynamical timescale is:

The Critical Inequality

Comparing these timescales yields the fundamental constraint:

This inequality is robust across the plausible parameter space. Sensitivity analysis shows that only at densities $n \gtrsim 1$ cm$^{-3}$ (an order of magnitude higher than typical circumgalactic values) does the ratio approach unity. While dust-gas collisional cooling can shorten timescales in some environments, high-velocity shocks ($v \sim 1000$ km/s) efficiently destroy dust grains via sputtering (Draine & Salpeter 1979), reducing the efficacy of this pathway in the immediate post-shock region. For fiducial parameters, shock-heated gas at $10^7$ K would expand and rarefy long before radiating sufficient energy to reach star-forming temperatures ($T \lesssim 10^4$ K).

The Observational Verdict

Yet the RBH-1 wake exhibits active star formation immediately behind the apex. The observed stellar continuum colors are "well-fit by a simple model that has a monotonically increasing age with distance from the tip" (van Dokkum et al. 2023)—the youngest stars are at the tip, not 35 kpc behind it where the cooling delay would place them. This creates a fundamental tension:

• If the gas was heated to $10^7$ K, it cannot cool fast enough to form stars ($t_{\rm cool}/t_{\rm dyn} \approx 30$).
• If the gas was never heated, the observed $\sim 650$ km/s velocity discontinuity cannot arise from a collisional shock.

Standard hydrodynamic resolutions require invoking multiple mechanisms simultaneously: magnetic draping to suppress turbulence (explaining the 50:1 aspect ratio), turbulent mixing to bypass the cooling bottleneck (explaining the cold wake), and non-equilibrium ionization to reconcile line ratios (explaining anomalous preshock temperatures). Critically, these mechanisms are dynamically antagonistic—magnetic draping creates the laminar sheath that suppresses the turbulent mixing required to solve the cooling problem.

This motivates considering a non-thermal driver. It is proposed that the observed velocity discontinuity ($\sim 650$ km/s) may reflect a coherent redshift gradient—a metric shock—in which the velocity jump is an apparent effect of differential proper time rather than bulk thermalization.

The Geometry Problem

The wake's geometry is also nontrivial. Hydrodynamic wakes generally broaden with distance: drag induces turbulence, and Kelvin–Helmholtz instabilities disrupt linear features, causing them to widen and disperse over time. Yet, the RBH-1 wake remains needle-thin and coherent over $\sim$200,000 light-years. It does not broaden as a typical turbulent wake; it remains exceptionally collimated.

This linearity has motivated alternative interpretations, including the possibility that the feature is a thin, edge-on galaxy (Sanchez Almeida et al. 2023). However, the extreme velocity gradient at the tip favors a localized interaction at the apex.

Implications

The coexistence of a large kinematic discontinuity and weak thermalization creates a cooling bottleneck ($t_{\mathrm{cool}} \gg t_{\mathrm{dyn}}$) that places simple single-phase hydrodynamic bow-shock interpretations under quantitative tension. Section 2 establishes the theoretical framework for a gravitational soliton. Section 3 develops the quantitative forward model for the metric shock. Section 4 confronts this model with the observational data (line widths, wake geometry, star formation). Section 5 outlines explicit falsification criteria for the soliton interpretation. Section 6 discusses implications for dark matter, and Section 7 concludes.

2. Theoretical Framework: The Gravitational Soliton

The driver of the RBH-1 wake may not be a ballistic projectile, but rather a propagating structure in spacetime itself—a gravitational soliton.^† This is a coherent region of deep gravitational potential moving through the cosmos (consistent with non-topological soliton solutions; see Kusenko 1997). As this structure traverses a gas cloud, it does not push atoms kinetically; instead, it alters the local flow of time.

^† Terminology note: Here, "soliton" refers specifically to a non-topological defect in a scalar field (a Q-ball or oscillon analog) that saturates at a finite density $\rho_c$, distinct from the vacuum singularity solutions of pure General Relativity. While Schwarzschild and Kerr black holes are sometimes called "gravitational solitons" in the mathematical sense of stationary, localized solutions, the objects considered here have no event horizon and are characterized by a finite core density rather than a central singularity.

