Evidence for Horizons and the Absence of Surfaces

An event horizon is a global causal boundary, so an astronomical observer does not detect it by receiving light emitted from the horizon. The empirical question is instead whether a candidate behaves as though infalling energy and matter can disappear from causal contact, or whether a material surface must absorb, reflect, store, or reradiate them. Existing evidence strongly restricts important surface models, but it does not establish a horizon without assumptions about accretion, compactness, equilibration, stability, and alternative channels. This is a dated frontier assessment, not a universal verdict.

Required background. Probability and inference for gravity supplies upper-limit likelihoods, nuisance parameters, and model comparison.

Helpful background. Black-Hole Geometry supplies event horizons and near-horizon redshift; Relativistic Matter and Compact Objects supplies explicit surface and horizonless models; Gravitational-Wave Astronomy supplies ringdown and residual-search inference.

A compact surface and its energy budget

In the site convention $c=1$, write a static spherical surface outside the Schwarzschild radius as

$$R=2GM(1+\epsilon), \qquad \epsilon>0.$$

Its gravitational redshift relative to infinity is

$$1+z_s=\left(1-\frac{2GM}{R}\right)^{-1/2} =\sqrt{\frac{1+\epsilon}{\epsilon}}.$$

For $\epsilon\ll1$, photons are strongly redshifted, escape through a narrow cone, and may return to the surface many times. Those effects delay and soften the emergent radiation. They do not by themselves erase energy. If a surface reaches steady state, absorbs accretion power, has no invisible energy channel, and is thermally coupled on the system’s age, the energy deposited as measured at infinity must eventually escape as radiation measured at infinity.

Schematically,

$$L_{\infty,\rm surf} =L_{\infty,\rm dep} -\frac{dE_{\infty,\rm stored}}{dt} -L_{\infty,\rm other}.$$

A steady thermal-surface test sets the storage term to zero and bounds the other channel. It then combines a mass and size prior, an accretion-power estimate, extinction and foregrounds, a spectral model, and flux upper limits. Broderick and Narayan 2006, pp. L21–L23 applies this logic to Sagittarius A*. The conclusion is conditional: changing the accretion rate, equilibration time, emissivity, surface heat capacity, or unobserved channel changes the excluded model.

Why gravitational redshift does not remove the energy budget

Consider a small rest mass $dm$ falling from rest at infinity and brought to rest at the static surface, neglecting changes of the background mass during the event. Restoring $c$, its initial conserved energy is $dm\,c^2$, while its final rest energy measured at infinity is $dm\,c^2\sqrt{1-2GM/(Rc^2)}$. The available energy release is therefore

$$\begin{aligned} dE_{\infty,\rm release} &=\eta_{\rm surf}\,dm\,c^2,\\ \eta_{\rm surf} &=1-\sqrt{1-\frac{2GM}{Rc^2}} =\frac{z_s}{1+z_s}. \end{aligned}$$

This reproduces the efficiency in Broderick and Narayan 2006, eqs. (1)–(2). For $R\gg GM/c^2$, expansion gives $\eta_{\rm surf}\simeq GM/(Rc^2)$, the Newtonian binding energy per unit rest energy. As $R$ approaches $2GM/c^2$, the efficiency approaches unity. Strong redshift therefore does not force the eventual released energy at infinity to vanish. It can make the time required to reach that steady state very long.

This is an idealized energy calculation, not an assertion that all of that power appears at the surface. A radiating disk can release part of the energy before impact; outflows can remove mass and energy; a rotating boundary changes the energy and angular-momentum accounting. The relevant $\dot M$ is the rest-mass rate reaching the boundary, measured per unit distant-observer time, and steady reradiation must be checked rather than assumed.

Four families of surface-sensitive tests

Thermalization and reradiation. Gas striking a material surface can convert kinetic and binding energy into heat. A sufficiently old, steadily accreting surface should radiate unless energy is stored, reflected, carried away non-electromagnetically, or the accretion estimate is wrong. Redshift changes the observed temperature and response time, so both the spectral band and equilibration history matter.

Bursts, impacts, and tidal survival. Accreted fuel on some surfaces could undergo thermonuclear instability, while a star or clump striking a surface could make a transient. The absence of Type I bursts in dynamically selected black-hole X-ray binaries constrains particular surface gravities, fuel supply, thermal states, and burning models; it is not a theorem covering arbitrary exotic matter (Narayan and Heyl 2002, pp. L139–L142). Tidal disruption or prompt capture likewise probes the exterior field and compactness before it probes a boundary condition.

Horizon-scale imaging. A central brightness depression and lensed ring constrain an ultracompact source after emissivity, optical depth, scattering, variability, and interferometric calibration are modeled. The visibility features, geometric fits, and physical-library comparison for M87* are separated explicitly in EHT Collaboration 2019, §§ 3–6. A material surface that is bright, opaque, and thermally coupled may be disfavored. A dark, absorbing, delayed, or weakly illuminated surface can evade the same image. Image morphology is therefore one row in a joint argument, not a direct picture of the event horizon.

Merger response. A horizon has ingoing boundary conditions and characteristic absorption; a material surface or throat can reflect perturbations and may produce altered tidal response, postmerger modes, or delayed echoes. Detectability depends on compactness, reflectivity as a function of frequency, spin, start time, waveform model, and detector noise. Null echo searches constrain a declared template family. They do not exclude every causal response compatible with an exterior Kerr-like metric.

