Emergent gravity: From statistical point of view

TL;DR

This paper explores the emergent nature of gravity by linking conformal symmetry near black hole horizons, entropy, and thermodynamic relations, suggesting gravity arises from underlying statistical mechanics principles.

Contribution

It demonstrates that holographic modes and entropy definitions lead to the equipartition law and relate gravity to thermodynamics, highlighting gravity's emergent properties.

Findings

Entropy is proportional to the gravity action.

The generalized Smarr formula is expressed as a thermodynamic relation.

Gravity can be interpreted as an emergent phenomenon from statistical mechanics.

Abstract

Near the event horizon of a black hole, the effective theory is two dimensional conformal theory. Here we show that the holographic modes characterising this underlying conformal symmetry and the basic definition of entropy $S$ in statistical mechanics lead the equipartition law of energy. We also show that $S$ is proportional to the gravity action which suggests the emergent nature of gravity. This is further bolstered by expressing the generalised Smarr formula as a thermodynamic relation, $S = E/ 2T$, where $T$ is the Hawking temperature and $E$ is shown to be the Komar energy.