Thermoelectric Conduction in General Relativity: A Causal, Stable, and Well Posed Theory

Abstract

We present a covariantly stable first-order framework for describing charge and heat transport in isotropic rigid media embedded in curved spacetime. Working in the Lorenz gauge, we show that the associated initial value problem is both causal and locally well-posed in the fully nonlinear regime. We then apply such framework to explore a range of gravitothermoelectric effects in metals undergoing relativistic acceleration. These include (1) the separation of charge through acceleration, (2) the non-uniformity of Joule heating across accelerating circuits due to time dilation, and (3) the effect of redshift on magnetic diffusion. As an astrophysical application, we derive a relativistic Thomas-Fermi equation governing the charge distribution inside a compact object, also accounting for Seebeck charge displacements driven by cooling.

arXiv comment6 pages and 5 figures (main text) + 6 pages and 1 figure (supplementary material), published in PRL (see https://journals.aps.org/prl/abstract/10.1103/b2k6-thdy)

References in corpus (29)

• Electrically charged compact stars and formation of charged black holes
• First-order relativistic hydrodynamics is stable
• Electric fields at the quark surface of strange stars in the color-flavor locked phase
• Nonlinear causality of general first-order relativistic viscous hydrodynamics
• Electrically Charged Strange Quark Stars
• Relativistic magnetohydrodynamics
• On the Causality and Stability of the Relativistic Diffusion Equation
• Electromagnetic Field and Cylindrical Compact Objects in Modified Gravity
• Structure of the electrospheres of bare strange stars
• Charged polytropic compact stars
• When the entropy has no maximum: A new perspective on the instability of the first-order theories of dissipation
• Diffusion processes involving multiple conserved charges: a first study from kinetic theory and implications to the fluid-dynamical modeling of heavy ion collisions
• Bounds on transport from hydrodynamic stability
• Superconductor in a weak static gravitational field
• Study of Charged Compact Stars in Non-minimally Coupled Gravity
• Dissipative relativistic magnetohydrodynamics of a multicomponent mixture and its application to neutron stars
• Charge diffusion in relativistic resistive second-order dissipative magnetohydrodynamics
• Study of the charged super-Chandrasekhar limiting mass white dwarfs in the $f(R,\mathcal{T})$ gravity
• White dwarfs with a surface electrical charge distribution: Equilibrium and stability
• Effects of Electromagnetic Field on the Structure of Massive Compact Objects
• Temperature in relativistic fluids
• General Relativistic Thermoelectric Effects in Superconductors
• Stability of multicomponent Israel-Stewart-Maxwell theory for charge diffusion
• Infinite Order Hydrodynamics: An Analytical Example
• Thermal Conductivity and Thermal Hall Effect in Dense Electron-Ion Plasma
• Heat propagation in rotating relativistic bodies
• Revisiting thermoelectric effects in the crust of neutron stars
• Stability of electrically charged stars, regular black holes, quasiblack holes, and quasinonblack holes
• Spontaneous charge separation in accelerating relativistic plasmas