2026/03/18 by Alberto Saa
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Astrophysical Phenomena and Observations
paper · pdf · doi:10.1088/1361-6382/ae811c
Abstract We propose a Robinson–Trautman evolution in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> -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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>u</mml:mi> <mml:mo>,</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> , 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>u</mml:mi> <mml:mo>,</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> whose stationary configurations correspond, for negative cosmological constant, to boosted BTZ black holes. Numerical solutions strongly support the relaxation of generic regular initial data <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> 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.