Abstract
We examine the conditions imposed on spacetime geometry by linear and extended thermodynamics. In this analysis we confine ourselves on shear-free spacetimes with divergence-free Weyl tensor. This results in a variety of well-known spacetimes which have to have simple kinematic properties as well as very restricted source structure. In all cases the thermodynamical considerations show the privileged role of the equation p = −ρ which can be interpreted as cosmological constant. Moreover, it is interesting to observe that the restrictions imposed on the spacetime geometry in the case of extended thermodynamics (for vanishing anisotropic pressure) are much stronger than in the linear case.
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Chrobok, T., v. Borzeszkowski, HH. Thermodynamical laws and spacetime geometry. Gen Relativ Gravit 37, 365–381 (2005). https://doi.org/10.1007/s10714-005-0024-0
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DOI: https://doi.org/10.1007/s10714-005-0024-0