Master equation as a radial constraint

Abstract

We revisit the problem of perturbations of Schwarzschild-AdS${}_4$ black holes by using a combination of the Martel-Poisson formalism for perturbations of four-dimensional spherically symmetric spacetimes and the Kodama-Ishibashi formalism. We clarify the relationship between both formalisms and express the Brown-York-Balasubramanian-Krauss boundary stress-energy tensor, ${\bar{T}}_{\mu \nu }$, on a finite-$r$ surface purely in terms of the even and odd master functions. Then, on these surfaces we find that the spacelike components of the conservation equation ${\bar{\mathcal{D}}}^{\mu }{\bar{T}}_{\mu \nu }=0$ are equivalent to the wave equations for the master functions. The renormalized stress-energy tensor at the boundary $\frac{r}{L}\underset{r\to \infty }{\lim }{\bar{T}}_{\mu \nu }$ is calculated directly in terms of the master functions.

10 pages, RevTeX

References in corpus (4)

• Nonlinear Fluid Dynamics from Gravity
• Gravity & Hydrodynamics: Lectures on the fluid-gravity correspondence
• Gravitational quasinormal modes of AdS black branes in d spacetime dimensions
• Energy-momentum/Cotton tensor duality for AdS4 black holes

Cited by in corpus (1)

• Instability of asymptotically anti de Sitter black holes under Robin conditions at the timelike boundary