# Near-Horizon Carnot Engines Beyond Schwarzschild: Exploring Black Brane Thermodynamics

## TL;DR

This paper explores how thermodynamic principles can be applied to black branes, offering new insights into energy extraction in curved spacetime.

## Contribution

The paper introduces a novel application of Carnot engine principles to black brane thermodynamics in non-asymptotically flat spacetimes.

## Key findings

- Analytic solutions reveal energy transfer processes driven by temperature and gravitational potential differences in black brane systems.
- The study highlights the relationship between gravitational temperature ratios and entropy changes in curved spacetime.
- Findings suggest implications for understanding energy dynamics in gravitational systems and black hole analogues.

## Abstract

Sadi Carnot’s seminal work laid the foundation for exploring the effects of thermodynamics across diverse domains of physics, stretching from quantum to cosmological scales. Here, we build on the principles of the original Carnot heat engine, and apply it in the context of a particular toy model black brane. This theoretical construct of an effectively two-dimensional, stable, and stationary gravitational object in four-dimensional spacetime derives from a hypothetical flat planet collapsed under the influence of gravity. By constructing a thermodynamic cycle involving three such black branes, we explore the possibility of energy extraction or mining, driven by the temperature gradients and gravitational potential differences characteristic of curved spacetime. Analytic solutions obtainable within this toy model illuminate key aspects of black hole thermodynamics in general, particularly for spacetimes that are not asymptotically flat. Central to these findings is the relation between gravitationally induced temperature ratios and entropy changes, which collectively offer a novel perspective on obtainable energy transfer processes around gravitational structures. This analysis highlights potential implications for understanding energy dynamics in gravitational systems in general, including for black hole evaporation and experimentally implemented black hole analogues. The presented findings not only emphasise the universality of the thermodynamic principles first uncovered by Carnot, but also suggest future research directions in gravitational thermodynamics.