Charged torus-like black holes as heat engines

TL;DR

This paper explores the thermodynamics of charged torus-like black holes, modeling them as heat engines, analyzing their efficiency, and establishing bounds on their charge to ensure positive temperature.

Contribution

It introduces a detailed thermodynamic analysis of charged torus-like black holes as heat engines, including efficiency calculations and bounds on charge.

Findings

Efficiency depends on volume and cycle type.

Charge bounds are necessary to maintain positive temperature.

Benchmark scheme confirms calculation accuracy.

Abstract

We investigate the thermodynamical properties of charged torus-like black holes and take it as the working substance to study the heat engines. In the extended phase space, by interpreting the cosmological constant as the thermodynamic pressure, we derive the thermodynamical quantities by the first law of black hole thermodynamics and obtain the equation of state. Then, we calculate the efficiency of the heat engine in Carnot cycle as well as rectangular cycle, and investigate how the efficiency changes with respect to volume. In addition, to avoid a negative temperature, we emphasize that the charge of this black hole can not be arbitrary. Last, we check the calculation accuracy of a benchmark scheme and discuss the upper bound and lower bound for charged torus-like black hole in the scheme.