For non-viscous fluids in normal flow on static or stationary spacetimes, the redshifted heat current is conserved and the redshifted temperature obeys a curved-space Laplace-type heat equation.
(30) assuming α to be constant reduces to, µ T = A + q0 α ∫ 1 r2( 1 − 2m r − Λ r2 3 ) 3/ 2 dr , (C3) which doesn’t have a simplified or compact form
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General relativistic heat flow from first order hydrodynamics
For non-viscous fluids in normal flow on static or stationary spacetimes, the redshifted heat current is conserved and the redshifted temperature obeys a curved-space Laplace-type heat equation.