Equipartition of energy in the horizon degrees of freedom and the emergence of gravity

Understand

It is possible to provide a physical interpretation for the field equations of gravity based on a thermodynamical perspective.

• The virtual degrees of freedom associated with the horizons perceived by the local Rindler observers, play a crucial role in this approach.
• In this context, the relation S=E/2T between the entropy (S), active gravitational mass (E) and temperature (T) - obtained previously in gr-qc/0308070 [CQG, 21, 4485 (2004)] - can be reinterpreted as the law of equipartition E = (1/2) nkT where n=A/L_P^2 is the number (density) of microscopic horizon degrees of freedom.
• Conversely, one can use the equipartition argument to provide a thermodynamic interpretation of even non-relativistic gravity.