Maximal extension of Schwarzschild-like spacetimes in Lorentz gauge theory
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917518273150976 |
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| author | Fathi, Mohsen |
| author_facet | Fathi, Mohsen |
| contents | We study the maximal analytic extension of the Schwarzschild-like black hole solution in Lorentz gauge theory. The lapse function is $f(r)=A_0^{-2}-2\m/r$, so the horizon is located at $r_+=2\m A_0^2$ and the non-affinity coefficient of the horizon generator is $κ=1/(4\m A_0^4)$. We first analyze the radial null curves in the Schwarzschild-Droste (SD) and ingoing Eddington-Finkelstein (IEF) charts, and then construct the Kruskal-Szekeres (KS) chart adapted to the LGT geometry. The KS extension contains two exterior regions, a black-hole region and a white-hole region. We also present the standard and regular Carter-Penrose (CP) compactifications. The conformal skeleton is Schwarzschild-like, but the physical scale of the horizon, the surface gravity and the constant-radius curves remain controlled by $A_0$. Hence the solution has the same causal topology as Schwarzschild, while it is geometrically inequivalent to it when $A_0\neq1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21823 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Maximal extension of Schwarzschild-like spacetimes in Lorentz gauge theory Fathi, Mohsen General Relativity and Quantum Cosmology High Energy Physics - Theory We study the maximal analytic extension of the Schwarzschild-like black hole solution in Lorentz gauge theory. The lapse function is $f(r)=A_0^{-2}-2\m/r$, so the horizon is located at $r_+=2\m A_0^2$ and the non-affinity coefficient of the horizon generator is $κ=1/(4\m A_0^4)$. We first analyze the radial null curves in the Schwarzschild-Droste (SD) and ingoing Eddington-Finkelstein (IEF) charts, and then construct the Kruskal-Szekeres (KS) chart adapted to the LGT geometry. The KS extension contains two exterior regions, a black-hole region and a white-hole region. We also present the standard and regular Carter-Penrose (CP) compactifications. The conformal skeleton is Schwarzschild-like, but the physical scale of the horizon, the surface gravity and the constant-radius curves remain controlled by $A_0$. Hence the solution has the same causal topology as Schwarzschild, while it is geometrically inequivalent to it when $A_0\neq1$. |
| title | Maximal extension of Schwarzschild-like spacetimes in Lorentz gauge theory |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.21823 |