The ultrarelativistic limit of Kerr
Abstract The massless (or ultrarelativistic) limit of a Schwarzschild black hole with fixed energy was determined long ago in the form of the Aichelburg-Sexl shockwave, but the status of the same limit for a Kerr black hole is less clear. In this paper, we explore the ultrarelativistic limit of Kerr...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-02-01
|
| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP02(2023)107 |
| _version_ | 1797779141710315520 |
|---|---|
| author | Tim Adamo Andrea Cristofoli Piotr Tourkine |
| author_facet | Tim Adamo Andrea Cristofoli Piotr Tourkine |
| author_sort | Tim Adamo |
| collection | DOAJ |
| description | Abstract The massless (or ultrarelativistic) limit of a Schwarzschild black hole with fixed energy was determined long ago in the form of the Aichelburg-Sexl shockwave, but the status of the same limit for a Kerr black hole is less clear. In this paper, we explore the ultrarelativistic limit of Kerr in the class of Kerr-Schild impulsive pp-waves by exploiting a relation between the metric profile and the eikonal phase associated with scattering between a scalar and the source of the metric. This gives a map between candidate metrics and tree-level, 4-point scattering amplitudes. At large distances from the source, we find that all candidates for the massless limit of Kerr in this class do not have spin effects. This includes the metric corresponding to the massless limit of the amplitude for gravitational scattering between a scalar and a massive particle of infinite spin. One metric, discovered by Balasin and Nachbagauer, does have spin and finite size effects at short distances, leading to a remarkably compact scattering amplitude with many interesting properties. We also discuss the classical single copy of the ultrarelativistic limit of Kerr in electromagnetism. |
| first_indexed | 2024-03-12T23:26:30Z |
| format | Article |
| id | doaj.art-be0ff8e46ad84e0287910173b0263373 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-12T23:26:30Z |
| publishDate | 2023-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-be0ff8e46ad84e0287910173b02633732023-07-16T11:07:09ZengSpringerOpenJournal of High Energy Physics1029-84792023-02-012023213010.1007/JHEP02(2023)107The ultrarelativistic limit of KerrTim Adamo0Andrea Cristofoli1Piotr Tourkine2School of Mathematics and Maxwell Institute for Mathematical Sciences, University of EdinburghSchool of Mathematics and Maxwell Institute for Mathematical Sciences, University of EdinburghLAPTh, CNRS et Université Savoie Mont-BlancAbstract The massless (or ultrarelativistic) limit of a Schwarzschild black hole with fixed energy was determined long ago in the form of the Aichelburg-Sexl shockwave, but the status of the same limit for a Kerr black hole is less clear. In this paper, we explore the ultrarelativistic limit of Kerr in the class of Kerr-Schild impulsive pp-waves by exploiting a relation between the metric profile and the eikonal phase associated with scattering between a scalar and the source of the metric. This gives a map between candidate metrics and tree-level, 4-point scattering amplitudes. At large distances from the source, we find that all candidates for the massless limit of Kerr in this class do not have spin effects. This includes the metric corresponding to the massless limit of the amplitude for gravitational scattering between a scalar and a massive particle of infinite spin. One metric, discovered by Balasin and Nachbagauer, does have spin and finite size effects at short distances, leading to a remarkably compact scattering amplitude with many interesting properties. We also discuss the classical single copy of the ultrarelativistic limit of Kerr in electromagnetism.https://doi.org/10.1007/JHEP02(2023)107Classical Theories of GravityScattering Amplitudes |
| spellingShingle | Tim Adamo Andrea Cristofoli Piotr Tourkine The ultrarelativistic limit of Kerr Journal of High Energy Physics Classical Theories of Gravity Scattering Amplitudes |
| title | The ultrarelativistic limit of Kerr |
| title_full | The ultrarelativistic limit of Kerr |
| title_fullStr | The ultrarelativistic limit of Kerr |
| title_full_unstemmed | The ultrarelativistic limit of Kerr |
| title_short | The ultrarelativistic limit of Kerr |
| title_sort | ultrarelativistic limit of kerr |
| topic | Classical Theories of Gravity Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP02(2023)107 |
| work_keys_str_mv | AT timadamo theultrarelativisticlimitofkerr AT andreacristofoli theultrarelativisticlimitofkerr AT piotrtourkine theultrarelativisticlimitofkerr AT timadamo ultrarelativisticlimitofkerr AT andreacristofoli ultrarelativisticlimitofkerr AT piotrtourkine ultrarelativisticlimitofkerr |