Phenomenology of the Time Lens

In this framework, RBH-1 acts as a moving "time lens." Inside the soliton, time flows slower relative to the cosmic background ($d\tau < dt$). This creates a refractive effect: just as glass bends light because light moves slower within it, a region of time dilation bends the trajectories of matter. To an external observer, gas entering this region appears to redshift and change velocity—not because it has been physically pushed, but because the local clock rate has changed.

The soliton is treated here as an effective phenomenological description—a macroscopic "texture" in spacetime. One theoretical realization arises from the bi-metric scalar-tensor structure of TEP (Smawfield 2025a, 2025g), where the gravitational metric $g_{\mu\nu}$ governs curvature while an effective matter metric $\tilde{g}_{\mu\nu}$ encodes the local proper-time rate. This implies a decoupling where kinematics (driven by $\tilde{g}_{\mu\nu}$) can be strong while lensing (driven by the conformal-invariant null geodesics of $g_{\mu\nu}$) remains weak. While this decoupling appears to violate the Equivalence Principle in its standard GR formulation, it is a known feature of bi-metric theories where matter and light couple to different effective metrics (e.g., Disformal Gravity models). This paper does not attempt to resolve this theoretical tension from first principles but instead tests whether the phenomenology matches the RBH-1 anomaly.

The saturation density $\rho_c \approx 20$ g/cm³, which governs the soliton size, is not a free parameter in this analysis. It is an external input derived from terrestrial constraints in the companion "Universal Critical Density" paper (Smawfield 2025g). This analysis tests whether this specific value, calibrated on Earth, correctly predicts the wake properties of a distant supermassive black hole.

Forward Model: From Field Gradient to Velocity Shift

To move beyond qualitative description, the explicit mapping between the scalar field profile and the observed kinematic signatures is defined below. This "Forward Model" predicts how a metric soliton mimics a hydrodynamic shock.

The Metric Redshift Relation

In the TEP framework, the effective matter metric $\tilde{g}_{\mu\nu}$ is conformally related to the gravitational metric $g_{\mu\nu}$ by a scalar function $A(\phi)$. The proper time interval $d\tau$ for a comoving observer is related to the coordinate time $dt$ by: $ d\tau = \sqrt{A(\phi)} dt $

An emitter located within the soliton (where the field value is $\phi$) emits photons with a proper frequency $\nu_0$. To an external observer at infinity (where $A(\phi_\infty) \to 1$), the received frequency $\nu_{\text{obs}}$ is redshifted solely by the change in the local clock rate: $ 1 + z_{\text{metric}} = \frac{\nu_0}{\nu_{\text{obs}}} = \frac{1}{\sqrt{A(\phi)}} $

This produces an apparent Doppler shift. Even if the gas is static ($v_{\text{pec}} = 0$), an observer interprets the frequency shift as a line-of-sight velocity $v_{\text{app}}$: $ v_{\text{app}} \approx c \cdot z_{\text{metric}} \approx c \left( \frac{1}{\sqrt{A(\phi)}} - 1 \right) $

Predicting the Velocity Discontinuity

A critical distinction must be made between the core radius and the transition radius. The core radius $R_{\rm sol} \sim 7.8 \times 10^7$ km is the fundamental geometric scale where the field saturates (derived from $\rho_c$). However, because the object is screened, the observable kinematic effects manifest at the transition radius $R_{\rm trans} \sim 0.1$–$1$ kpc, where the field gradient becomes unscreened.

The connection is that $R_{\rm trans}$ is not arbitrary; it scales with the core mass. In the Vainshtein mechanism, $R_{\rm trans} \propto (R_{\rm sol}^3 \lambda_C^{-2})^{1/5}$ (where $\lambda_C$ is the Compton wavelength). While the exact prefactor depends on the coupling strength, the existence of a transition zone at $\sim$kpc scales for a $10^7 M_\odot$ object is a consequence of the underlying soliton geometry. The "shock" observed at the RBH-1 tip corresponds to the gradient of $A(\phi)$ at this transition boundary.

