Heat conduction in general relativity
arXiv:2206.09555 · doi:10.1088/1361-6382/aca1a1
Abstract
We study the problem of heat conduction in general relativity by using Carter's variational formulation. We write the creation rates of the entropy and the particle as combinations of the vorticities of temperature and chemical potential. We pay attention to the fact that there are two additional degrees of freedom in choosing the relativistic analog of Cattaneo equation for the parts binormal to the caloric and the number flows. Including the contributions from the binormal parts, we find a heat-flow equations and discover their dynamical role in thermodynamic systems. The benefit of introducing the binormal parts is that it allows room for a physical ansatz for describing the whole evolution of the thermodynamic system. Taking advantage of this platform, we propose a proper ansatz that deals with the binormal contributions starting from the physical properties of thermal equilibrium systems. We also consider the stability of a thermodynamic system in a flat background. We find that "Klein" modes exist in addition to the known ones. We also find that the stability requirement is less stringent than those in the literature.
arXiv comment19 pages, 1 figure
References in corpus (20)
- GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
- Hot Accretion Flows Around Black Holes
- Relativistic Fluid Dynamics: Physics for Many Different Scales
- Merger of binary neutron stars with realistic equations of state in full general relativity
- 2D Cooling of Magnetized Neutron Stars
- Magnetic fields within color superconducting neutron star cores
- Thermal Dynamics in General Relativity
- A lower limit on the heat capacity of the neutron star core
- Variational multi-fluid dynamics and causal heat conductivity
- The dynamics of dissipative multi-fluid neutron star cores
- Linear stability of Israel-Stewart theory in the presence of net-charge diffusion
- Covariant analysis of Newtonian multi-fluid models for neutron stars: III Transvective, viscous, and superfluid drag dissipation
- Stability and causality of Carter's multifluid theory
- A covariant action principle for dissipative fluid dynamics: From formalism to fundamental physics
- Tolman-like temperature gradients in stationary spacetimes
- A consistent first-order model for relativistic heat flow
- Thermodynamic Equilibrium in General Relativity
- Relativistic Two-stream Instability
- Entropy entrainment and dissipation in superfluid Helium
- Local temperature in general relativity
Cited by in corpus (5)
- Tolman-Ehrenfest's criterion of thermal equilibrium extended to conformally static spacetimes
- How the Schwarzschild-de Sitter horizons remain in thermal equilibrium at vastly different temperatures
- Temperature upper bound of an ideal gas
- Steady heat conduction in general relativity
- Linear response in a charged gas in curved spacetime and covariant heat equation