Constraints on thermalizing surfaces from infrared observations of supermassive black holes

TL;DR

Infrared observations of supermassive black holes challenge the existence of physical surfaces in thermal equilibrium, providing constraints on horizonless objects by analyzing their thermalization timescales and behavior.

Contribution

We introduce a parametrization of energy balance in horizonless objects to quantify their similarity to black holes and analyze their thermalization timescales.

Findings

Thermalization timescale can be arbitrarily large for objects mimicking black holes.

Observations restrict the dynamical behavior of horizonless objects.

Infinite thermalization timescale for true black holes.

Abstract

Infrared observations of Sgr A$^*$ and M87$^*$ are incompatible with the assumption that these sources have physical surfaces in thermal equilibrium with their accreting environments. In this paper we discuss a general parametrization of the energy balance in a horizonless object, which permits to quantify how close a horizonless object is in its behavior to a black hole, and analyze the timescale in which its surface can thermalize. We show that the thermalization timescale is unbounded, growing large for objects that mimic closely the behavior of a black hole (and being infinite for the latter). In particular, the thermalization timescale is proportional to the time that energy spends inside the horizonless object due to propagation and interactions with the bulk. Hence, these observations can be used to quantitatively restrict the dynamical behavior of horizonless objects, without being able to discard the existence of a physical surface.