Non-closed scalar charge in four-dimensional Einstein-scalar-Gauss-Bonnet black hole thermodynamics
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917416587493376 |
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| author | Ballesteros, Romina Cárdenas, Marcela Lescano, Eric |
| author_facet | Ballesteros, Romina Cárdenas, Marcela Lescano, Eric |
| contents | We develop a covariant differential-form framework to define scalar charges for stationary, asymptotically flat black holes in $4$--dimensional Einstein-scalar-Gauss-Bonnet gravity with a general scalar coupling function. Contracting the scalar field equation of motion with the horizon generator $k$ yields a non-closed-form scalar charge, revealing a bulk contribution encoded in a $3$--form, which measures the obstruction to its closedness. In the presence of shift-symmetry, this obstruction vanishes and the $2$--form scalar charge satisfies a Gauss law, depending solely on boundary data. Geometrically, this reproduces known topological results in the shift-symmetric limit. This framework allows us to analyze the role of the non-closed scalar charges in black hole thermodynamics through the Smarr formula for more general couplings and provide a covariant, charge-based interpretation of the spontaneous scalarization mechanism, showing how the behavior of the scalar charge and the bulk term capture the instability of scalar-free black holes and the emergence of scalar hair. Our results offer a unified geometric understanding of the role of scalar charges and the mechanism of spontaneous scalarization in Einstein-scalar-Gauss-Bonnet gravity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08686 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-closed scalar charge in four-dimensional Einstein-scalar-Gauss-Bonnet black hole thermodynamics Ballesteros, Romina Cárdenas, Marcela Lescano, Eric High Energy Physics - Theory General Relativity and Quantum Cosmology We develop a covariant differential-form framework to define scalar charges for stationary, asymptotically flat black holes in $4$--dimensional Einstein-scalar-Gauss-Bonnet gravity with a general scalar coupling function. Contracting the scalar field equation of motion with the horizon generator $k$ yields a non-closed-form scalar charge, revealing a bulk contribution encoded in a $3$--form, which measures the obstruction to its closedness. In the presence of shift-symmetry, this obstruction vanishes and the $2$--form scalar charge satisfies a Gauss law, depending solely on boundary data. Geometrically, this reproduces known topological results in the shift-symmetric limit. This framework allows us to analyze the role of the non-closed scalar charges in black hole thermodynamics through the Smarr formula for more general couplings and provide a covariant, charge-based interpretation of the spontaneous scalarization mechanism, showing how the behavior of the scalar charge and the bulk term capture the instability of scalar-free black holes and the emergence of scalar hair. Our results offer a unified geometric understanding of the role of scalar charges and the mechanism of spontaneous scalarization in Einstein-scalar-Gauss-Bonnet gravity. |
| title | Non-closed scalar charge in four-dimensional Einstein-scalar-Gauss-Bonnet black hole thermodynamics |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2510.08686 |