Hidden symmetries and separability structures of Ovcharenko-Podolský and conformal-to-Carter spacetimes
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| Format: | Preprint |
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2025
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| _version_ | 1866909927849590784 |
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| author | Gray, Finnian Kubiznak, David Ovcharenko, Hryhorii Podolsky, Jiri |
| author_facet | Gray, Finnian Kubiznak, David Ovcharenko, Hryhorii Podolsky, Jiri |
| contents | Recently, a remarkable new class of spacetimes describing black holes immersed in a non-aligned electromagnetic field has been found. While still of type D, this class goes beyond the famous Plebański--Demiański family. Here we demonstrate that the whole class admits a hidden symmetry encoded in the non-degenerate conformal Killing--Yano 2-form. Interestingly, as a direct consequence of non-alignment of the electromagnetic field and contrary to the Plebański--Demiański class (where the field is aligned), such a symmetry no longer generates the full "tower of symmetries". Despite this, it enables one to separate variables in massless Hamilton--Jacobi, conformal wave, and massless Dirac equations, as well as allows one to tackle massless vector and tensor perturbations. These results provide a useful mathematical tool for discussing numerous (astrophysical) applications to be described by these metrics. Moreover, as we shall show, the novel spacetimes provide an interesting test-ground for studying the recently defined Penrose charges whose existence is intrinsically related to hidden rather than explicit symmetries. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_21538 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hidden symmetries and separability structures of Ovcharenko-Podolský and conformal-to-Carter spacetimes Gray, Finnian Kubiznak, David Ovcharenko, Hryhorii Podolsky, Jiri General Relativity and Quantum Cosmology High Energy Physics - Theory Recently, a remarkable new class of spacetimes describing black holes immersed in a non-aligned electromagnetic field has been found. While still of type D, this class goes beyond the famous Plebański--Demiański family. Here we demonstrate that the whole class admits a hidden symmetry encoded in the non-degenerate conformal Killing--Yano 2-form. Interestingly, as a direct consequence of non-alignment of the electromagnetic field and contrary to the Plebański--Demiański class (where the field is aligned), such a symmetry no longer generates the full "tower of symmetries". Despite this, it enables one to separate variables in massless Hamilton--Jacobi, conformal wave, and massless Dirac equations, as well as allows one to tackle massless vector and tensor perturbations. These results provide a useful mathematical tool for discussing numerous (astrophysical) applications to be described by these metrics. Moreover, as we shall show, the novel spacetimes provide an interesting test-ground for studying the recently defined Penrose charges whose existence is intrinsically related to hidden rather than explicit symmetries. |
| title | Hidden symmetries and separability structures of Ovcharenko-Podolský and conformal-to-Carter spacetimes |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.21538 |