Gravitational thermodynamics and universal holographic duality in dynamical spacetimes

TL;DR

This paper develops a thermodynamic framework for dynamic spacetimes, deriving a universal Cardy-Verlinde formula and holographic duality insights through generalized Smarr relations and horizon thermodynamics.

Contribution

It introduces a generalized Smarr formula and a universal Cardy-Verlinde formula applicable to dynamic spacetimes, linking thermodynamics with holographic duality.

Findings

Derived a generalized Smarr formula for dynamic spacetimes.

Established a universal Cardy-Verlinde formula with braneworld interpretation.

Demonstrated the tightening of the AdS-Bekenstein bound for multi-charge black holes.

Abstract

We construct a generalized Smarr formula which could provide a thermodynamic route to derive the covariant field equation of general theories of gravity in dynamic spacetimes. Combining some thermodynamic variables and a new chemical potential conjugated to the number of degree of freedom on the holographic screen, we find a universal Cardy-Verlinde formula and give its braneworld interpretation. We demonstrate that the associated AdS-Bekenstein bound is tighten than the previous expression for multi-charge black holes in the gauged supergravities. The Cardy-Verlinde formula and the AdS-Bekenstein bound are derived from the thermodynamics of bulk trapping horizons, which strongly suggests the underlying holographic duality between dynamical bulk spacetime and boundary field theory.