Hawking Radiation in Lorentz Violating Gravity: A Tale of Two Horizons

TL;DR

This paper demonstrates that Hawking radiation persists in Lorentz violating gravity theories through universal horizons, showing a thermal, species-independent emission linked to surface gravity, despite modified dispersion relations.

Contribution

It provides a comprehensive analysis showing that universal horizons emit Hawking radiation with properties similar to those in General Relativity, even with Lorentz violation.

Findings

Universal horizons emit species-independent Hawking radiation.

Low-energy spectrum is affected by Killing horizon, resembling an effective refractive index.

Hawking radiation remains robust despite Lorentz symmetry breaking.

Abstract

Since their proposal, Lorentz violating theories of gravity have posed a potential threat to black hole thermodynamics, as superluminal signals appeared to be incompatible with the very black hole notion. Remarkably, it was soon realized that in such theories causally disconnected regions of space-time can still exist thanks to the presence of universal horizons: causal barriers for signals of arbitrary high speed. Several investigations, sometimes with contrasting results, have been performed so to determine if these horizons can be associated with healthy thermodynamic properties similar to those associated with Killing horizons in General Relativity. In this work we offer what we deem to be the final picture emerging from this and previous studies. In summary we show that: 1) there is a thermal, and most of all species-independent, emission associated to universal horizons, determined by their surface gravity; 2) due to the modified dispersion relation of the matter fields, the low energy part of the emitted spectrum is affected by the presence of the Killing horizon, in a way similar to an effective refractive index, leading at low energies (w.r.t. the Lorentz breaking scale) to an emission that mimics a standard Hawking spectrum (i.e. one determined by the Killing horizon surface gravity); 3) the whole picture is compatible with a globally well defined vacuum state i.e. an Unruh state associated with preferred observers, which however at very low energies it is basically indistinguishable from the standard Unruh vacuum associated to metric free-falling observers. One can then conclude that Hawking radiation is remarkably resilient even within the context of gravitational theories entailing the breakdown of local Lorentz invariance.