Transverse expansion of the metric at null infinity
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908814062649344 |
|---|---|
| author | Mars, Marc Sánchez-Pérez, Gabriel |
| author_facet | Mars, Marc Sánchez-Pérez, Gabriel |
| contents | In this paper we analyze the conformal Einstein equations to all orders at null infinity without imposing any restriction on the spacetime dimension, the topology of $\mathscr{I}$, or fall-off conditions for the Weyl tensor. In particular, we study how the equations constrain the geometry of null infinity when it is assumed to be foliated by cross-sections, not necessarily spheres. Our approach is coordinate-free and treats the conformal factor $Ω$ as a dynamical variable. After identifying the free data at $\mathscr{I}$, we show that any two asymptotically flat spacetimes sharing the same free data at null infinity are necessarily isometric to infinite order. In addition, we provide a detached definition of null infinity and prove an existence theorem for asymptotically flat spacetimes solving the field equations to infinite order at $\mathscr{I}$ realizing the prescribed initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05061 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Transverse expansion of the metric at null infinity Mars, Marc Sánchez-Pérez, Gabriel General Relativity and Quantum Cosmology Differential Geometry In this paper we analyze the conformal Einstein equations to all orders at null infinity without imposing any restriction on the spacetime dimension, the topology of $\mathscr{I}$, or fall-off conditions for the Weyl tensor. In particular, we study how the equations constrain the geometry of null infinity when it is assumed to be foliated by cross-sections, not necessarily spheres. Our approach is coordinate-free and treats the conformal factor $Ω$ as a dynamical variable. After identifying the free data at $\mathscr{I}$, we show that any two asymptotically flat spacetimes sharing the same free data at null infinity are necessarily isometric to infinite order. In addition, we provide a detached definition of null infinity and prove an existence theorem for asymptotically flat spacetimes solving the field equations to infinite order at $\mathscr{I}$ realizing the prescribed initial data. |
| title | Transverse expansion of the metric at null infinity |
| topic | General Relativity and Quantum Cosmology Differential Geometry |
| url | https://arxiv.org/abs/2602.05061 |