Results and limitations through 2026-08-18

The matrix separates the result from the surface class it tests and from the assumption that could fail. The review in Cardoso and Pani 2019, § 5.2, pp. 60–61, and § 6 supplies a broader model-by-model context.

Evidence or result	Surface model or process tested	Scope, limitation, or missing control
Low quiescent infrared luminosity compared with estimated accretion power in Sagittarius A*	Old, steady, thermally reradiating surface with ordinary escaping photons	Accretion rate, storage time, emissivity, foreground, and non-electromagnetic channels remain model inputs
Lack of Type I bursts in black-hole X-ray-binary candidates	Fuel-bearing material surfaces within the modeled gravity and accretion regime	Burning stability, composition, base temperature, spin, magnetic field, and duty cycle restrict the conclusion
Ring-like horizon-scale emission and a central brightness depression	Bright or opaque surfaces in specified emitting-flow and transfer libraries	Visibility calibration, scattering, electron model, illumination, absorption, and finite resolution are degenerate
Ringdown agreement and null searches for selected echoes	Surfaces with specified reflectivity, delay, mode content, and waveform start time	Template incompleteness, noise background, spin, frequency dependence, and environmental response limit coverage

The credible competing positions are therefore more specific than “horizon” versus “surface.” A classical black hole has no material boundary that returns deposited matter to the exterior. A conventional surface reradiates or responds on calculable thermal and dynamical times. An ultracompact surface may redshift, delay, absorb, or store energy. A wormhole-like or dissipative interior can have a different response again. Each position needs a formation channel, a lifetime, a stable configuration, and a complete forward prediction in the relevant parameter regime.

The current evidence does not establish that every possible horizonless model is absent. It does establish that an alternative cannot be saved by compactness alone: it must survive thermal, dynamical, imaging, and merger-response constraints simultaneously without assigning a separate freely tuned evasion to each observation.

How to make the test discriminating

Choose a concrete surface model with $R$, frequency-dependent absorptivity, heat capacity, internal energy channels, and formation age. Propagate a measured or bounded inflow through the exterior flow to the deposited energy. Compute the escape, repeated-return, redshift, and thermal response. Fold the emerging spectrum or transient through the actual instrument response and source selection. Then test the same model against dynamics, imaging, and merger response.

An independent check is global energy closure. If the model suppresses thermal light by long-term storage, calculate the accumulated internal energy and whether the configuration remains stable. If it reflects energy, predict the reflected spectrum or dynamical response. If it sends energy to another sector, state the coupling and its observable consequences. A label such as “perfectly dark surface” is a boundary condition, not an explanation.

What could change the conclusion. The interpretation could change after a new calibrated EHT data release, a materially stronger and model-explicit surface-luminosity limit, a credible merger echo or absorption result with controlled backgrounds, or a formation-and-stability calculation that produces a quantitative surface response across the relevant source population.

Common pitfalls

Saying that redshift hides energy forever. Redshift can make escape slow and cool. In a steady old system, it does not remove the need to balance deposited energy unless storage or another channel is demonstrated.

Treating a null result as model-free. Every upper limit is conditional on a signal family, calibration, selection, and prior volume. State which surface behavior was tested.

Equating a dark image center with a horizon. Image brightness depends on source and transfer physics. The horizon interpretation is supported by consistency with geometry and other evidence, not by darkness alone.

Compute the redshift of a near-horizon surface

A proposed surface has $R=2GM(1+\epsilon)$ with $\epsilon=10^{-6}$. Compute $1+z_s$. If a local microscopic process lasts $1\ {\rm s}$ in the static surface frame, what is its gravitationally redshifted duration for a distant observer in this idealized static estimate? What does the calculation not show?

Solution

The redshift factor is

$$1+z_s=\sqrt{\frac{1+10^{-6}}{10^{-6}}} \simeq1.00\times10^3.$$

A locally measured one-second process is therefore received over roughly

$$\Delta t_\infty=(1+z_s)\Delta\tau_s\simeq10^3\ {\rm s}$$

in the static redshift mapping. This calculation shows strong time dilation and photon-energy redshift. It does not calculate the photon escape cone, repeated returns, surface heat capacity, accretion power, stability, or the eventual steady luminosity. Those additional ingredients decide whether a particular surface evades an observational test.

References

• Broderick, Avery E., and Ramesh Narayan. “On the Nature of the Compact Dark Mass at the Galactic Center.” Astrophysical Journal Letters 638 (2006): L21–L24. DOI.
• Cardoso, Vitor, and Paolo Pani. “Testing the Nature of Dark Compact Objects: A Status Report.” Living Reviews in Relativity 22 (2019): 4. DOI.
• Event Horizon Telescope Collaboration. “First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole.” Astrophysical Journal Letters 875 (2019): L6. arXiv:1906.11243.
• Narayan, Ramesh, and Jeremy S. Heyl. “On the Lack of Type I X-Ray Bursts in Black Hole X-Ray Binaries: Evidence for the Event Horizon?” Astrophysical Journal Letters 574 (2002): L139–L142. DOI.

Dated Research assessment. For open questions and recent results, follow the link below. Each assessment states the date through which it considers results and the limits of its conclusions.

• Evidence for Event Horizons Versus Material Surfaces