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Thermodynamic Remnants in Black-hole Evaporation

Ivan Arraut, Abhishek Kumar Mehta

TL;DR

This paper shows that black-hole remnants naturally emerge from Hawking’s original computations when considering the small-mass limit and conformal symmetry, avoiding additional assumptions. By reformulating the mass-loss rate with greybody factors and a Laplace transform, the authors derive a remnant mass M_r tied to integrals of F(p). A fermionized, 2D horizon description via matrix-model density and a horizon pressure leads to a remnant condition σ = γ, fixing M_r up to the Fermi energy ν. The work links semiclassical gravity to microscopic fermionic/matrix-model pictures, offering symmetry-backed constraints on quantum gravity theories.

Abstract

We show that black-hole remnant scenario naturally arises in the original computations of Hawking without extra assumptions.

Thermodynamic Remnants in Black-hole Evaporation

TL;DR

This paper shows that black-hole remnants naturally emerge from Hawking’s original computations when considering the small-mass limit and conformal symmetry, avoiding additional assumptions. By reformulating the mass-loss rate with greybody factors and a Laplace transform, the authors derive a remnant mass M_r tied to integrals of F(p). A fermionized, 2D horizon description via matrix-model density and a horizon pressure leads to a remnant condition σ = γ, fixing M_r up to the Fermi energy ν. The work links semiclassical gravity to microscopic fermionic/matrix-model pictures, offering symmetry-backed constraints on quantum gravity theories.

Abstract

We show that black-hole remnant scenario naturally arises in the original computations of Hawking without extra assumptions.

Paper Structure

This paper contains 6 sections, 37 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Remnants in thermodynamic black-hole evaporation
  3. Fermionization of Black-hole Event Horizon
  4. Discussion
  5. Summary and conclusions
  6. Flat space limit

Figures (1)

  • Figure 1: A plot of $\gamma_{\nu} = \frac{\widetilde{\beta}^3}{32\pi^2}\left[\frac{\widetilde{\beta}^2}{2}\ln\widetilde{\beta}~\nu^2-\ln\sqrt{2\pi} +\operatorname{Re}\psi^{(-2)}\left(1+i\nu\widetilde{\beta}\right)\right]$, which represents the pressure $\gamma$ as a function of $\widetilde{\beta}$ for a given Fermi energy $\nu$, and surface tension $\sigma = \frac{\widetilde{\beta}}{32\pi}$. The intersection of $\sigma$ and $\gamma_{\nu}$ computes the $\widetilde{\beta}$ that solves Eq. (\ref{['rem_eq']}) i.e. the remnant mass for a given $\nu$.