Equivalence of Noether charge and Hilbert action boundary term formulas for the black hole entropy in $F(R_{abcd})$ gravity theory
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909488795090944 |
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| author | Guo, Wei Guo, Xiyao Li, Mingfeng Mou, Zili Zhang, Hongbao |
| author_facet | Guo, Wei Guo, Xiyao Li, Mingfeng Mou, Zili Zhang, Hongbao |
| contents | By working with the covariant phase space formalism, we have shown that not only can the Hamiltonian conjugate to a Killing vector field $ξ$ be expressed as the sum of the associated Noether charge and $ξ$ contracted with the Hilbert action boundary term for $F(R_{abcd})$ gravity, but also be written as its contraction with another $ξ$ independent tensor field. With this, we have proven the equivalence of Noether charge and Hilbert action boundary term formulae for the stationary black hole entropy in $F(R_{abcd})$ gravity, which is further substantiated by our explicit computation using both formulae. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_15138 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivalence of Noether charge and Hilbert action boundary term formulas for the black hole entropy in $F(R_{abcd})$ gravity theory Guo, Wei Guo, Xiyao Li, Mingfeng Mou, Zili Zhang, Hongbao High Energy Physics - Theory General Relativity and Quantum Cosmology By working with the covariant phase space formalism, we have shown that not only can the Hamiltonian conjugate to a Killing vector field $ξ$ be expressed as the sum of the associated Noether charge and $ξ$ contracted with the Hilbert action boundary term for $F(R_{abcd})$ gravity, but also be written as its contraction with another $ξ$ independent tensor field. With this, we have proven the equivalence of Noether charge and Hilbert action boundary term formulae for the stationary black hole entropy in $F(R_{abcd})$ gravity, which is further substantiated by our explicit computation using both formulae. |
| title | Equivalence of Noether charge and Hilbert action boundary term formulas for the black hole entropy in $F(R_{abcd})$ gravity theory |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2406.15138 |