Vanishing of nonlinear tidal Love numbers of Schwarzschild black holes
Massimiliano Maria Riva, Luca Santoni, Nikola Savić, Filippo Vernizzi
Abstract
It is well known that asymptotically flat Schwarzschild black holes in general relativity in four spacetime dimensions have vanishing induced linear tidal response. We extend this result beyond linear order for the polar sector, by solving the static nonlinear Einstein equations for the perturbations of the Schwarzschild metric and computing the quadratic corrections to the electric-type tidal Love numbers. After explicitly performing the matching with the point-particle effective theory at leading order in the derivative expansion, we show that the Love number couplings remain zero at higher order in perturbation theory.
Topics & Concepts
Schwarzschild radiusPhysicsNonlinear systemMathematical physicsClassical mechanicsQuantum mechanicsGravitationBlack Holes and Theoretical PhysicsPulsars and Gravitational Waves ResearchCosmology and Gravitation Theories