Symmetries of vanishing nonlinear Love numbers of Schwarzschild black holes
Abstract The tidal Love numbers parametrize the conservative induced tidal response of self-gravitating objects. It is well established that asymptotically-flat black holes in four-dimensional general relativity have vanishing Love numbers. In linear perturbation theory, this result was shown to be...
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SpringerOpen
2025-03-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP03(2025)124 |
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| author | Oscar Combaluzier-Szteinsznaider Lam Hui Luca Santoni Adam R. Solomon Sam S. C. Wong |
| author_facet | Oscar Combaluzier-Szteinsznaider Lam Hui Luca Santoni Adam R. Solomon Sam S. C. Wong |
| author_sort | Oscar Combaluzier-Szteinsznaider |
| collection | DOAJ |
| description | Abstract The tidal Love numbers parametrize the conservative induced tidal response of self-gravitating objects. It is well established that asymptotically-flat black holes in four-dimensional general relativity have vanishing Love numbers. In linear perturbation theory, this result was shown to be a consequence of ladder symmetries acting on black hole perturbations. In this work, we show that a black hole’s tidal response induced by a static, parity-even tidal field vanishes for all multipoles to all orders in perturbation theory. Our strategy is to focus on static and axisymmetric spacetimes for which the dimensional reduction to the fully nonlinear Weyl solution is well-known. We define the nonlinear Love numbers using the point-particle effective field theory, matching with the Weyl solution to show that an infinite subset of the static, parity-even Love number couplings vanish, to all orders in perturbation theory. This conclusion holds even if the tidal field deviates from axisymmetry. Lastly, we discuss the symmetries underlying the vanishing of the nonlinear Love numbers. An $$\mathfrak{s}\mathfrak{l}$$ (2, ℝ) algebra acting on a covariantly-defined potential furnishes ladder symmetries analogous to those in linear theory. This is because the dynamics of the potential are isomorphic to those of a static, massless scalar on a Schwarzschild background. We comment on the connection between the ladder symmetries and the Geroch group that is well-known to arise from dimensional reduction. |
| format | Article |
| id | doaj-art-cfffc53541094d758b85b0cff8ec50a5 |
| institution | DOAJ |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-cfffc53541094d758b85b0cff8ec50a52025-08-20T03:06:48ZengSpringerOpenJournal of High Energy Physics1029-84792025-03-012025314410.1007/JHEP03(2025)124Symmetries of vanishing nonlinear Love numbers of Schwarzschild black holesOscar Combaluzier-Szteinsznaider0Lam Hui1Luca Santoni2Adam R. Solomon3Sam S. C. Wong4Université Paris Cité, CNRS, Astroparticule et CosmologieCenter for Theoretical Physics, Department of Physics, Columbia UniversityUniversité Paris Cité, CNRS, Astroparticule et CosmologieDepartment of Physics and Astronomy, McMaster UniversityDepartment of Physics, City University of Hong KongAbstract The tidal Love numbers parametrize the conservative induced tidal response of self-gravitating objects. It is well established that asymptotically-flat black holes in four-dimensional general relativity have vanishing Love numbers. In linear perturbation theory, this result was shown to be a consequence of ladder symmetries acting on black hole perturbations. In this work, we show that a black hole’s tidal response induced by a static, parity-even tidal field vanishes for all multipoles to all orders in perturbation theory. Our strategy is to focus on static and axisymmetric spacetimes for which the dimensional reduction to the fully nonlinear Weyl solution is well-known. We define the nonlinear Love numbers using the point-particle effective field theory, matching with the Weyl solution to show that an infinite subset of the static, parity-even Love number couplings vanish, to all orders in perturbation theory. This conclusion holds even if the tidal field deviates from axisymmetry. Lastly, we discuss the symmetries underlying the vanishing of the nonlinear Love numbers. An $$\mathfrak{s}\mathfrak{l}$$ (2, ℝ) algebra acting on a covariantly-defined potential furnishes ladder symmetries analogous to those in linear theory. This is because the dynamics of the potential are isomorphic to those of a static, massless scalar on a Schwarzschild background. We comment on the connection between the ladder symmetries and the Geroch group that is well-known to arise from dimensional reduction.https://doi.org/10.1007/JHEP03(2025)124Black HolesClassical Theories of GravitySpace-Time SymmetriesEffective Field Theories |
| spellingShingle | Oscar Combaluzier-Szteinsznaider Lam Hui Luca Santoni Adam R. Solomon Sam S. C. Wong Symmetries of vanishing nonlinear Love numbers of Schwarzschild black holes Journal of High Energy Physics Black Holes Classical Theories of Gravity Space-Time Symmetries Effective Field Theories |
| title | Symmetries of vanishing nonlinear Love numbers of Schwarzschild black holes |
| title_full | Symmetries of vanishing nonlinear Love numbers of Schwarzschild black holes |
| title_fullStr | Symmetries of vanishing nonlinear Love numbers of Schwarzschild black holes |
| title_full_unstemmed | Symmetries of vanishing nonlinear Love numbers of Schwarzschild black holes |
| title_short | Symmetries of vanishing nonlinear Love numbers of Schwarzschild black holes |
| title_sort | symmetries of vanishing nonlinear love numbers of schwarzschild black holes |
| topic | Black Holes Classical Theories of Gravity Space-Time Symmetries Effective Field Theories |
| url | https://doi.org/10.1007/JHEP03(2025)124 |
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