Robinson-Trautman spacetimes in (2+1) dimensions
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908899903275008 |
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| author | Saa, Alberto |
| author_facet | Saa, Alberto |
| contents | We propose a Robinson-Trautman evolution in $(2+1)$-dimensional spacetime that retains key structural features of the four-dimensional case. We consider a recently studied exact family of metrics to select a nonstationary geometry with a cosmological constant, sourced by a null fluid. The metric is completely determined by a single positive function $P(u,ϕ)$, while the corresponding matter content is encoded in a null-fluid density. Motivated by the role of the area-preserving Calabi flow in four dimensions, we introduce a fourth-order length-preserving evolution equation for $P(u,ϕ)$ whose stationary configurations correspond, for negative cosmological constant, to boosted BTZ black holes. Numerical solutions strongly support the relaxation of generic regular initial data $P(0,ϕ)$ toward the stationary sector. The resulting system provides a simple toy model for dissipative dynamics driven by null radiation in lower-dimensional gravity, with several structural similarities to phenomena associated with genuine gravitational radiation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18209 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Robinson-Trautman spacetimes in (2+1) dimensions Saa, Alberto General Relativity and Quantum Cosmology We propose a Robinson-Trautman evolution in $(2+1)$-dimensional spacetime that retains key structural features of the four-dimensional case. We consider a recently studied exact family of metrics to select a nonstationary geometry with a cosmological constant, sourced by a null fluid. The metric is completely determined by a single positive function $P(u,ϕ)$, while the corresponding matter content is encoded in a null-fluid density. Motivated by the role of the area-preserving Calabi flow in four dimensions, we introduce a fourth-order length-preserving evolution equation for $P(u,ϕ)$ whose stationary configurations correspond, for negative cosmological constant, to boosted BTZ black holes. Numerical solutions strongly support the relaxation of generic regular initial data $P(0,ϕ)$ toward the stationary sector. The resulting system provides a simple toy model for dissipative dynamics driven by null radiation in lower-dimensional gravity, with several structural similarities to phenomena associated with genuine gravitational radiation. |
| title | Robinson-Trautman spacetimes in (2+1) dimensions |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.18209 |