For a weak-field conformal coupling, $A(\phi) \approx 1 + 2\beta_{\text{eff}}\Phi/c^2$ where $\Phi = -GM/r$ is the Newtonian potential and $\beta_{\text{eff}}$ is the effective coupling strength (scalar charge) at the screening boundary. Substituting into the apparent velocity formula:

Predicting Line Widths (The Discriminator)

The crucial distinction lies in the second moment of the line distribution (line width).

• Thermal Shock: The velocity jump comes from chaotic thermalization. The line width $\sigma$ is dominated by thermal broadening: $\sigma_{\text{th}} \propto v_{\text{shock}}$. For $v \sim 1000$ km/s, $\sigma \sim 100$ km/s.
• Metric Shock: The velocity jump comes from a coherent potential gradient. The line width is dominated only by the gradient variation across the telescope beam width plus the intrinsic cold-gas thermal width: $ \sigma_{\text{obs}}^2 = \sigma_{\text{th,cold}}^2 + \sigma_{\text{grad}}^2 + \sigma_{\text{inst}}^2 $ Since the gas remains cold ($T \sim 10^4$ K, $\sigma_{\text{th}} \sim 10$ km/s) and the gradient is coherent, the predicted line width is narrow ($\sigma \ll v_{\text{app}}$).

Prediction: the metric shock model predicts a large centroid shift ($\sim 600$ km/s) with a narrow line width ($\sim 30$ km/s). This constitutes a specific discriminant between coherent redshift gradients and thermalized shocks.

Thermodynamics of a Metric Shock

This shift from "kinetic push" to "metric distortion" solves the temperature problem. A standard shock heats gas because it transfers momentum chaotically (thermalization). A metric shock is orderly. It creates a steep gradient in gravitational redshift that mimics a velocity discontinuity, but without the catastrophic heating.

1. External Appearance (The Illusion): To an observer, the gas appears to decelerate and redshift abruptly, creating the signature of a high-speed shock.
2. Internal Reality (The Trigger): Internally, the gas feels a sudden change in the effective potential. This lowers the threshold for gravitational collapse, as derived below.

The key point is that the Jeans-mass reduction is a derived consequence of the conformal coupling, not an ad hoc assumption. The magnitude depends on the depth of the potential well, which is constrained by the observed velocity discontinuity and the saturation density.

Crucially, this reinterprets the measured $\sim 600$ km/s velocity jump. It is not a bulk flow of hot plasma, but a differential proper-time lag across the soliton boundary. Furthermore, the observed speed of the object ($\sim 1000$ km/s $\approx 10^{-3}c$) is interpreted not as a ballistic trajectory, but as the characteristic group velocity of the scalar wave packet, set by the gradient of the local cosmic potential. In screened scalar-tensor theories, the group velocity scales as $v_g \sim c \sqrt{|\Phi|/c^2}$ where $\Phi$ is the ambient gravitational potential; for CGM environments with $|\Phi|/c^2 \sim 10^{-6}$, this yields $v_g \sim 10^{-3}c \sim 300$–$1000$ km/s—consistent with the observed proper motion.

The Discriminator: How can these models be distinguished? The primary discriminant is the line profile.
In a thermal shock where the emitting gas is predominantly hot, a large velocity change ($v$) implies a high temperature ($T \propto v^2$), which broadens spectral lines via thermal Doppler motion ($\sigma_v \propto \sqrt{T}$). Even in multiphase scenarios where [O III] arises from cooler zones, a substantial hot-phase contribution should produce detectable broad wings.
In a metric shock, the "velocity change" is a coherent redshift gradient. The centroid of the emission line shifts, but the line width remains narrow because the gas stays cold throughout.

