Nonstationary Law of Heat Flux in Linear Thermoelastic Solid Media in General Relativity

This paper seeks to obtain a solution to the general relativistic nonstationary problem of heat conduction at finite speed for linear anisotropic thermoelastic solid continuum, with an eye to some apparent disagreements and in the light or classical spirits conforming to the fundamental concepts of continuum mechanics and functional theory. Accordingly, heat flux vector is taken as a suitable functional representable by Velterra-type Riemann convolution in normed Hilbert space of vector- and tensor-valued time functions. Thereby, proper assumptions yield the desired nonstationary law which, as it should, leads back to Eckart-type equations in the stationary case. The isotropic problem is also discussed, and classical limits are restored. The spatial and objective covariant solution so achieved, seems to be satisfactory and fairly general for problems of this type.