# The large $D$ membrane paradigm for general four-derivative theory of gravity with a cosmological constant

## TL;DR

This paper derives the membrane equations governing black hole dynamics in the large D limit for a broad class of four-derivative gravity theories with a cosmological constant, including corrections up to linear order.

## Contribution

It extends the large D membrane paradigm to general four-derivative gravity theories with a cosmological constant, deriving covariant membrane equations and stress tensor.

## Key findings

- Membrane equations are covariant and include cosmological constant effects.
- Predicted light quasi-normal mode spectrum of black holes and branes.
- No ghost modes at linear order in four-derivative corrections.

## Abstract

We find the membrane equations which describe the leading order in $1/D$ dynamics of black holes in the $D\rightarrow\infty$ limit for the most general four-derivative theory of gravity in the presence of a cosmological constant. We work up to linear order in the parameter determining the strength of the four-derivative corrections to the gravity action and hence there are no ghost modes in the theory. We find that the effective membrane equations we obtain are the covariant version of the membrane equations in absence of the cosmological constant. We also find the world-volume stress tensor for the membrane whose conservation gives the membrane equations. We apply the membrane equations to predict the light quasi-normal mode spectrum of black holes and black branes in the theory of gravity under consideration.