Hawking radiation of charged Einstein-aether black holes at both Killing and universal horizons

TL;DR

This paper investigates Hawking radiation at both Killing and universal horizons of Einstein-aether black holes, revealing that high-frequency radiation remains thermal at Killing horizons, while non-relativistic particles are emitted from universal horizons with a temperature depending on the dispersion relation.

Contribution

It analytically examines quantum tunneling and Hawking radiation in Einstein-aether black holes considering nonlinear dispersion relations and high-order curvature corrections, highlighting differences at Killing and universal horizons.

Findings

Hawking radiation at Killing horizons remains thermal despite nonlinearity.

Non-relativistic particles are emitted from universal horizons with a temperature depending on the dispersion relation.

The derived Smarr formula suggests modifications are needed for the entropy or first law assumptions.

Abstract

We study analytically quantum tunneling of relativistic and non-relativistic particles at both Killing and universal horizons of Einstein-Maxwell-aether black holes, after high-order curvature corrections are taken into account, for which the dispersion relation of the particles becomes nonlinear. Our results at the Killing horizons confirm the previous ones, i.e., at high frequencies the corresponding radiation remains thermal and the nonlinearity of the dispersion does not alter the Hawking radiation significantly. In contrary, non-relativistic particles are created at universal horizons and are radiated out to infinity. The radiation also has a thermal spectrum, and the corresponding temperature takes the form, $T^{z}_{UH} = 2\kappa_{UH} (z-1)/(2\pi z)$, where $z$ denotes the power of the leading term in the nonlinear dispersion relation, $\kappa_{UH}$ is the surface gravity of the universal horizon, defined by peering behavior of ray trajectories at the universal horizon. We also study the Smarr formula by assuming that: (a) the entropy is proportional to the area of the universal horizon, and (b) the first law of black hole thermodynamics holds, whereby we derive the Smarr mass, which in general is different from the total mass obtained at infinity. This indicates that one or both of these assumptions must be modified.