The Robinson-Trautman (RT) spacetime is the simplest solution of General

Relativity (GR) describing a compact source surrounded by gravitational

waves. As an initial value problem, the RT spacetime evolution is a

well-posed mathematical problem. The pertinent dynamical equations are

equivalent to the so-called Calabi flow, and regular initial data evolve

smoothly towards a final state corresponding to a remnant Schwarzschild

black hole. Extensions of RT spacetimes for higher dimensions (D > 4)

were recently proposed, and the essence of the RT evolution is

unchanged: regular initial data evolve towards a final

higher-dimensional Schwarzschild black hole. The situation for D=3 is

quite different due to some peculiarities of low-dimensional GR. We will

present a D=3 RT flow mimicking the essential properties of the Calabi

flow. In particular, regular initial data evolve towards a final remnant

BTZ black hole, and any possible asymmetry in the initial data is

expelled as a radiation fluid.

# Robinson–Trautman solutions in (2+1) dimensions

Event type

Event date

Venue

Only on campus (Sala Sousa Pinto)

Speaker

Alberto Saa (IMECC - UNICAMP)