Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Critical Islands

Chethan Krishnan

Abstract

We discuss a doubly-holographic prescription for black holes in braneworlds with a vanishing cosmological constant. It involves calculating Ryu-Takayanagi surfaces in AdS black funnel spacetimes attached to braneworld black holes in the $ critical$ Randall-Sundrum II model. Critical braneworlds have the virtue of having massless gravitons. Our approach should be useful when the braneworld is a cosmological black hole interacting with deconfined, large-$N$ matter. In higher dimensions, explicit funnel metrics will have to be constructed numerically -- but based on the general structure of the geometry, we present a natural guess for where one might find the semi-classical island. In a 3-dimensional example where a toy analytic black funnel is known, we can check our guess by direct calculation. We argue that this resolves a version of the information paradox in these braneworld systems, by finding strong evidence for "cosmological islands". Comoving Ryu-Takayanagi surfaces and associated UV cut-offs on the brane, play natural roles.

Critical Islands

Abstract

We discuss a doubly-holographic prescription for black holes in braneworlds with a vanishing cosmological constant. It involves calculating Ryu-Takayanagi surfaces in AdS black funnel spacetimes attached to braneworld black holes in the Randall-Sundrum II model. Critical braneworlds have the virtue of having massless gravitons. Our approach should be useful when the braneworld is a cosmological black hole interacting with deconfined, large- matter. In higher dimensions, explicit funnel metrics will have to be constructed numerically -- but based on the general structure of the geometry, we present a natural guess for where one might find the semi-classical island. In a 3-dimensional example where a toy analytic black funnel is known, we can check our guess by direct calculation. We argue that this resolves a version of the information paradox in these braneworld systems, by finding strong evidence for "cosmological islands". Comoving Ryu-Takayanagi surfaces and associated UV cut-offs on the brane, play natural roles.

Paper Structure

This paper contains 7 sections, 5 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Black Holes on RSII Braneworlds
  3. Critical Islands from the Geometry of Black Funnels
  4. Islands and Funnels in AdS$_3$
  5. Cosmological Islands
  6. Conclusion
  7. Acknowledgments

Figures (3)

  • Figure 1: The sub-critical Karch-Randall braneworld.
  • Figure 5: Spatial slice of the AdS$_3$ black funnel.
  • Figure 6: Plots of extremal surfaces with $x=0$ and $dz/dx|_{x=0}=0$. The vertical axis is $z$ and the horizontal axis is $x$. The "island" extremal surfaces are the ones that straddle the horizon, note that the bump in the horizon as shown in Fig. \ref{['AdS3']} happens in this plot at $(x=0, z=\sqrt{2})$.