Boundary Term in the Gravitational Action is the Heat Content of the Null surfaces

Understand

The Einstein-Hilbert Lagrangian has no well-defined variational derivative with respect to the metric.

• This issue has to be tackled by adding a suitable surface term to the action, which is a peculiar feature of gravity.
• We also know that null surfaces in spacetime exhibit (observer-dependent) thermodynamic features.
• This suggests a possible thermodynamic interpretation of the boundary term when the boundary is a null surface.