Heat propagation in rotating relativistic bodies

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.

14 pages, 3 captioned figures, published on PRD (see https://journals.aps.org/prd/abstract/10.1103/4g4w-ypmf)

References in corpus (17)

• Relativistic viscous hydrodynamics, conformal invariance, and holography
• On the convergence of the gradient expansion in hydrodynamics
• Magnetic, thermal and rotational evolution of isolated neutron stars
• Thermal time and the Tolman-Ehrenfest effect: temperature as the "speed of time"
• Relativistic hydrodynamics - causality and stability
• Thermal Dynamics in General Relativity
• When the entropy has no maximum: A new perspective on the instability of the first-order theories of dissipation
• Bounds on transport from hydrodynamic stability
• Stability and causality of Carter's multifluid theory
• The stochastic relativistic advection diffusion equation from the Metropolis algorithm
• The Hydrohedron: Bootstrapping Relativistic Hydrodynamics
• Universality Classes of Relativistic Fluid Dynamics: Foundations
• Temperature in relativistic fluids
• Standard cooling of rapidly rotating isolated neutron stars in 2D
• Infinite Order Hydrodynamics: An Analytical Example
• Noncovariant parabolic theories of relativistic diffusion
• Steady heat conduction in general relativity

Cited by in corpus (4)

• The initial data of effective field theories of relativistic viscous fluids and gravity
• Lorentz-boosted diffusion: initial value formulation and exact solutions
• The diffusion equation is compatible with special relativity
• Thermoelectric Conduction in General Relativity: A Causal, Stable, and Well Posed Theory