# Heat propagation in rotating relativistic bodies

## TL;DR

This paper develops a universal, hyperbolic heat conduction equation for rotating relativistic bodies, incorporating gravitational effects, and demonstrates its application to rotating cylinders and black body cooling.

## Contribution

It introduces a first-order gradient expansion leading to a causal, stable heat equation that unifies rotational and gravitational effects in relativity.

## Key findings

- Derived a universal hyperbolic heat equation for rotating bodies.
- Showed the equation accounts for Tolman-Ehrenfest effects.
- Computed relativistic corrections to black body cooling laws.

## Abstract

We investigate heat propagation in rigidly rotating bodies within the theory of general relativity. Using a first-order gradient expansion, we derive a universal partial differential equation governing the temperature evolution. This equation is hyperbolic, causal, and stable, and it naturally accounts for both rotational and gravitational Tolman-Ehrenfest effects. Any other first-order theory consistent with established physics (including the parabolic theories used in neutron star cooling models) must be equivalent to our formulation within an error that is of higher order in gradients. As a case study, we analyze heat transfer in solid cylinders rotating around their symmetry axis, so that the tangential speed approaches the speed of light on the surface. We also compute the relativistic rotational corrections to the cooling law of black bodies.