Relativistic figures of equilibrium in the Wald magnetosphere
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910120968978432 |
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| author | Doruchowski, Paweł Mach, Patryk Trova, Audrey Juraev, Bakhtinur |
| author_facet | Doruchowski, Paweł Mach, Patryk Trova, Audrey Juraev, Bakhtinur |
| contents | We consider a self-gravitating, rigidly rotating charged perfect fluid immersed in the Wald magnetosphere, constructed out of two linearly independent Killing vectors present in stationary and axially-symmetric spacetimes. We show that in non-vacuum spacetimes, Wald's solution can be compatible with the electric current associated with a rotating charged perfect fluid characterized by the vanishing electric conductivity. We prove that for rigidly rotating fluids with a constant energy density or described by the polytropic equation of state, the resulting equations expressing the conservation of the energy-momentum tensor can be integrated. Consequently, the system can be described by nearly standard Einstein-Euler equations known from the theory of general-relativistic rotating fluids, with modifications introduced in the Euler-Bernoulli equation. Numerical solutions of the Einstein-Euler equations are provided for these two cases by introducing suitable modifications in the pseudospectral code by Ansorg, Kleinwächter, and Meinel. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_09912 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Relativistic figures of equilibrium in the Wald magnetosphere Doruchowski, Paweł Mach, Patryk Trova, Audrey Juraev, Bakhtinur General Relativity and Quantum Cosmology We consider a self-gravitating, rigidly rotating charged perfect fluid immersed in the Wald magnetosphere, constructed out of two linearly independent Killing vectors present in stationary and axially-symmetric spacetimes. We show that in non-vacuum spacetimes, Wald's solution can be compatible with the electric current associated with a rotating charged perfect fluid characterized by the vanishing electric conductivity. We prove that for rigidly rotating fluids with a constant energy density or described by the polytropic equation of state, the resulting equations expressing the conservation of the energy-momentum tensor can be integrated. Consequently, the system can be described by nearly standard Einstein-Euler equations known from the theory of general-relativistic rotating fluids, with modifications introduced in the Euler-Bernoulli equation. Numerical solutions of the Einstein-Euler equations are provided for these two cases by introducing suitable modifications in the pseudospectral code by Ansorg, Kleinwächter, and Meinel. |
| title | Relativistic figures of equilibrium in the Wald magnetosphere |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2604.09912 |