On the central singularity of the BTZ geometries
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910404504977408 |
|---|---|
| author | Briceño, Matías Martínez, Cristián Zanelli, Jorge |
| author_facet | Briceño, Matías Martínez, Cristián Zanelli, Jorge |
| contents | The nature of the central singularity of the BTZ geometries -- stationary vacuum solutions of 2+1 gravity with negative cosmological constant $Λ=-\ell^{-2}$ and $SO(2)\times \mathbb{R}$ isometry -- is discussed. The essential tool for this analysis is the holonomy operator on a closed path (i.e., Wilson loop) around the central singularity. The study considers the holonomies for the Lorentz and AdS$_3$ connections. The analysis is carried out for all values of the mass $M$ and angular momentum $J$, namely, for black holes ($M \ell \ge |J|$) and naked singularities ($M \ell < |J|$). In general, both Lorentz and AdS$_3$ holonomies are nontrivial in the zero-radius limit revealing the presence of delta-like singularity at the origin in the curvature and torsion two-forms. However, in the cases $M\pm J/\ell=-n_{\pm}^2$, with $n_{\pm} \in \mathbb{N}$, recently identified in \cite{GMYZ} as BPS configurations, the AdS$_3$ holonomy reduces to the identity. Nevertheless, except for the AdS$_{3}$ spacetime ($M=-1$, $J=0$), all BTZ geometries have a central singularity which is not revealed by local operations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06552 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the central singularity of the BTZ geometries Briceño, Matías Martínez, Cristián Zanelli, Jorge General Relativity and Quantum Cosmology High Energy Physics - Theory The nature of the central singularity of the BTZ geometries -- stationary vacuum solutions of 2+1 gravity with negative cosmological constant $Λ=-\ell^{-2}$ and $SO(2)\times \mathbb{R}$ isometry -- is discussed. The essential tool for this analysis is the holonomy operator on a closed path (i.e., Wilson loop) around the central singularity. The study considers the holonomies for the Lorentz and AdS$_3$ connections. The analysis is carried out for all values of the mass $M$ and angular momentum $J$, namely, for black holes ($M \ell \ge |J|$) and naked singularities ($M \ell < |J|$). In general, both Lorentz and AdS$_3$ holonomies are nontrivial in the zero-radius limit revealing the presence of delta-like singularity at the origin in the curvature and torsion two-forms. However, in the cases $M\pm J/\ell=-n_{\pm}^2$, with $n_{\pm} \in \mathbb{N}$, recently identified in \cite{GMYZ} as BPS configurations, the AdS$_3$ holonomy reduces to the identity. Nevertheless, except for the AdS$_{3}$ spacetime ($M=-1$, $J=0$), all BTZ geometries have a central singularity which is not revealed by local operations. |
| title | On the central singularity of the BTZ geometries |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2404.06552 |