Regular Frames for Spherically Symmetric Black Holes Revisited
We consider a space-time of a spherically symmetric black hole with one simple horizon. As a standard coordinate frame fails in its vicinity, this requires continuation across the horizon and constructing frames which are regular there. Up to now, several standard frames of such a kind are known. It...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/1/40 |
| _version_ | 1797490165997895680 |
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| author | Alexey V. Toporensky Oleg B. Zaslavskii |
| author_facet | Alexey V. Toporensky Oleg B. Zaslavskii |
| author_sort | Alexey V. Toporensky |
| collection | DOAJ |
| description | We consider a space-time of a spherically symmetric black hole with one simple horizon. As a standard coordinate frame fails in its vicinity, this requires continuation across the horizon and constructing frames which are regular there. Up to now, several standard frames of such a kind are known. It was shown in the literature before, how some of them can be united in one picture as different limits of a general scheme. However, some types of frames (the Kruskal–Szekeres and Lemaître ones) and transformations to them from the original one remained completely disjoint. We show that the Kruskal–Szekeres and Lemaître frames stem from the same root. Overall, our approach in some sense completes the procedure and gives the most general scheme. We relate the parameter of transformation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>e</mi><mn>0</mn></msub></semantics></math></inline-formula> to the specific energy of fiducial observers and show that in the limit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>e</mi><mn>0</mn></msub><mo>→</mo><mn>0</mn></mrow></semantics></math></inline-formula>, a homogeneous metric under the horizon can be obtained by a smooth limiting transition. |
| first_indexed | 2024-03-10T00:27:08Z |
| format | Article |
| id | doaj.art-e5ce337b89f64453a1f631bdbe18b1bc |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T00:27:08Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e5ce337b89f64453a1f631bdbe18b1bc2023-11-23T15:32:28ZengMDPI AGSymmetry2073-89942021-12-011414010.3390/sym14010040Regular Frames for Spherically Symmetric Black Holes RevisitedAlexey V. Toporensky0Oleg B. Zaslavskii1Sternberg Astronomical Institute, Lomonosov Moscow State University, 119991 Moscow, RussiaInstitute of Mathematics and Mechanics, Kazan Federal University, Kremlevskaya 18, 420008 Kazan, RussiaWe consider a space-time of a spherically symmetric black hole with one simple horizon. As a standard coordinate frame fails in its vicinity, this requires continuation across the horizon and constructing frames which are regular there. Up to now, several standard frames of such a kind are known. It was shown in the literature before, how some of them can be united in one picture as different limits of a general scheme. However, some types of frames (the Kruskal–Szekeres and Lemaître ones) and transformations to them from the original one remained completely disjoint. We show that the Kruskal–Szekeres and Lemaître frames stem from the same root. Overall, our approach in some sense completes the procedure and gives the most general scheme. We relate the parameter of transformation <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>e</mi><mn>0</mn></msub></semantics></math></inline-formula> to the specific energy of fiducial observers and show that in the limit <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>e</mi><mn>0</mn></msub><mo>→</mo><mn>0</mn></mrow></semantics></math></inline-formula>, a homogeneous metric under the horizon can be obtained by a smooth limiting transition.https://www.mdpi.com/2073-8994/14/1/40frameblack holecoordinate transformations |
| spellingShingle | Alexey V. Toporensky Oleg B. Zaslavskii Regular Frames for Spherically Symmetric Black Holes Revisited Symmetry frame black hole coordinate transformations |
| title | Regular Frames for Spherically Symmetric Black Holes Revisited |
| title_full | Regular Frames for Spherically Symmetric Black Holes Revisited |
| title_fullStr | Regular Frames for Spherically Symmetric Black Holes Revisited |
| title_full_unstemmed | Regular Frames for Spherically Symmetric Black Holes Revisited |
| title_short | Regular Frames for Spherically Symmetric Black Holes Revisited |
| title_sort | regular frames for spherically symmetric black holes revisited |
| topic | frame black hole coordinate transformations |
| url | https://www.mdpi.com/2073-8994/14/1/40 |
| work_keys_str_mv | AT alexeyvtoporensky regularframesforsphericallysymmetricblackholesrevisited AT olegbzaslavskii regularframesforsphericallysymmetricblackholesrevisited |