On the classification of static vacuum metrics in presence of a cosmological constant. Part I – Solutions with zero mass

Venue:  Seminar Room “-1” – Department of Mathematics
Time: 14:00

• Speaker: Stefano Borghini (University of Trento)

Abstract:

Static vacuum metrics probably represent the most basic objects in General Relativity. In fact they are solutions to the Einstein Field Equations with vanishing Stress-Energy tensor (vacuum), featuring a very special metric structure (warped product). Such a structure induces a natural foliation of the spacetime into space-like slices which are all isometric to each other, so that the corresponding physical universe is static.

For this class of solutions we discuss the definition of an appropriate notion of mass. This is particularly relevant when the cosmological constant Λ is positive and the model solutions are compact so that – unlike in the asymptotically flat (Λ = 0) and asymptotically hyperbolic (Λ < 0) situation – a general notion of mass is not available in the literature. Building on this, we characterize the De Sitter solution as the only static vacuum metric with zero mass.

Finally, exploiting some particular features of our formalism, we show how the same analysis can be fruitfully employed to treat the case of negative cosmological constant, leading to a uniqueness theorem for the Anti-De Sitter spacetime.

Contact person: Davide Pastorello