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

Understand

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.