An exact stationary axisymmetric vacuum solution within a metric--affine bumblebee gravity
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911939515383808 |
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| author | Filho, A. A. Araújo Nascimento, J. R. Petrov, A. Yu. Porfírio, P. J. |
| author_facet | Filho, A. A. Araújo Nascimento, J. R. Petrov, A. Yu. Porfírio, P. J. |
| contents | Within the framework of the spontaneous Lorentz symmetry breaking, we consider a metric--affine generalization of the gravitational sector of the Standard--Model Extension (SME), including the Lorentz--violating (LV) coefficients $u$ and $s^{μν}$. In this model, we derive the modified Einstein field equations in order to obtain a new axisymmetric vacuum spinning solution for a particular bumblebee's profile. Such a solution has the remarkable property of incorporating the effects of Lorentz symmetry breaking (LSB) through the LV dimensionless parameter $X=ξb^2$, as the LSB is turned off, $X=0$, we recover the well--established result, the Kerr solution, as expected. Afterwards, we calculate the geodesics, the radial acceleration and thermodynamic quantities for this new metric. We also estimate an upper bound for $X$ by using astrophysical data of the advance Mercury's perihelion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13014 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An exact stationary axisymmetric vacuum solution within a metric--affine bumblebee gravity Filho, A. A. Araújo Nascimento, J. R. Petrov, A. Yu. Porfírio, P. J. General Relativity and Quantum Cosmology Within the framework of the spontaneous Lorentz symmetry breaking, we consider a metric--affine generalization of the gravitational sector of the Standard--Model Extension (SME), including the Lorentz--violating (LV) coefficients $u$ and $s^{μν}$. In this model, we derive the modified Einstein field equations in order to obtain a new axisymmetric vacuum spinning solution for a particular bumblebee's profile. Such a solution has the remarkable property of incorporating the effects of Lorentz symmetry breaking (LSB) through the LV dimensionless parameter $X=ξb^2$, as the LSB is turned off, $X=0$, we recover the well--established result, the Kerr solution, as expected. Afterwards, we calculate the geodesics, the radial acceleration and thermodynamic quantities for this new metric. We also estimate an upper bound for $X$ by using astrophysical data of the advance Mercury's perihelion. |
| title | An exact stationary axisymmetric vacuum solution within a metric--affine bumblebee gravity |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2402.13014 |