ELFT HÍRADÓ

["Szabados,L." <lbszab AT rmki.kfki.hu>]

RELATIVITASELMELETI SZEMINARIUM


Eloado:  Dr. Martin Scholtz
         Czech Technical University in Prague

Az eloadas cime: Helical symmetry in GR and the non-existence
                 of asymptotically flat periodic spacetimes

t:       2011 julius 15 (pentek), 11.00
(x,y,z): KFKI RMKI III. epulet, tanacsterem

Kivonat:
The notion of helical symmetry, while clear and intuitive in the flat
space-time, cannot be easily defined in general curved space-time. In
the first part of the talk we concentrate on selected helically symmetric
solutions in flat space-time, then we briefly discuss two definitions
of helical Killing vector in curved space-time, given by Bonnazola and
Friedman. It is concluded that no exact helically symmetric solution in
GR is known, and in addition, its existence remains an open question.

On the other hand, there are physical arguments that helically symmetric
solutions cannot be asymptotically flat. Thus, we raise a more general
question whether any periodic solution of Einstein's equations (including
those with helical symmetry) can be asymptotically flat. In the second
part of the talk we present a generalization (and, in fact, correction)
of the proof by Gibbons and Stewart, that asymptotically flat solutions
periodic at infinity are necessarilly stationary. We discuss the proof
of G&S and its drawbacks, then we present its generalization to the
presence of the electromagnetic and scalar fields.