Modifying horizon thermodynamics by surface tensions

TL;DR

This paper explores how surface tensions modify the thermodynamic laws at black hole and cosmological horizons, revealing differences in temperature and pressure relations across various horizons.

Contribution

It introduces a new approach to modify horizon thermodynamics using surface tensions, applicable to black holes and cosmological models, and derives corresponding Smarr relations.

Findings

Modified first laws of thermodynamics at horizons

Surface tensions influence temperature and pressure relations

Differences between black hole and cosmological horizon laws

Abstract

The modified first laws of thermodynamics at the black hole horizon and the cosmological horizon of the Schwarzschild de Sitter black hole and the apparent horizon of the Friedmann-Robertson-Walker cosmology are derived by the surface tensions, respectively. The corresponding Smarr relations are obeyed. For the black hole, the cosmological constant is first treated as a fixed constant, and then as a variable associated to the pressure. The law at the apparent horizon takes the same form as that at the cosmological horizon, but is different from that at the black hole horizon. The positive temperatures guarantee the appearance of the worked terms in the modified laws at the cosmological and apparent horizons. While they can disappear at the black hole horizon.