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

Area of Science:

• Relativistic astrophysics
• Condensed matter physics
• Gravitational physics

Background:

• Understanding charge and heat transport in curved spacetime is crucial for astrophysics and materials science.
• Existing models often simplify spacetime curvature or material properties.

Purpose of the Study:

• To present a stable, first-order framework for charge and heat transport in curved spacetime.
• To investigate gravitothermoelectric effects in accelerating relativistic media.
• To apply the framework to astrophysical scenarios like compact objects.

Main Methods:

• Developed a covariantly stable, first-order framework for transport equations.
• Utilized the Lorenz gauge for a causal and locally well-posed initial value problem.
• Applied the framework to analyze charge separation, Joule heating variations, and magnetic diffusion in accelerating metals.

Main Results:

• Demonstrated causality and local well-posedness in the nonlinear regime.
• Identified charge separation due to acceleration.
• Showcased nonuniform Joule heating from time dilation and redshift effects on magnetic diffusion.
• Derived a relativistic Thomas-Fermi equation for compact object charge distribution.

Conclusions:

• The presented framework accurately describes relativistic transport phenomena.
• Gravitothermoelectric effects are significant in accelerating systems.
• The derived relativistic Thomas-Fermi equation offers insights into compact object interiors.