Curvature independence of statistical entropy

Abstract

We examine the statistical number of states, from which statistical entropy can be derived, and we show that it is an explicit function of the metric and thus observer dependent. We find a constraint on a transformation of the metric that preserves the number of states but does not preserve curvature. In showing exactly how curvature independence arises in the conventional definition of statistical entropy, we gain a precise understanding of the direction in which it needs to be redefined in the treatment of black hole entropy.

References in corpus (4)

• Equipartition of energy in the horizon degrees of freedom and the emergence of gravity
• Surface Density of Spacetime Degrees of Freedom from Equipartition Law in theories of Gravity
• Ideal Gas in a strong Gravitational field: Area dependence of Entropy
• Black hole entropy divergence and the uncertainty principle