Implications of Raychaudhuri equation and geodesic focusing in interacting two fluid systems
Abstract The present work analyses Raychaudhuri equation (RE) in Einstein gravity for two interacting fluids. Focusing theorem, a consequence of RE, is directly related to the singularity theorems of Penrose and Hawking. In the present work, the signature of the Raychaudhuri scalar or convergence sc...
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| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-025-13850-6 |
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| author | Madhukrishna Chakraborty Subenoy Chakraborty |
| author_facet | Madhukrishna Chakraborty Subenoy Chakraborty |
| author_sort | Madhukrishna Chakraborty |
| collection | DOAJ |
| description | Abstract The present work analyses Raychaudhuri equation (RE) in Einstein gravity for two interacting fluids. Focusing theorem, a consequence of RE, is directly related to the singularity theorems of Penrose and Hawking. In the present work, the signature of the Raychaudhuri scalar or convergence scalar has been examined for two types of interaction forms namely, (i) $$Q=H(\alpha \rho _1+\beta \rho _2)$$ Q = H ( α ρ 1 + β ρ 2 ) (linear) and (ii) $$Q=\dfrac{H\xi \rho _1\rho _2}{\alpha \rho _1+\beta \rho _2}$$ Q = H ξ ρ 1 ρ 2 α ρ 1 + β ρ 2 (non-linear). Finally, the phenomena of focusing of a congruence of geodesics and possible avoidance of singularity have been discussed based on the nature of the two fluids and the interaction term operating between them. |
| format | Article |
| id | doaj-art-e95373d181794eb6b813c22d87664f3b |
| institution | Kabale University |
| issn | 1434-6052 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj-art-e95373d181794eb6b813c22d87664f3b2025-02-02T12:38:14ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522025-01-0185111010.1140/epjc/s10052-025-13850-6Implications of Raychaudhuri equation and geodesic focusing in interacting two fluid systemsMadhukrishna Chakraborty0Subenoy Chakraborty1Department of Mathematics, Techno India UniversityDepartment of Mathematics, Brainware UniversityAbstract The present work analyses Raychaudhuri equation (RE) in Einstein gravity for two interacting fluids. Focusing theorem, a consequence of RE, is directly related to the singularity theorems of Penrose and Hawking. In the present work, the signature of the Raychaudhuri scalar or convergence scalar has been examined for two types of interaction forms namely, (i) $$Q=H(\alpha \rho _1+\beta \rho _2)$$ Q = H ( α ρ 1 + β ρ 2 ) (linear) and (ii) $$Q=\dfrac{H\xi \rho _1\rho _2}{\alpha \rho _1+\beta \rho _2}$$ Q = H ξ ρ 1 ρ 2 α ρ 1 + β ρ 2 (non-linear). Finally, the phenomena of focusing of a congruence of geodesics and possible avoidance of singularity have been discussed based on the nature of the two fluids and the interaction term operating between them.https://doi.org/10.1140/epjc/s10052-025-13850-6 |
| spellingShingle | Madhukrishna Chakraborty Subenoy Chakraborty Implications of Raychaudhuri equation and geodesic focusing in interacting two fluid systems European Physical Journal C: Particles and Fields |
| title | Implications of Raychaudhuri equation and geodesic focusing in interacting two fluid systems |
| title_full | Implications of Raychaudhuri equation and geodesic focusing in interacting two fluid systems |
| title_fullStr | Implications of Raychaudhuri equation and geodesic focusing in interacting two fluid systems |
| title_full_unstemmed | Implications of Raychaudhuri equation and geodesic focusing in interacting two fluid systems |
| title_short | Implications of Raychaudhuri equation and geodesic focusing in interacting two fluid systems |
| title_sort | implications of raychaudhuri equation and geodesic focusing in interacting two fluid systems |
| url | https://doi.org/10.1140/epjc/s10052-025-13850-6 |
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