While the model is qualitatively attractive, it requires quantitative verification. If RBH-1 is a soliton, it must have a specific size. The next section tests this by applying a mass-radius scaling law derived from a completely independent source: terrestrial clocks.

3. Quantitative Predictions: Testing the Metric Shock

The metric-shock hypothesis proposes that the observed velocity discontinuity Δv ~ 650 km/s arises from a spatial gradient in the conformal factor A(φ), which relates the matter metric to the gravitational metric via $\tilde{g}_{\mu\nu} = A(\phi) g_{\mu\nu}$. This section derives the required field parameters and checks for internal consistency.

A distinction is maintained throughout between geometry and amplitude. The soliton core radius (and associated geometric scaling) is fixed a priori by $\rho_c$ (Paper 7), while the magnitude of the apparent kinematic discontinuity depends on screening/transition physics through the effective coupling at $R_{\text{trans}}$ and is therefore treated here as an empirical constraint rather than an independent free fit.

Table 2: Model Inputs vs. Predictions

Required Conformal Factor Gradient

A redshift-like velocity offset Δv corresponds to a fractional frequency shift:

In the conformal time framework, clock rates scale as √A. A spatial gradient in A produces an apparent Doppler shift for observers using coordinate time. The required change in ln(√A) across the discontinuity is:

If this gradient occurs over a characteristic scale L ~ 1 kpc (the observed width of the kinematic discontinuity), the implied gradient is:

Lensing and Clock Signatures

A critical prediction of the conformal scalar-tensor framework is the decoupling of matter and light sectors. The scalar field $A(\phi)$ modifies the proper time for massive particles ($d\tau^2 = A dt^2$), creating the large apparent velocity and "Phantom Halo" effects. In the weak-field limit of a purely conformal coupling, null geodesics remain unaffected because the conformal factor cancels in the null condition $ds^2 = 0$. Therefore, gravitational lensing is governed primarily by the bare gravitational metric $g_{\mu\nu}$ (the baryonic mass), not the enhanced scalar potential. (Note: disformal couplings or strong-field corrections could modify this; the prediction here assumes the conformal limit.)

For light passing through the wake boundary ($b \sim 1$ kpc), the deflection angle depends only on the bare mass $M \approx 2 \times 10^7 M_\odot$:

This value ($\sim 0.8$ milliarcseconds) is far below current observational limits (HST resolution $\sim 50$ mas).

For stars formed within the wake, the metric gradient would produce a systematic redshift offset in their absorption lines relative to stars formed outside the wake. If the wake interior has $\Delta \ln(\sqrt{A}) \sim 10^{-3}$ relative to the ambient medium, stellar spectra should show:

This is a testable prediction: spatially resolved spectroscopy of individual stellar clusters along the wake should reveal systematic velocity offsets correlated with position, distinct from the Hubble flow and peculiar velocities.

Screening and Parameter Consistency

The above estimates assume the scalar field is in the Vainshtein-screened regime, where the effective coupling β_eff is suppressed relative to the bare coupling β₀. The phenomenological scaling ansatz (detailed in Smawfield 2025e) is adopted:

For RBH-1 at the crossover mass (M ~ 10⁷ M_☉, ρ ~ ρ_c ~ 20 g/cm³), the screening factor is S ~ 1, meaning the field is near the transition between screened and unscreened regimes. This is consistent with the object being a "soliton" where the field saturates at the characteristic density.

At higher densities (e.g., white dwarfs, neutron stars), S >> 1, and the scalar contribution is suppressed below observational limits, explaining why precision GR tests show no deviation. At lower densities (e.g., galaxies), S < 1, and the scalar field produces observable "phantom mass" effects (detailed in the companion paper, Smawfield 2025e).

5. Falsification Criteria

This paper treats the saturation density $\rho_c \approx 20$ g/cm³ as a fixed input derived in Paper 7. This makes the RBH-1 analysis a consistency check: the model does not have the freedom to fit the core radius; it must match the geometric scale dictated by the $10^7 M_\odot$ mass and the universal density. Note that $R_{\rm sol}$ itself is not directly observable at $z \sim 1$; the testable prediction is that the transition-zone phenomenology (at $R_{\rm trans} \sim$ kpc scales) should be consistent with a core of this size.

