On light surfaces in black hole thermodynamics

TL;DR

This paper introduces a new framework for black hole thermodynamics based on light surfaces and their frequencies, providing insights into black hole transitions and potential observational signatures near the poles.

Contribution

It presents a novel parametrization of black hole metrics using maximum extractable energy and analyzes conditions for black hole transitions in Kerr geometry.

Findings

Identifies specific spin values with anomalies in energy extraction and surface gravity.

Derives conditions for black hole transitions based on initial and final masses.

Suggests observational signatures of light surface frequencies near black hole poles.

Abstract

We discuss the fundamentals of classical black hole (BH) thermodynamics in a new framework determined by light surfaces and their frequencies. This new approach allows us to study BH transitions inside the Kerr geometry. In the case of BHs, we introduce a new parametrization of the metric in terms of the maximum extractable rotational energy or, correspondingly, the irreducible mass, which is an alternative to the spin parametrization. It turns out that BH spacetimes with spins $a/M= \sqrt {8/9}$ and $a/M=1/\sqrt{2}$ show anomalies in the rotational energy extraction and surface gravity whereas the case $a/M=\sqrt{3}/2$ is of particular relevance to study the variations of the horizon area. We find the general conditions under which BH transitions can occur and express them in terms of the masses of the initial and final states. This shows that BH transitions in the Kerr geometry are not arbitrary but depend on the relationship between the mass and spin of the initial and final states. From an observational point of view, we argue that near the BH poles it is possible to detect photon orbits with frequencies that characterize the light surfaces analyzed in this work.