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When Black Holes Relax in a Cold Bath: Evolving Page Curves for Black Holes Coupled to Cooling Baths

Waheed A. Dar, Nirmalya Kajuri, Rinkesh Panigrahi

Abstract

We consider scenarios where Jackiw-Teitelboim black holes are attached to baths whose temperatures can be manipulated externally. We consider the bath to be cooled continuously and numerically investigate the subsequent evolution of the generalized entropies of the black hole. Page curves corresponding to several different cooling profiles of the bath are obtained.

When Black Holes Relax in a Cold Bath: Evolving Page Curves for Black Holes Coupled to Cooling Baths

Abstract

We consider scenarios where Jackiw-Teitelboim black holes are attached to baths whose temperatures can be manipulated externally. We consider the bath to be cooled continuously and numerically investigate the subsequent evolution of the generalized entropies of the black hole. Page curves corresponding to several different cooling profiles of the bath are obtained.

Paper Structure

This paper contains 18 sections, 48 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Jackiw-Teitelboim Gravity
  4. Quantum Extremal Surfaces
  5. Black Hole at Equilibrium
  6. Entropy in terms of boundary parametrization
  7. Dynamical Setup and Numerical Framework
  8. Breaking equilibrium: time-dependent bath temperature
  9. Instantaneous change in bath temperature: Boundary parametrization
  10. Instantaneous Change in Temperature: Entropy saddles
  11. Hawking saddle
  12. Island saddle
  13. Black Hole Evaporation: General Cooling Profiles
  14. Bath Energy follows Newton's law of cooling
  15. Linear Decrease in Incoming Stress Tensor
  16. ...and 3 more sections

Figures (11)

  • Figure 1: Quantum Extremal Surface
  • Figure 2: Interpolation of derivatives
  • Figure 3: Numerical check with analytical result
  • Figure 4: Hawking saddle represented geometrically. Entropy is related to the proper distance between the two points.
  • Figure 5: Entropy of Hawking saddle vs Boundary time
  • ...and 6 more figures