The Soliton Size Prediction

Given $\rho_c \approx 20$ g/cm³ (from Paper 7), the predicted soliton radius for RBH-1 ($M \approx 2 \times 10^7 M_\odot$) is:

Uncertainty Propagation

The prediction uncertainty derives from two inputs: the mass estimate and the saturation density. For the mass $M \sim 2 \times 10^7 M_\odot$ (van Dokkum et al. 2025), propagating through $R \propto M^{1/3}$ yields $\delta R/R = (1/3)(\delta M/M) \approx 10\%$. The saturation density $\rho_c \approx 20$ g/cm³ carries systematic uncertainty of order $\pm 30\%$ from the GNSS calibration (Paper 7), contributing $\delta R/R = (1/3)(\delta\rho_c/\rho_c) \approx 10\%$. Combined in quadrature:

The correspondence $R_{\text{sol}} \approx 1.3 R_S$ means the soliton surface is just outside the Schwarzschild horizon. This predicts a "naked halo" phenomenology: the object interacts with the environment via its metric gradient (the "hair") rather than just its horizon.

Explicit Falsification Criteria

The hypothesis that RBH-1 is a Gravitational Soliton makes specific, falsifiable predictions. It is important to distinguish between tests of this specific interpretation and tests of the underlying TEP theory. A failure in the object-specific tests below would rule out the soliton model for RBH-1 (returning it to the status of an unexplained anomaly), but would not falsify the broader TEP framework.

1. Mass falsification (Object Specific): The prediction $R_{\text{sol}} \approx 1.3 R_S$ is sensitive to mass. If future dynamical measurements revise $M_{\text{RBH-1}}$ to > 3 × 10$^7$ $M_\odot$ (where $R_{\text{sol}} < R_S$), the predicted soliton size would fall inside the horizon, falsifying the soliton interpretation for this specific object.
2. Discriminant falsification (Spectroscopy): If deep spectroscopy reveals:
   • Strong coronal-line emission ([Fe X], [Fe XIV]) or soft X-rays consistent with $T \sim 10^7$ K gas dominating the emission measure, the "no heating" claim is falsified for this object.
   • Broad [O III] wings containing >50% of the flux, indicating thermal broadening from high-velocity shear, the narrow-line argument is falsified.
   • No systematic velocity offsets in stellar absorption lines along the wake (contradicting the metric-gradient prediction).
3. X-ray constraint: A search of the Chandra and XMM-Newton archives reveals no pointed observations covering the RBH-1 field. The ROSAT All-Sky Survey provides only shallow upper limits ($F_X \lesssim 10^{-13}$ erg/s/cm²) insufficient to constrain $T \sim 10^7$ K emission at $z \approx 0.96$. Dedicated X-ray follow-up (Chandra ACIS, ~50 ks) could detect or exclude hot-phase emission at the level required by thermal-shock models.
4. Universal Calibration Failure (Theory Level): Unlike the object-specific tests above, if the external input $\rho_c \approx 20$ g/cm³ is invalidated by independent replication of the GNSS analysis (Paper 7), the basis for the specific quantitative prediction collapses.

6. Discussion: Implications for Dark Matter

Observational Context

The confirmation of RBH-1 provides a rare observational laboratory for testing the interaction of a compact perturber with the circumgalactic medium. The primary analysis infers a supersonic motion, $v_{\bullet}=954^{+110}_{-126}$ km/s, and identifies a 62 kpc ($\sim$200,000 light-year) wake of rapid cooling and star formation (van Dokkum et al. 2025). Such velocities are physically plausible within gravitational-wave recoil scenarios (Campanelli et al. 2007; Colpi & Dotti 2011; Komossa 2012). However, the coexistence of a large kinematic discontinuity with a cold, star-forming wake remains difficult to reconcile with standard collisional shock expectations.

