General Theory of Large D Membranes Consistent with Second Law of Thermodynamics

Understand

We write down the most general membrane equations dual to black holes for a general class of gravity theories, up to sub-leading order in $1/D$ in large $D$ limit.

• We derive a "minimal" entropy current which satisfies a local form of second law from these membrane equations.
• We find that consistency with second law requires the membrane equations to satisfy certain constraints.
• We find additional constraints on the membrane equations from the existence of membrane solutions dual to stationary black holes.