Hidden symmetry of the static response of black holes: applications to Love numbers
Abstract We show that any static linear perturbations around Schwarzschild black holes enjoy a set of conserved charges which forms a centrally extended Schrödinger algebra sh $$ \mathfrak{sh} $$ (1) = sl $$ \mathfrak{sl} $$ (2, ℝ) ⋉ H $$ \mathcal{H} $$ . The central charge is given by the black hol...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2022-07-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP07(2022)112 |
| _version_ | 1818509781314306048 |
|---|---|
| author | Jibril Ben Achour Etera R. Livine Shinji Mukohyama Jean-Philippe Uzan |
| author_facet | Jibril Ben Achour Etera R. Livine Shinji Mukohyama Jean-Philippe Uzan |
| author_sort | Jibril Ben Achour |
| collection | DOAJ |
| description | Abstract We show that any static linear perturbations around Schwarzschild black holes enjoy a set of conserved charges which forms a centrally extended Schrödinger algebra sh $$ \mathfrak{sh} $$ (1) = sl $$ \mathfrak{sl} $$ (2, ℝ) ⋉ H $$ \mathcal{H} $$ . The central charge is given by the black hole mass, echoing results on black hole entropy from near-horizon diffeomorphism symmetry. The finite symmetry transformations generated by these conserved charges correspond to Galilean and conformal transformations of the static field and of the coordinates. This new structure allows one to discuss the static response of a Schwarzschild black hole in the test field approximation from a symmetry-based approach. First we show that the (horizontal) symmetry protecting the vanishing of the Love numbers recently exhibited by Hui et al., dubbed the HJPSS symmetry, coincides with one of the sl $$ \mathfrak{sl} $$ (2, ℝ) generators of the Schrödinger group. Then, it is demonstrated that the HJPSS symmetry is selected thanks to the spontaneous breaking of the full Schrödinger symmetry at the horizon down to a simple abelian sub-group. The latter can be understood as the symmetry protecting the regularity of the test field at the horizon. In the 4-dimensional case, this provides a symmetry protection for the vanishing of the Schwarzschild Love numbers. Our results trivially extend to the Kerr case. |
| first_indexed | 2024-12-10T22:50:09Z |
| format | Article |
| id | doaj.art-e6346cd68fe14ebaaf1145a8c3dd80ff |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-12-10T22:50:09Z |
| publishDate | 2022-07-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-e6346cd68fe14ebaaf1145a8c3dd80ff2022-12-22T01:30:28ZengSpringerOpenJournal of High Energy Physics1029-84792022-07-012022713110.1007/JHEP07(2022)112Hidden symmetry of the static response of black holes: applications to Love numbersJibril Ben Achour0Etera R. Livine1Shinji Mukohyama2Jean-Philippe Uzan3Arnold Sommerfeld Center for Theoretical PhysicsEcole Normale Supérieure de LyonCenter for Gravitational Physics, Yukawa Institute for Theoretical PhysicsInstitut d’Astrophysique de Paris, CNRS UMR 7095, Sorbonne UniversitésAbstract We show that any static linear perturbations around Schwarzschild black holes enjoy a set of conserved charges which forms a centrally extended Schrödinger algebra sh $$ \mathfrak{sh} $$ (1) = sl $$ \mathfrak{sl} $$ (2, ℝ) ⋉ H $$ \mathcal{H} $$ . The central charge is given by the black hole mass, echoing results on black hole entropy from near-horizon diffeomorphism symmetry. The finite symmetry transformations generated by these conserved charges correspond to Galilean and conformal transformations of the static field and of the coordinates. This new structure allows one to discuss the static response of a Schwarzschild black hole in the test field approximation from a symmetry-based approach. First we show that the (horizontal) symmetry protecting the vanishing of the Love numbers recently exhibited by Hui et al., dubbed the HJPSS symmetry, coincides with one of the sl $$ \mathfrak{sl} $$ (2, ℝ) generators of the Schrödinger group. Then, it is demonstrated that the HJPSS symmetry is selected thanks to the spontaneous breaking of the full Schrödinger symmetry at the horizon down to a simple abelian sub-group. The latter can be understood as the symmetry protecting the regularity of the test field at the horizon. In the 4-dimensional case, this provides a symmetry protection for the vanishing of the Schwarzschild Love numbers. Our results trivially extend to the Kerr case.https://doi.org/10.1007/JHEP07(2022)112Global SymmetriesBlack HolesClassical Theories of Gravity |
| spellingShingle | Jibril Ben Achour Etera R. Livine Shinji Mukohyama Jean-Philippe Uzan Hidden symmetry of the static response of black holes: applications to Love numbers Journal of High Energy Physics Global Symmetries Black Holes Classical Theories of Gravity |
| title | Hidden symmetry of the static response of black holes: applications to Love numbers |
| title_full | Hidden symmetry of the static response of black holes: applications to Love numbers |
| title_fullStr | Hidden symmetry of the static response of black holes: applications to Love numbers |
| title_full_unstemmed | Hidden symmetry of the static response of black holes: applications to Love numbers |
| title_short | Hidden symmetry of the static response of black holes: applications to Love numbers |
| title_sort | hidden symmetry of the static response of black holes applications to love numbers |
| topic | Global Symmetries Black Holes Classical Theories of Gravity |
| url | https://doi.org/10.1007/JHEP07(2022)112 |
| work_keys_str_mv | AT jibrilbenachour hiddensymmetryofthestaticresponseofblackholesapplicationstolovenumbers AT eterarlivine hiddensymmetryofthestaticresponseofblackholesapplicationstolovenumbers AT shinjimukohyama hiddensymmetryofthestaticresponseofblackholesapplicationstolovenumbers AT jeanphilippeuzan hiddensymmetryofthestaticresponseofblackholesapplicationstolovenumbers |