https://doi.org/10.1140/epjc/s10052-025-14138-5
Regular Article - Theoretical Physics
Geometric conservation in curved spacetime and entropy
1
Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, 606-8502, Kyoto, Japan
2
Yukawa Institute for Theoretical Physics, Kyoto University, 606-8502, Kyoto, Japan
3
Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN, 351-0198, Wako, Saitama, Japan
4
School of Physics, Korea Institute for Advanced Study, 02455, Seoul, Korea
Received:
6
January
2025
Accepted:
2
April
2025
Published online:
15
April
2025
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.
© The Author(s) 2025
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