Foiling Black Hole Foils: Revealing Horizon Alternatives with Baryonic Atmospheres

TL;DR

This work develops a minimal, relativistic model of a horizonless compact object surrounded by a steady, subsonic baryonic settling layer that transports energy by radiative diffusion. By encoding the unknown surface physics in local boundary data (surface transmission 𝒯 and base temperature T_f) and enforcing Killing-energy conservation, the authors show that for typical accreting systems the emergent photosphere luminosity closely tracks the accretion power, largely independent of the surface redshift in the optically thick regime. The analysis spans non-relativistic intuition to full relativistic treatment, including optional extensions for radiation pressure, radiative inertia, and transonic inner behavior, and derives a robust diffusion framework with explicit boundary and microphysical constraints. The central result is that redshift and diffusion do not generally hide accretion power from distant observers, meaning that the absence or presence of a thermal photosphere provides a powerful observational constraint on horizonless horizon alternatives across a wide mass range. The framework offers concrete criteria for optical depth, boundary conditions, and microphysical floors, thereby enabling tests against astrophysical observations of near-horizon objects like M87* and Sgr A*.

Abstract

Event horizons are a defining feature of black holes. Consequently, there have been many efforts to probe their existence in astrophysical black hole candidates, spanning ten orders of magnitude in mass. Nevertheless, horizons remain an obstacle to unifying general relativity and quantum mechanics, most sharply presented by the information paradox. This has motivated a proliferation of horizonless alternatives (black hole foils) that avoid event horizons and are therefore benign. We show that for typical accreting astronomical targets, largely independent of a foil's underlying microphysics, a horizonless compact surface will generically be ensconced within an optically thick, scattering dominated baryonic settling layer that efficiently reprocesses the kinetic energy of infalling matter into observable thermal emission. The emergent photosphere luminosity is driven toward the accretion-powered equilibrium value and is only weakly sensitive to the foil redshift. These atmospheres are convectively stable and naturally imply that the emitting photosphere forms at modest redshift even when the surface redshift is extreme. Moreover, local gas-surface interaction provides a microphysical lower bound on the effective base temperature, insulating the atmosphere from arbitrarily cold foils. The unknown properties of the foil enter only through local boundary conditions controlling baryon processing and thermal coupling at the surface, making the solutions broadly applicable to horizonless alternatives that do not invoke significant additional nonlocal interactions. Thus, under minimal assumptions (GR exterior and local surface interactions), horizonless foils are generically observationally exposed: the absence of a thermal photosphere directly constrains or rules out broad classes of such models.

Figures (2)

• Figure 1: Surface luminosity at the top of the baryonic atmosphere as a function of atmosphere optical depth across one scale height for various foil luminosities. Curves correspond to different intrinsic foil luminosities $L_{\rm foil}/L_{\rm eq}$ (labels). In the optically thin limit $\bar{\tau}\ll 1$, the layer is transparent and $L_{\rm surf}\simeq L_{\rm foil}$. In the optically thick limit $(3/4)\bar{\tau}\gg 1$, diffusion forces the emergent luminosity to $L_{\rm surf}\to L_{\rm eq}$, essentially independent of $L_{\rm foil}$.
• Figure 2: Microphysical floor on the base temperature from \ref{['eq:dimless_cubic']} on log-log axes. Blue curve shows the solution of $t^{3}(t-s_\bullet)=1$ with $t_f\equiv T_f/T_L$ and $s_\bullet\equiv T_\bullet/T_L$. Black dashed line shows $t_f=1$ ($T_f=T_L$). Red dotted line shows $t_f=s_\bullet$ ($T_f=T_\bullet$). For $s_\bullet \gg 1$ (hot foil), $t_f\to s_\bullet$ with a small upward offset $T_L^4/T_\bullet^3$. Thus $T_L$ sets a hard lower bound for the gas temperature at the base; it depends on $\epsilon$, $\lambda_c/\lambda$, and the normalized luminosity $|L|/L_{\mathrm{eq}}$ via \ref{['eq:TL_def']}.