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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.05240 |
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| _version_ | 1866908941516013568 |
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| author | Chen, Wen-Xiang |
| author_facet | Chen, Wen-Xiang |
| contents | We extend the residue-based Robson-Villari-Biancalana (RVB) method from the calculation of Hawking temperature to the determination of black hole entropy within f(Q) gravity. Starting from the residue-corrected temperature prescription developed in recent RVB analyses of f(Q) black holes, we combine this approach with the first law of black hole thermodynamics to derive a general expression for the entropy of static, spherically symmetric configurations.
By expressing the metric in a standard Schwarzschild-like decomposition with an additional correction term, we show that the entropy satisfies a universal integral relation. The integrand depends explicitly on horizon data as well as on a residue-induced temperature shift parameter. For the specific quadratic model, we obtain an explicit closed-form expression for the entropy at first order in the residue parameter.
In the limit where the residue contribution vanishes, the standard Bekenstein-Hawking area law is recovered. However, once the complex contour contribution is retained, a correction beyond the area law naturally emerges. This framework should be interpreted as a residue-induced thermodynamic extension of the temperature-based method, rather than as a universal Noether charge formulation applicable to all f(Q) black hole solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_05240 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Black Hole Entropy in f(Q) Gravity from the RVB Residue Method Chen, Wen-Xiang General Relativity and Quantum Cosmology We extend the residue-based Robson-Villari-Biancalana (RVB) method from the calculation of Hawking temperature to the determination of black hole entropy within f(Q) gravity. Starting from the residue-corrected temperature prescription developed in recent RVB analyses of f(Q) black holes, we combine this approach with the first law of black hole thermodynamics to derive a general expression for the entropy of static, spherically symmetric configurations. By expressing the metric in a standard Schwarzschild-like decomposition with an additional correction term, we show that the entropy satisfies a universal integral relation. The integrand depends explicitly on horizon data as well as on a residue-induced temperature shift parameter. For the specific quadratic model, we obtain an explicit closed-form expression for the entropy at first order in the residue parameter. In the limit where the residue contribution vanishes, the standard Bekenstein-Hawking area law is recovered. However, once the complex contour contribution is retained, a correction beyond the area law naturally emerges. This framework should be interpreted as a residue-induced thermodynamic extension of the temperature-based method, rather than as a universal Noether charge formulation applicable to all f(Q) black hole solutions. |
| title | Black Hole Entropy in f(Q) Gravity from the RVB Residue Method |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.05240 |