Quantum Schwarzschild-(A)dS black holes: unitarity and singularity resolution
Abstract We consider the canonical quantisation of spherically symmetric spacetimes within unimodular gravity, leaving sign choices in the metric general enough to include both the interior and exterior Schwarzschild-(Anti-)de Sitter spacetime. In unimodular gravity the cosmological constant appears...
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SpringerOpen
2025-06-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP06(2025)074 |
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| author | Steffen Gielen Sofie Ried |
| author_facet | Steffen Gielen Sofie Ried |
| author_sort | Steffen Gielen |
| collection | DOAJ |
| description | Abstract We consider the canonical quantisation of spherically symmetric spacetimes within unimodular gravity, leaving sign choices in the metric general enough to include both the interior and exterior Schwarzschild-(Anti-)de Sitter spacetime. In unimodular gravity the cosmological constant appears as an integration constant analogous to a total energy, and the quantum Wheeler-DeWitt equation takes the form of a Schrödinger equation in unimodular time. We discuss self-adjoint extensions of the Schrödinger-like Hamiltonian arising from the requirement of unitarity in unimodular time, and identify a physically motivated one-parameter family of extensions. For semiclassical states we are able to derive analytical expressions for expectation values of the metric, representing a quantum-corrected, nonsingular extension of the classical Schwarzschild-(A)dS geometry which describes a quantum transition between asymptotic black hole and white hole states. The sign of the self-adjoint extension parameter corresponds to the allowed sign of the black hole/white hole mass, and so it can be chosen to ensure that this mass is always positive. We also discuss tunnelling states which allow for a change in the sign of the mass, but which are not semiclassical in high-curvature regions. Our mechanism for singularity resolution and the explicit form of the quantum-corrected metric can be compared to other proposals for black holes in quantum gravity, and in the asymptotically AdS case can be contrasted with holographic arguments. |
| format | Article |
| id | doaj-art-29b95620f56344f7853956a0542256da |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-29b95620f56344f7853956a0542256da2025-08-20T03:45:44ZengSpringerOpenJournal of High Energy Physics1029-84792025-06-012025614310.1007/JHEP06(2025)074Quantum Schwarzschild-(A)dS black holes: unitarity and singularity resolutionSteffen Gielen0Sofie Ried1School of Mathematical and Physical Sciences, University of SheffieldSchool of Mathematical and Physical Sciences, University of SheffieldAbstract We consider the canonical quantisation of spherically symmetric spacetimes within unimodular gravity, leaving sign choices in the metric general enough to include both the interior and exterior Schwarzschild-(Anti-)de Sitter spacetime. In unimodular gravity the cosmological constant appears as an integration constant analogous to a total energy, and the quantum Wheeler-DeWitt equation takes the form of a Schrödinger equation in unimodular time. We discuss self-adjoint extensions of the Schrödinger-like Hamiltonian arising from the requirement of unitarity in unimodular time, and identify a physically motivated one-parameter family of extensions. For semiclassical states we are able to derive analytical expressions for expectation values of the metric, representing a quantum-corrected, nonsingular extension of the classical Schwarzschild-(A)dS geometry which describes a quantum transition between asymptotic black hole and white hole states. The sign of the self-adjoint extension parameter corresponds to the allowed sign of the black hole/white hole mass, and so it can be chosen to ensure that this mass is always positive. We also discuss tunnelling states which allow for a change in the sign of the mass, but which are not semiclassical in high-curvature regions. Our mechanism for singularity resolution and the explicit form of the quantum-corrected metric can be compared to other proposals for black holes in quantum gravity, and in the asymptotically AdS case can be contrasted with holographic arguments.https://doi.org/10.1007/JHEP06(2025)074Models of Quantum GravitySpacetime SingularitiesBlack Holes |
| spellingShingle | Steffen Gielen Sofie Ried Quantum Schwarzschild-(A)dS black holes: unitarity and singularity resolution Journal of High Energy Physics Models of Quantum Gravity Spacetime Singularities Black Holes |
| title | Quantum Schwarzschild-(A)dS black holes: unitarity and singularity resolution |
| title_full | Quantum Schwarzschild-(A)dS black holes: unitarity and singularity resolution |
| title_fullStr | Quantum Schwarzschild-(A)dS black holes: unitarity and singularity resolution |
| title_full_unstemmed | Quantum Schwarzschild-(A)dS black holes: unitarity and singularity resolution |
| title_short | Quantum Schwarzschild-(A)dS black holes: unitarity and singularity resolution |
| title_sort | quantum schwarzschild a ds black holes unitarity and singularity resolution |
| topic | Models of Quantum Gravity Spacetime Singularities Black Holes |
| url | https://doi.org/10.1007/JHEP06(2025)074 |
| work_keys_str_mv | AT steffengielen quantumschwarzschildadsblackholesunitarityandsingularityresolution AT sofieried quantumschwarzschildadsblackholesunitarityandsingularityresolution |