ALBERTO SAA
[arXiv:2603.18209]
Abstract
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.
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[13] http://vigo.ime.unicamp.br/RT3
[2] P. Chrusciel, Comm. Math. Phys. 137, 289 (1991).
[3] R.P. Macedo and A. Saa, Phys. Rev. D78, 104025 (2008). [arXiv:0809.3039]
[4] J. Podolsky and M. Ortaggio, Class. Quantum Grav. 23, 5785 (2006). [arXiv:gr-qc/0605136]
[5] M. Banados, C. Teitelboim, J. Zanelli, Phys. Rev. Lett. 69, 1849 (1992). [arXiv:hep-th/9204099]
[6] J. Podolsky, R. Svarc, H. Maeda, Class. Quantum Grav. 36, 015009 (2019). [arXiv:1809.02480]
[7] W. Kinnersley, Phys. Rev. 186, 1335 (1969).
[8] W. B. Bonnor, Class. Quantum Grav. 11, 2007 (1994).
[9] J. Podolsky, Phys. Rev. D 78, 044029 (2008). [arXiv:0806.2966]
[10] J. Podolsky, Int. J. Mod. Phys. D 20, 335 (2011). [arXiv:1006.1583]
[11] A. Novick-Cohen, Chapter 4: The Cahn-Hilliard Equation, in Handbook of Differential Equations: Evolutionary Equations, Vol. IV, Eds: C.M. Dafermos and M. Pokorny, Elsevier (2008). Full textavailable at DOI:10.1016/S1874-5717(08)00004-2
[12] X. Lu, G.H. Gao, and Z.Z. Sun, Numer. Methods Partial Differ. Eq. 39, 447 (2023).
[13] http://vigo.ime.unicamp.br/RT3