A note on electrical and thermodynamic properties of Isolated Horizon

TL;DR

This paper explores the electrical and thermodynamic properties of Isolated Horizons, establishing laws analogous to classical physics and demonstrating their thermodynamic behavior through a Carnot cycle model.

Contribution

It introduces electrical laws for Isolated Horizons and demonstrates their thermodynamic nature, extending the Membrane Paradigm to quasi-local black holes.

Findings

Established Ohm's and Joule's laws for IH

Constructed a Carnot cycle with IH as a cold reservoir

Confirmed thermodynamic behavior of IH

Abstract

The electrical laws and Carnot cycle of Isolated Horizon (IH) are investigated in this paper. We establish the Ohm's law and Joule's law of an Isolated Horizon, and find that the conceptual picture of black holes (Membrane Paradigm) can also apply to this kind of quasi-local black holes. We also investigate the geometrical properties near a non-rotating IH, and find that under the first-order approximation of r, there exist a Killing vector and a Hamiltonian conjugate to it, so this vector is a physical observer. We calculate the energy as measured at infinity of a particle at rest outside a non-rotating IH, and use this result to construct a reversible Carnot cycle with the Isolated Horizon as a cold reservoir, which confirms the thermodynamic nature of Isolated Horizon.