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

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.

25 pages, LaTeX, typos corrected, version to appear in Classical and Quantum Gravity

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• Ricci flow and black holes
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• Twisted Tachyon Condensation in Closed String Field Theory
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• Modified Ricci flow and asymptotically non-flat spaces
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