Corrections to Kerr-Newman black hole from Noncommutative Einstein-Maxwell equation
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918106012581888 |
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| author | Požar, Filip |
| author_facet | Požar, Filip |
| contents | In this letter we introduce the noncommutative geometry into the standard Einstein-Hilbert-Maxwell action via the $\partial_t\wedge\partial_φ$ Drinfeld twist and solve the equation of motion pertubatively in the expansion of the noncommutative parameter $a$. The equation of motion, the NC Einstein-Maxwell equation, turns out to be effectively a problem in nonlinear electrodynamics where the energy-momentum tensor $T_{μν}$ obtains correction terms with three Faraday tensors $F_{μν}$. A solution with nonzero $a^1$ terms turns out to be the Kerr-Newman black hole modified with nonzero $g_{tθ}, g_{rφ}, g_{tr}$ and $g_{φθ}$ components proportional to $a$, while the electromagnetic potential is the Seiberg-Witten expanded Kerr-Newman potential which introduces a nonzero $A_θ$ term proportional to $a$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03337 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Corrections to Kerr-Newman black hole from Noncommutative Einstein-Maxwell equation Požar, Filip General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics In this letter we introduce the noncommutative geometry into the standard Einstein-Hilbert-Maxwell action via the $\partial_t\wedge\partial_φ$ Drinfeld twist and solve the equation of motion pertubatively in the expansion of the noncommutative parameter $a$. The equation of motion, the NC Einstein-Maxwell equation, turns out to be effectively a problem in nonlinear electrodynamics where the energy-momentum tensor $T_{μν}$ obtains correction terms with three Faraday tensors $F_{μν}$. A solution with nonzero $a^1$ terms turns out to be the Kerr-Newman black hole modified with nonzero $g_{tθ}, g_{rφ}, g_{tr}$ and $g_{φθ}$ components proportional to $a$, while the electromagnetic potential is the Seiberg-Witten expanded Kerr-Newman potential which introduces a nonzero $A_θ$ term proportional to $a$. |
| title | Corrections to Kerr-Newman black hole from Noncommutative Einstein-Maxwell equation |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2502.03337 |