Black holes in presence of cosmological constant: Second order in 1/D

TL;DR

This paper extends the large dimension expansion of black hole solutions with a cosmological constant to second order, revealing non-trivial metric corrections and deriving membrane dynamics and quasinormal mode spectra.

Contribution

It introduces a background-covariant formalism for second-order corrections in large D black holes with cosmological constant, providing explicit membrane equations and spectra.

Findings

Derived second-order metric corrections in large D expansion.

Established membrane equations in curved backgrounds with cosmological constant.

Matched quasinormal mode spectra with gravity results.

Abstract

We have extended the results of arXiv:1704.06076 upto second subleading order in an expansion around large dimension D. Unlike the previous case, there are non-trivial metric corrections at this order. Due to our `background-covariant' formalism, the dependence on Ricci and the Riemann curvature tensor of the background is manifest here. The gravity system is dual to a dynamical membrane coupled with a velocity field. The dual membrane is embedded in some smooth background geometry that also satisfies the Einstein equation in presence of cosmological constant. We explicitly computed the corrections to the equation governing the membrane-dynamics. Our results match with earlier derivations in appropriate limits. We calculated the spectrum of QNM from our membrane equations and matched them against similar results derived from gravity.