Spectral Methods in General Relativity and Large Randall-Sundrum II Black Holes

TL;DR

This paper introduces a new spectral numerical method to find large static RSII black hole solutions, confirming their properties and comparing them with previous solutions, revealing that their temperature and entropy match Schwarzschild black holes while the horizon area is slightly larger.

Contribution

A novel spectral numerical approach for large static RSII black holes, providing solutions consistent with prior methods and new insights into their thermodynamic properties.

Findings

Solutions closely match previous perturbative results

Hawking temperature and entropy are identical to Schwarzschild black holes

Horizon area is increased by approximately 4.7/(-Λ)

Abstract

Using a novel numerical spectral method, we have found solutions for large static Randall-Sundrum II (RSII) black holes by perturbing a numerical AdS_5-CFT_4 solution to the Einstein equation with a negative cosmological constant Lambda that is asymptotically conformal to the Schwarzschild metric. We used a numerical spectral method independent of the Ricci-DeTurck-flow method used by Figueras, Lucietti, and Wiseman for a similar numerical solution. We have compared our black-hole solution to the one Figueras and Wiseman have derived by perturbing their numerical AdS_5-CFT_4 solution, showing that our solution agrees closely with theirs. We have also deduced the new results that to first order in 1/(-\Lambda M^2), the Hawking temperature and entropy of an RSII static black hole have the same values as the Schwarzschild metric with the same mass, but the horizon area is increased by about 4.7/(-\Lambda).