Seminários em Geometria e Topologia na UFSC – 13/05/2016
Seminários em Geometria e Topologia
“On the rigidity problem for geodesically complete Brinkmann gravitational waves”
Palestrante: Jonatan Herrera (UFSC)
Resumo: Since the appearence of the so-called singularity theorems, the gravitational collapse, as happen in black holes and the Big Bang, has been described by geodesic incompleteness of null or timelike geodesics. As gravity is naturally thought as an atractive force, gravitational collapse should be rather common. This lead to the conjecture of Geroch that solutions of Einstein field equations geodesically complete should be scarce.
In this sense, Anderson proved in 2000 the following remarkable result about solutions of the vacuum Einstein equations: any 4-dimensional stationary spacetime without closed timelike curves, Ricci-flat and geodesically complete should be isometric to a quotient of the Minkowski model.
My aim in this seminar is to present a recent work, in collaboration with Ivan P. Costa e Silva (UFSC) and José Luis Flores (UMA), where we prove a null analog of Anderson’s result. Concretely, I will show that any 4-dimensional Brinkmann model, strongly causal, Ricci-flat, geodesically complete and transversally Killing is isometric to a plane wave. I will also discuss about the relation of this rigidity problem and the well-known Elhers Kundt conjecture on pp-waves.
Dia – Horário: 13/05/2016 – 15:30
Local: Auditório do Departamento de Matemática (LAED)
E. Krukoski