Entropy function from the gravitational surface action for an extremal near horizon black hole

Understand

It is often argued that {\it all the information of a gravitational theory is encoded in the surface term of the action}; which means one can find several physical quantities just from the surface term without incorporating the bulk part of the action.

• This has been observed in various instances; e.g.
• derivation of the Einstein's equations, surface term calculated on the horizon leads to entropy, etc.
• Here I investigate the role of it in the context of entropy function and entropy of extremal near horizon black holes.