2020年12月10日13:00 - 14:30 (JST)

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We propose a manifestly covariant definition of a conserved charge in gravity. We first define a charge density from the energy momentum tensor with a Killing vector, if exists in the system, and calculate the energy (and angular momentum) of the black hole by a volume integral. Our definition of energy leads to a correction of the known mass formula of a compact star, which includes the gravitational interaction energy and is shown to be 68\% of the leading term in some case. Secondly we propose a new method to define a conserved charge in the absence of Killing vectors, and argue that the conserved charge can be regarded as entropy, by showing the 1st law of thermodynamic for a special case. We apply this new definition to the expanding universe, gravitational plane waves and the black hole. We discuss future directions of our research.

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## References

1. S. Aoki, T. Onogi, S. Yokoyama, arXiv:2005.13233
2. S. Aoki, T. Onogi, S. Yokoyama, arXiv:2010.07660