Magnetized Dusty Black Holes and Wormholes
We consider the generalized Tolman solution of general relativity, describing the evolution of a spherical dust cloud in the presence of an external electric or magnetic field. The solution contains three arbitrary functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/Math...
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MDPI AG
2021-11-01
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| Online Access: | https://www.mdpi.com/2218-1997/7/11/419 |
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| author | Kirill A. Bronnikov Pavel E. Kashargin Sergey V. Sushkov |
| author_facet | Kirill A. Bronnikov Pavel E. Kashargin Sergey V. Sushkov |
| author_sort | Kirill A. Bronnikov |
| collection | DOAJ |
| description | We consider the generalized Tolman solution of general relativity, describing the evolution of a spherical dust cloud in the presence of an external electric or magnetic field. The solution contains three arbitrary functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>τ</mi><mn>0</mn></msub><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, where <i>R</i> is a radial coordinate in the comoving reference frame. The solution splits into three branches corresponding to hyperbolic (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>), parabolic (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>) and elliptic (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo><</mo><mn>0</mn></mrow></semantics></math></inline-formula>) types of motion. In such models, we study the possible existence of wormhole throats defined as spheres of minimum radius at a fixed time instant, and prove the existence of throats in the elliptic branch under certain conditions imposed on the arbitrary functions. It is further shown that the normal to a throat is a timelike vector (except for the instant of maximum expansion, when this vector is null), hence a throat is in general located in a T-region of space-time. Thus, if such a dust cloud is placed between two empty (Reissner–Nordström or Schwarzschild) space-time regions, the whole configuration is a black hole rather than a wormhole. However, dust clouds with throats can be inscribed into closed isotropic cosmological models filled with dust to form wormholes which exist for a finite period of time and experience expansion and contraction together with the corresponding cosmology. Explicit examples and numerical estimates are presented. The possible traversability of wormhole-like evolving dust layers is established by a numerical study of radial null geodesics. |
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| spelling | doaj.art-130c01a5a5b04dc6a2040bf65b2d467c2023-11-23T01:50:21ZengMDPI AGUniverse2218-19972021-11-0171141910.3390/universe7110419Magnetized Dusty Black Holes and WormholesKirill A. Bronnikov0Pavel E. Kashargin1Sergey V. Sushkov2Center of Gravitation and Fundamental Metrology, VNIIMS, Ozyornaya Ul. 46, 119361 Moscow, RussiaInstitute of Physics, Kazan Federal University, Kremliovskaya St. 16a, 420008 Kazan, RussiaInstitute of Physics, Kazan Federal University, Kremliovskaya St. 16a, 420008 Kazan, RussiaWe consider the generalized Tolman solution of general relativity, describing the evolution of a spherical dust cloud in the presence of an external electric or magnetic field. The solution contains three arbitrary functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>τ</mi><mn>0</mn></msub><mrow><mo>(</mo><mi>R</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, where <i>R</i> is a radial coordinate in the comoving reference frame. The solution splits into three branches corresponding to hyperbolic (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>), parabolic (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>=</mo><mn>0</mn></mrow></semantics></math></inline-formula>) and elliptic (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo><</mo><mn>0</mn></mrow></semantics></math></inline-formula>) types of motion. In such models, we study the possible existence of wormhole throats defined as spheres of minimum radius at a fixed time instant, and prove the existence of throats in the elliptic branch under certain conditions imposed on the arbitrary functions. It is further shown that the normal to a throat is a timelike vector (except for the instant of maximum expansion, when this vector is null), hence a throat is in general located in a T-region of space-time. Thus, if such a dust cloud is placed between two empty (Reissner–Nordström or Schwarzschild) space-time regions, the whole configuration is a black hole rather than a wormhole. However, dust clouds with throats can be inscribed into closed isotropic cosmological models filled with dust to form wormholes which exist for a finite period of time and experience expansion and contraction together with the corresponding cosmology. Explicit examples and numerical estimates are presented. The possible traversability of wormhole-like evolving dust layers is established by a numerical study of radial null geodesics.https://www.mdpi.com/2218-1997/7/11/419wormholesblack holesdustlike mattercollapseTolman’s solutiongeneral relativity |
| spellingShingle | Kirill A. Bronnikov Pavel E. Kashargin Sergey V. Sushkov Magnetized Dusty Black Holes and Wormholes Universe wormholes black holes dustlike matter collapse Tolman’s solution general relativity |
| title | Magnetized Dusty Black Holes and Wormholes |
| title_full | Magnetized Dusty Black Holes and Wormholes |
| title_fullStr | Magnetized Dusty Black Holes and Wormholes |
| title_full_unstemmed | Magnetized Dusty Black Holes and Wormholes |
| title_short | Magnetized Dusty Black Holes and Wormholes |
| title_sort | magnetized dusty black holes and wormholes |
| topic | wormholes black holes dustlike matter collapse Tolman’s solution general relativity |
| url | https://www.mdpi.com/2218-1997/7/11/419 |
| work_keys_str_mv | AT kirillabronnikov magnetizeddustyblackholesandwormholes AT pavelekashargin magnetizeddustyblackholesandwormholes AT sergeyvsushkov magnetizeddustyblackholesandwormholes |