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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.10123 |
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| _version_ | 1866909057767440384 |
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| author | Fawzi, Ali Stojkovic, Dejan |
| author_facet | Fawzi, Ali Stojkovic, Dejan |
| contents | The Kruskal-Szekeres coordinates construction for the Schwarzschild spacetime could be viewed geometrically as a squeezing of the $t$-line associated with the asymptotic observer into a single point, at the event horizon $r=2M$. Starting from this point, we extend the Kruskal charting to spacetimes with two horizons, in particular the Reissner-Nordström manifold, $\mathcal{M}_{RN}$. We develop a new method for constructing Kruskal-like coordinates and find two algebraically distinct classes charting $\mathcal{M}_{RN}$. We pedagogically illustrate our method by constructing two compact, conformal, and global coordinate systems labeled $\mathcal{GK_{I}}$ and $\mathcal{GK_{II}}$ for each class respectively. In both coordinates, the metric differentiability can be promoted to $C^\infty$. The conformal metric factor can be explicitly written in terms of the original $t$ and $r$ coordinates for both charts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10123 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the generalization of the Kruskal-Szekeres coordinates: a global conformal charting of the Reissner-Nordstrom spacetime Fawzi, Ali Stojkovic, Dejan General Relativity and Quantum Cosmology The Kruskal-Szekeres coordinates construction for the Schwarzschild spacetime could be viewed geometrically as a squeezing of the $t$-line associated with the asymptotic observer into a single point, at the event horizon $r=2M$. Starting from this point, we extend the Kruskal charting to spacetimes with two horizons, in particular the Reissner-Nordström manifold, $\mathcal{M}_{RN}$. We develop a new method for constructing Kruskal-like coordinates and find two algebraically distinct classes charting $\mathcal{M}_{RN}$. We pedagogically illustrate our method by constructing two compact, conformal, and global coordinate systems labeled $\mathcal{GK_{I}}$ and $\mathcal{GK_{II}}$ for each class respectively. In both coordinates, the metric differentiability can be promoted to $C^\infty$. The conformal metric factor can be explicitly written in terms of the original $t$ and $r$ coordinates for both charts. |
| title | On the generalization of the Kruskal-Szekeres coordinates: a global conformal charting of the Reissner-Nordstrom spacetime |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2309.10123 |