The central tension concerns the wake rather than the recoil. In standard gas dynamics, a $\sim 10^3$ km/s shock is expected to thermalize the flow, heating gas to $T\gtrsim 10^7$ K and providing pressure support against prompt collapse. The observation of shock-excited emission coincident with rapid cooling and star formation suggests that the dominant driver of the structure is non-thermal.

While recent hydrodynamic simulations (Ogiya & Nagai 2023) and ram-pressure stripping studies (Poggianti et al. 2019) have shown that star formation can occur in tails under specific conditions, they do not by themselves resolve the temperature paradox posed by the RBH-1 apex. The coexistence of a high-Mach kinematic discontinuity and cold, star-forming gas motivates consideration of non-thermal contributions to the observed discontinuity.

Resolution via Temporal Solitons

A metric-driven interpretation offers an alternative to a purely hydrodynamic bow-shock model. If RBH-1 is modeled as a propagating region of altered proper-time rate (a temporal soliton), then the dominant observational signature at the apex could be a spatial gravitational-redshift gradient rather than irreversible collisional heating. In this scenario, the wake can remain comparatively cold while the effective collapse threshold behind the front is modified, enabling star formation without a long-lived hot phase. The trail is then interpreted as an imprint of a transient metric perturbation rather than material entrained by a compact projectile.

Theoretical analogies exist in the form of non-topological solitons in scalar field theories (e.g., Kusenko 1997; Heeck et al. 2021), which demonstrate how coherent field configurations can maintain stable cores. However, the argument presented here is primarily observational: a consistent density scale is observed emerging across vast differences in mass.

RBH-1 as a Naked Halo Candidate

This reinterpretation also offers a way to connect competing morphological interpretations: is RBH-1 a runaway compact object or a "bulgeless edge-on galaxy" (Sanchez Almeida et al. 2023)? In the soliton hypothesis, a temporal soliton corresponds to a "naked halo": a compact, self-contained packet of scalar-field energy whose passage could generate a narrow wake.

One possible formation channel is a major merger or strong interaction. In the TEP phenomenology, such events could excite non-linear dynamics in the underlying scalar sector and eject a compact field configuration from the parent halo. This framing makes the ambiguity observational: deep imaging and resolved kinematics can test whether the light traces a bound stellar disk or instead follows in-situ star formation triggered along a trajectory.

Signatures of Internal Dynamics

Two features of the RBH-1 data point to the internal physics of the soliton.

1. Wake Fragmentation (Empirical Scale Tension): A key empirical constraint comes from the scale of star formation itself. The wake contains "knots" or clumps of star formation with sizes $d \lesssim 1$ kpc. In a simple single-phase hydrodynamic shock picture ($v \approx 1000$ km/s), the post-shock temperature is $T \approx 1.4 \times 10^7$ K. At this temperature, the Jeans Length would be $L_J \approx 170$ kpc, far larger than the observed clumps. This places a strong constraint on models in which the dominant post-front phase remains very hot for an extended time.
2. Gravitational Echoes: A future test lies in gravitational waves. When two black holes merge, the resulting "ringdown" signal decays exponentially. If the objects are horizonless solitons, gravitational waves could be partially trapped between the photon sphere and an interior reflective boundary, producing repeating pulses or "gravitational echoes" (Cardoso et al. 2016).

Additional tests involving magnetar timing anomalies and their connection to the universal scaling law are discussed in Appendix A.

Broader Context

The saturation density $\rho_c \approx 20$ g/cm³ used to predict the RBH-1 wake geometry is not arbitrary. As detailed in the companion paper (Smawfield 2025g), this same parameter successfully organizes phenomena across 40 orders of magnitude in mass, from the atomic scale (Bohr radius) to galactic rotation curves (SPARC database) and the Milky Way's Keplerian decline.

