Geometrically Significant Surfaces of Black Holes from a Single Scalar
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915933213163520 |
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| author | Agca, Cagdas Ulus Tekin, Bayram |
| author_facet | Agca, Cagdas Ulus Tekin, Bayram |
| contents | Black hole spacetimes contain several geometrically distinguished hypersurfaces, including event and Cauchy horizons, stationary-limit surfaces, curvature singularities, and asymptotic infinity. These structures are usually identified by different geometric or causal criteria. Here, we show that for the Kerr-Newman black hole, a single scalar function encodes all of them at once. The function arises by analytically continuing the membrane-paradigm pressure of the stretched horizon into the full spacetime. In fully factorized form, its zeros locate the outer and inner horizons, its poles locate the outer and inner stationary-limit surfaces, its higher-order divergence identifies the ring singularity, and its decay at large $r$ captures the asymptotic region. Thus, the analytically continued membrane pressure serves as a unified global detector of the critical surfaces in the Kerr-Newman geometry. We further note that the same analytic structure admits a secondary interpretation as an effective generalized multi-component van der Waals-type equation of state, whose intrinsic scales are fixed by the distinguished radii of the spacetime itself. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_10289 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometrically Significant Surfaces of Black Holes from a Single Scalar Agca, Cagdas Ulus Tekin, Bayram General Relativity and Quantum Cosmology Astrophysics of Galaxies High Energy Physics - Theory Mathematical Physics Black hole spacetimes contain several geometrically distinguished hypersurfaces, including event and Cauchy horizons, stationary-limit surfaces, curvature singularities, and asymptotic infinity. These structures are usually identified by different geometric or causal criteria. Here, we show that for the Kerr-Newman black hole, a single scalar function encodes all of them at once. The function arises by analytically continuing the membrane-paradigm pressure of the stretched horizon into the full spacetime. In fully factorized form, its zeros locate the outer and inner horizons, its poles locate the outer and inner stationary-limit surfaces, its higher-order divergence identifies the ring singularity, and its decay at large $r$ captures the asymptotic region. Thus, the analytically continued membrane pressure serves as a unified global detector of the critical surfaces in the Kerr-Newman geometry. We further note that the same analytic structure admits a secondary interpretation as an effective generalized multi-component van der Waals-type equation of state, whose intrinsic scales are fixed by the distinguished radii of the spacetime itself. |
| title | Geometrically Significant Surfaces of Black Holes from a Single Scalar |
| topic | General Relativity and Quantum Cosmology Astrophysics of Galaxies High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2604.10289 |