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arXiv · 2312.09712

Geometric conservation in curved spacetime and entropy

Sinya Aoki·Yoshimasa Hidaka·Kiyoharu Kawana·Kengo Shimada
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Abstract

We provide an improved definition of new conserved quantities derived from the energy-momentum tensor in curved spacetime by introducing an additional scalar function. We find that the conserved current and the associated conserved charge become geometric under a certain initial condition of the scalar function, and show that such a conserved geometric current generally exists in curved spacetime. Furthermore, we demonstrate that the geometric conserved current agrees with the entropy current in an effective theory of a perfect fluid, thus the conserved charge is the total entropy of the system. While the geometric charge can be regarded as the entropy for a nondissipative fluid, its physical meaning should be investigated for more general cases.

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Sinya Aoki, Yoshimasa Hidaka, Kiyoharu Kawana, Kengo Shimada. 2023-12-15. Geometric conservation in curved spacetime and entropy. https://arxiv.org/abs/2312.09712

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