Robinson-Trautman solutions with scalar hair and Ricci flow
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866911783391854592 |
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| author | Nozawa, Masato Torii, Takashi |
| author_facet | Nozawa, Masato Torii, Takashi |
| contents | The vacuum Robinson-Trautman solution admits a shear-free and twist-free null geodesic congruence with a nonvanishing expansion. We perform a comprehensive classification of solutions exhibiting this property in Einstein's gravity with a massless scalar field, assuming that the solution belongs at least to Petrov-type II and some of the components of Ricci tensor identically vanish. We find that these solutions can be grouped into three distinct classes: (I-a) a natural extension of the Robinson-Trautman family incorporating a scalar hair satisfying the time derivative of the Ricci flow equation, (I-b) a novel non-asymptotically flat solution characterized by two functions satisfying Perelman's pair of the Ricci flow equations, and (II) a dynamical solution possessing ${\rm SO}(3)$, ${\rm ISO}(2)$ or ${\rm SO}(1,2)$ symmetry. We provide a complete list of all explicit solutions falling into Petrov type D for classes (I-a) and (I-b). Moreover, leveraging the massless solution in class (I-a), we derive the neutral Robinson-Trautman solution to the ${\cal N}=2$ gauged supergravity with the prepotential $F(X) =-iX^0X^1$. By flipping the sign of the kinetic term of the scalar field, the Petrov-D class (I-a) solution leads to a time-dependent wormhole with an instantaneous spacetime singularity. Although the general solution is unavailable for class (II), we find a new dynamical solution with spherical symmetry from the AdS-Roberts solution via AdS/Ricci-flat correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_05460 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Robinson-Trautman solutions with scalar hair and Ricci flow Nozawa, Masato Torii, Takashi High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics The vacuum Robinson-Trautman solution admits a shear-free and twist-free null geodesic congruence with a nonvanishing expansion. We perform a comprehensive classification of solutions exhibiting this property in Einstein's gravity with a massless scalar field, assuming that the solution belongs at least to Petrov-type II and some of the components of Ricci tensor identically vanish. We find that these solutions can be grouped into three distinct classes: (I-a) a natural extension of the Robinson-Trautman family incorporating a scalar hair satisfying the time derivative of the Ricci flow equation, (I-b) a novel non-asymptotically flat solution characterized by two functions satisfying Perelman's pair of the Ricci flow equations, and (II) a dynamical solution possessing ${\rm SO}(3)$, ${\rm ISO}(2)$ or ${\rm SO}(1,2)$ symmetry. We provide a complete list of all explicit solutions falling into Petrov type D for classes (I-a) and (I-b). Moreover, leveraging the massless solution in class (I-a), we derive the neutral Robinson-Trautman solution to the ${\cal N}=2$ gauged supergravity with the prepotential $F(X) =-iX^0X^1$. By flipping the sign of the kinetic term of the scalar field, the Petrov-D class (I-a) solution leads to a time-dependent wormhole with an instantaneous spacetime singularity. Although the general solution is unavailable for class (II), we find a new dynamical solution with spherical symmetry from the AdS-Roberts solution via AdS/Ricci-flat correspondence. |
| title | Robinson-Trautman solutions with scalar hair and Ricci flow |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology Mathematical Physics |
| url | https://arxiv.org/abs/2310.05460 |