Gravity from spacetime thermodynamics

Abstract

The Einstein-Hilbert action (and thus the dynamics of gravity) can be obtained by: (i) combining the principle of equivalence, special relativity and quantum theory in the Rindler frame and (ii) postulating that the horizon area must be proportional to the entropy. This approach uses the local Rindler frame as a natural extension of the local inertial frame, and leads to the interpretation that the gravitational action represents the free energy of the spacetime geometry. As an aside, one obtains an insight into the peculiar structure of Einstein-Hilbert action and a natural explanation to the questions: (i) Why does the covariant action for gravity contain second derivatives of the metric tensor? (ii) Why is the gravitational coupling constant positive? Some geometrical features of gravitational action are clarified.