The fact that a single calibration, derived from terrestrial GNSS clocks, correctly predicts the wake properties of a distant $10^7 M_\odot$ black hole provides strong evidence that RBH-1 is not a unique anomaly, but a standard astrophysical object manifesting universal scalar-field dynamics. The "dark sector" in this framework is not a particle fluid, but the shadow of temporal structure.

7. Conclusion

The data currently available—specifically the coexistence of high-velocity kinematics ($\Delta v \sim 650$ km/s) with narrow spectral lines ($\sigma \approx 31$ km/s)—place strong constraints on single-phase thermal-shock interpretations. The soliton interpretation simultaneously addresses (i) the narrow morphology, (ii) the limited evidence for dominant hot-phase thermalization, and (iii) the characteristic scale predicted by the universal $\rho_c$ calibration.

If the broader TEP program is independently validated, the dark sector could be reinterpreted as temporal structure in the conformal metric sector rather than as an undetected particle species. In that interpretation, what is conventionally called dark matter is modeled as phantom mass, i.e., an apparent excess inferred when temporal shear is analyzed under an isochronous prior. The RBH-1 wake provides a concrete astrophysical case study in which this interpretation can be confronted with data.

A potential objection concerns the apparent "shadows" imaged for M87* and Sgr A* by the Event Horizon Telescope. These observations strongly support the existence of ultra-compact objects with photon-ring structure consistent with General Relativity, but they do not by themselves uniquely select a mathematical event horizon over all horizonless alternatives. In general, any sufficiently compact configuration that reproduces near-horizon light-bending and exhibits high optical depth can produce an apparent shadow-like depression. The RBH-1 hypothesis therefore does not require that all supermassive black holes be identical solitons; rather, it motivates a targeted comparison between RBH-1 and EHT-class objects, with particular emphasis on whether the central brightness depression behaves as a true absorbing horizon or as a saturating refractive core (Event Horizon Telescope Collaboration 2019; Event Horizon Telescope Collaboration 2022).

The key next step is falsification. The soliton hypothesis makes concrete observational predictions:

• Line-Width Thermometry: Spectra should show redshift discontinuities with suppressed thermal broadening (the "Cold Shock"). This is the primary discriminant based on existing data.
• Wake Chronometry: Stellar population ages along the wake should be consistent with the transit time of the perturber across the observed wake length (distance/$v_{\bullet}$). Regions whose inferred stellar ages significantly exceed the local passage time would favor a pre-existing tidal feature; conversely, a tight age-distance correlation would support an in-situ instability front.
• Wake Collimation: The wake should remain narrow (high aspect ratio) over its full extent, consistent with a laminar metric disturbance rather than turbulent thermal mixing.

References

Appendix A: Future Directions

This appendix identifies potential future tests of the TEP framework. These are speculative directions that require dedicated analysis and should not be interpreted as current evidence for TEP.

A.1 EHT Polarimetry

Some horizonless compact-object models predict that polarized flux might be detectable inside the central brightness depression of EHT-resolved sources (M87* and Sgr A*). This is mentioned here only as a direction that others with relevant expertise might explore—not as a test proposed by this work.

• Status: No analysis has been performed by the author. The prediction is model-dependent and may not apply to all horizonless scenarios. Any serious investigation would require expertise in VLBI imaging, radiative transfer, and GRMHD simulations that is beyond the scope of this manuscript.

A.2 Additional JWST Case Studies

Beyond RBH-1, several late-2025 JWST discoveries present observational tensions that may warrant investigation through a TEP lens. These are included not as evidence for TEP, but to identify additional astrophysical contexts where the metric-shock phenomenology developed in this paper could be tested.

Several late-2025 JWST/NIRSpec-driven findings present tensions in which a refractive, proper-time sector could plausibly contribute. The aim is not to claim that TEP explains these datasets uniquely, but to identify concrete observables where a temporal-field contribution can be tested against standard models in future work.

