Bounds on the mass of superradiantly unstable scalar fields around Kerr black holes
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913342330765312 |
|---|---|
| author | Richartz, Maurício Rosa, João Luís Berti, Emanuele |
| author_facet | Richartz, Maurício Rosa, João Luís Berti, Emanuele |
| contents | In this work we compute numerical bounds on the mass $μ$ of superradiantly unstable scalar fields in a Kerr black hole background using the continued fraction method. We show that the normalized upper bound on the mass $μ$ increases with the angular momentum number $\ell$ and the azimuthal number $m$, approaching the most stringent analytical bound known to date when $\ell=m \gg 1$. We also provide an analytical fit to the numerically determined mass bound as a function of the dimensionless spin parameter $a/M$ of the black hole with an accuracy of the order $0.1\%$ for the fundamental mode with $\ell=m=1$, and of the order $1\%$ for higher-order modes (up to $\ell=m=20$). We argue that this analytical fit is particularly useful in astrophysical scenarios, since the lowest $\ell=m$ modes are capable of producing the strongest observable imprints of superradiance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01003 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bounds on the mass of superradiantly unstable scalar fields around Kerr black holes Richartz, Maurício Rosa, João Luís Berti, Emanuele General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena In this work we compute numerical bounds on the mass $μ$ of superradiantly unstable scalar fields in a Kerr black hole background using the continued fraction method. We show that the normalized upper bound on the mass $μ$ increases with the angular momentum number $\ell$ and the azimuthal number $m$, approaching the most stringent analytical bound known to date when $\ell=m \gg 1$. We also provide an analytical fit to the numerically determined mass bound as a function of the dimensionless spin parameter $a/M$ of the black hole with an accuracy of the order $0.1\%$ for the fundamental mode with $\ell=m=1$, and of the order $1\%$ for higher-order modes (up to $\ell=m=20$). We argue that this analytical fit is particularly useful in astrophysical scenarios, since the lowest $\ell=m$ modes are capable of producing the strongest observable imprints of superradiance. |
| title | Bounds on the mass of superradiantly unstable scalar fields around Kerr black holes |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2405.01003 |