Investigating stability of a class of black hole spacetimes under Ricci flow

TL;DR

This paper proves the linear stability of certain black hole spacetimes under Ricci flow, providing insights into their stability in string theory and quantum gravity contexts, with implications for numerical solution methods.

Contribution

It demonstrates the linear stability of Schwarzschild-Tangherlini and Anti-de Sitter black holes under Ricci flow for specific perturbations, advancing understanding of their off-shell stability.

Findings

Proved linear stability of Schwarzschild-Tangherlini black holes.

Extended stability results to Anti-de Sitter black holes.

Implications for numerical algorithms in Einstein equations.

Abstract

We prove the linear stability of Schwarzschild-Tangherlini spacetimes and their Anti-de Sitter counterparts under Ricci flow for a special class of perturbations. This is useful in the choice of suitable initial conditions in numerical Ricci-flow-based algorithms for obtaining new solutions to the Einstein equation when the cosmological constant is zero or negative. The Ricci flow is a first-order renormalization group (RG) flow in string theory, and its solutions are believed to approximate string field theory processes in certain cases. Thus this result offers insights into the off-shell stability of these Euclidean black hole geometries in string theory, as well as in the Euclidean path integral approach to quantum gravity.