A.2.1 Little Red Dots (LRDs)

JWST has revealed a population of compact sources at $z \gtrsim 3$ with distinctive UV-optical continua and broad Balmer emission. Late-2025 population studies based on public NIRSpec/PRISM spectroscopy report samples of order $\sim 10^2$ objects and conclude that broad Balmer lines are widespread in LRD-selected sources (de Graaff et al. 2025; Barro et al. 2025). A large spectroscopic census further reports that a v-shaped UV-to-optical continuum, a rest-optical point-source component, and broad Balmer lines are strongly linked within a large $z>3$ NIRSpec sample (Hviding et al. 2025). Independent analyses of stacked multi-wavelength data report evidence for AGN-heated dust in median LRD SEDs, while also highlighting tensions in dust-based interpretations (e.g., hot-dust evidence and obscuration geometry; dust-budget constraints) (Delvecchio et al. 2025; Chen et al. 2025).

• Potential TEP connection. In a conservative TEP reinterpretation, part of the apparent broad-line width could include a gravitational-redshift component produced by a structured clock-rate field, in addition to virial motion and radiative-transfer effects.
• Discrimination. Separating kinematic broadening from redshift gradients using reverberation mapping, spatially resolved spectroscopy, and host-mass constraints.

A.2.2 Massive Quiescent Galaxies at High Redshift

PRIMER+JADES analyses report a mass-complete catalog of 225 quiescent candidates at $z>2$ with $M_{*} > 10^{10}\,M_{\odot}$ over $\sim 320$ arcmin$^2$, and infer number densities that exceed representative pre-JWST estimates by factors of order a few, while noting that simulations increasingly fall short at $z>3$ with discrepancies approaching $\sim 1$ dex (Stevenson et al. 2025).

• Potential TEP connection. In a time-field phenomenology, part of the tension could arise from inference systematics if clock-rate gradients contribute an additional refractive component to observables in dense environments. Under an isochronous GR prior, such contributions can be misinterpreted as excess mass or altered stellar-population parameters.
• Discrimination. Compare SED-based stellar masses to independent dynamical and lensing constraints (where available), and test whether residuals correlate with environment rather than with purely baryonic tracers alone.

A.2.3 Strong-Lensing Time-Delay Cosmography

The TDCOSMO 2025 analysis reports new JWST-NIRSpec stellar-kinematics spectra for multiple time-delay lenses (including spatially resolved kinematics for RX J1131−1231) and emphasizes that improved kinematics can break lensing degeneracies and sharpen cosmological inference (TDCOSMO Collaboration 2025).

• Potential TEP connection. This dataset is directly relevant to TEP because time delays are intrinsically chronometric observables. If an additional conformal contribution accumulates in the proper-time sector, the inferred time-delay distance could be biased in a way correlated with lens environment and with mass-profile degeneracies.
• Discrimination. Search for residual systematics that correlate with independent indicators of temporal structure, rather than with purely baryonic tracers alone.

A.3 Magnetar Timing Anomalies

Standard neutron stars experience "glitches" (sudden spin-ups). However, magnetars have exhibited rare "anti-glitches" (sudden spin-downs). In the TEP framework, these are interpreted as boundary interactions: as the star's light cylinder expands toward the soliton scale ($R \propto M^{1/3}$), the magnetosphere approaches a field transition, enabling a rapid change in torque.

The magnetar 1E 2259+586 is particularly significant—its period matches the TEP-predicted critical period ($P_{\rm crit} \approx 6.8$ s for a $1.4 M_{\odot}$ neutron star, using the same $\rho_c$ calibration as RBH-1) to within 3%. This suggests the soliton physics is not unique to supermassive black holes but scales universally with mass.

• Potential TEP connection. The anti-glitch timing and magnitude could be correlated with the light-cylinder radius approaching the soliton boundary scale predicted by $\rho_c$.
• Discrimination. Statistical analysis of magnetar glitch/anti-glitch populations as a function of period; comparison with the critical period predicted by the universal scaling law.

A.4 Status

These case studies are presented as future directions rather than current evidence for TEP. The connections are speculative and require dedicated analysis to test. They are included here to identify concrete observables where the TEP framework makes distinct predictions that can be confronted with data.