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

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