Symmetries of the gravitational scattering in the absence of peeling
Abstract The symmetries of the gravitational scattering are intimately tied to the symmetries which preserve asymptotic flatness at null infinity. In Penrose’s definition of asymptotic flatness, a central role is played by the notion of asymptotic simplicity and the ensuing peeling behavior which di...
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2024-12-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP12(2024)081 |
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| author | Marc Geiller Alok Laddha Céline Zwikel |
| author_facet | Marc Geiller Alok Laddha Céline Zwikel |
| author_sort | Marc Geiller |
| collection | DOAJ |
| description | Abstract The symmetries of the gravitational scattering are intimately tied to the symmetries which preserve asymptotic flatness at null infinity. In Penrose’s definition of asymptotic flatness, a central role is played by the notion of asymptotic simplicity and the ensuing peeling behavior which dictates the decay rate of the Weyl tensor. However, there is now accumulating evidence that in a generic gravitational scattering the peeling property is broken, so that the spacetime is not asymptotically-flat in the usual sense. These obstructions to peeling can be traced back to the existence of universal radiative low frequency observables called “tails to the displacement memory”. As shown by Saha, Sahoo and Sen, these observables are uniquely fixed by the initial and final momenta of the scattering objects, and are independent of the details of the scattering. The universality of these tail modes is the statement of the classical logarithmic soft graviton theorem. Four-dimensional gravitation scattering therefore exhibits a rich infrared interplay between tail to the memory, loss of peeling, and universal logarithmic soft theorems. In this paper we study the solution space and the asymptotic symmetries for logarithmically-asymptotically-flat spacetimes. These are defined by a polyhomogeneous expansion of the Bondi metric which gives rise to a loss of peeling, and represent the classical arena which can accommodate a generic gravitational scattering containing tails to the memory. We show that while the codimension-two generalized BMS charges are sensitive to the loss of peeling at I $$ \mathcal{I} $$ +, the flux is insensitive to the fate of peeling. Due to the tail to the memory, the soft superrotation flux contains a logarithmic divergence whose coefficient is the quantity which is conserved in the scattering by virtue of the logarithmic soft theorem. In our analysis we also exhibit new logarithmic evolution equations and flux-balance laws, whose presence suggests the existence of an infinite tower of subleading logarithmic soft graviton theorems. |
| format | Article |
| id | doaj-art-c769f9bcec6141d1bb3e8e6fb4f7cd64 |
| institution | OA Journals |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | SpringerOpen |
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| series | Journal of High Energy Physics |
| spelling | doaj-art-c769f9bcec6141d1bb3e8e6fb4f7cd642025-08-20T01:59:43ZengSpringerOpenJournal of High Energy Physics1029-84792024-12-0120241213810.1007/JHEP12(2024)081Symmetries of the gravitational scattering in the absence of peelingMarc Geiller0Alok Laddha1Céline Zwikel2Univ Lyon, ENS de Lyon, CNRS, Laboratoire de PhysiqueChennai Mathematical Institute, H1Perimeter Institute for Theoretical PhysicsAbstract The symmetries of the gravitational scattering are intimately tied to the symmetries which preserve asymptotic flatness at null infinity. In Penrose’s definition of asymptotic flatness, a central role is played by the notion of asymptotic simplicity and the ensuing peeling behavior which dictates the decay rate of the Weyl tensor. However, there is now accumulating evidence that in a generic gravitational scattering the peeling property is broken, so that the spacetime is not asymptotically-flat in the usual sense. These obstructions to peeling can be traced back to the existence of universal radiative low frequency observables called “tails to the displacement memory”. As shown by Saha, Sahoo and Sen, these observables are uniquely fixed by the initial and final momenta of the scattering objects, and are independent of the details of the scattering. The universality of these tail modes is the statement of the classical logarithmic soft graviton theorem. Four-dimensional gravitation scattering therefore exhibits a rich infrared interplay between tail to the memory, loss of peeling, and universal logarithmic soft theorems. In this paper we study the solution space and the asymptotic symmetries for logarithmically-asymptotically-flat spacetimes. These are defined by a polyhomogeneous expansion of the Bondi metric which gives rise to a loss of peeling, and represent the classical arena which can accommodate a generic gravitational scattering containing tails to the memory. We show that while the codimension-two generalized BMS charges are sensitive to the loss of peeling at I $$ \mathcal{I} $$ +, the flux is insensitive to the fate of peeling. Due to the tail to the memory, the soft superrotation flux contains a logarithmic divergence whose coefficient is the quantity which is conserved in the scattering by virtue of the logarithmic soft theorem. In our analysis we also exhibit new logarithmic evolution equations and flux-balance laws, whose presence suggests the existence of an infinite tower of subleading logarithmic soft graviton theorems.https://doi.org/10.1007/JHEP12(2024)081Classical Theories of GravityGauge Symmetry |
| spellingShingle | Marc Geiller Alok Laddha Céline Zwikel Symmetries of the gravitational scattering in the absence of peeling Journal of High Energy Physics Classical Theories of Gravity Gauge Symmetry |
| title | Symmetries of the gravitational scattering in the absence of peeling |
| title_full | Symmetries of the gravitational scattering in the absence of peeling |
| title_fullStr | Symmetries of the gravitational scattering in the absence of peeling |
| title_full_unstemmed | Symmetries of the gravitational scattering in the absence of peeling |
| title_short | Symmetries of the gravitational scattering in the absence of peeling |
| title_sort | symmetries of the gravitational scattering in the absence of peeling |
| topic | Classical Theories of Gravity Gauge Symmetry |
| url | https://doi.org/10.1007/JHEP12(2024)081 |
| work_keys_str_mv | AT marcgeiller symmetriesofthegravitationalscatteringintheabsenceofpeeling AT alokladdha symmetriesofthegravitationalscatteringintheabsenceofpeeling AT celinezwikel symmetriesofthegravitationalscatteringintheabsenceofpeeling |