Entropic route to Brown-York tensor: A unified framework for null and timelike hypersurfaces
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| Format: | Preprint |
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2026
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| _version_ | 1866911704647991296 |
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| author | Bhattacharya, Krishnakanta Ram, Bhera Majhi, Bibhas Ranjan |
| author_facet | Bhattacharya, Krishnakanta Ram, Bhera Majhi, Bibhas Ranjan |
| contents | Building on Padmanabhan's entropy functional, originally introduced to derive Einstein's equations and highlight the emergent nature of gravity, we demonstrate its robustness in a broader context. Using the same entropy density, we show that the Brown-York (BY) tensor arises naturally as the projection of the canonical momentum conjugate to the normal vectors on the relevant hypersurface, thereby providing a common construction applicable to both timelike and null hypersurfaces. This perspective also offers insight into the structural differences of the null BY tensor, including its non-symmetric character. We further extend the analysis to scalar-tensor theories, showing that the entropy-based formulation reproduces the expected equations of motion along with the corresponding BY tensor, and, clarifies its non-conservation in the presence of additional scalar field which is non-minimally coupled. Our results provide a coherent variational interpretation of quasi-local gravitational quantities and reveal a common underlying structure linking bulk dynamics and boundary momentum. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_22434 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Entropic route to Brown-York tensor: A unified framework for null and timelike hypersurfaces Bhattacharya, Krishnakanta Ram, Bhera Majhi, Bibhas Ranjan General Relativity and Quantum Cosmology High Energy Physics - Theory Building on Padmanabhan's entropy functional, originally introduced to derive Einstein's equations and highlight the emergent nature of gravity, we demonstrate its robustness in a broader context. Using the same entropy density, we show that the Brown-York (BY) tensor arises naturally as the projection of the canonical momentum conjugate to the normal vectors on the relevant hypersurface, thereby providing a common construction applicable to both timelike and null hypersurfaces. This perspective also offers insight into the structural differences of the null BY tensor, including its non-symmetric character. We further extend the analysis to scalar-tensor theories, showing that the entropy-based formulation reproduces the expected equations of motion along with the corresponding BY tensor, and, clarifies its non-conservation in the presence of additional scalar field which is non-minimally coupled. Our results provide a coherent variational interpretation of quasi-local gravitational quantities and reveal a common underlying structure linking bulk dynamics and boundary momentum. |
| title | Entropic route to Brown-York tensor: A unified framework for null and timelike hypersurfaces |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.22434 |