Geometry and Relativity Meeting

December 4, 2007


Matematiska institutionen,  Linköpings universitet

Under the auspices of the Gravitation Section of the Swedish Physical Society


Program :  

All seminars in Glashuset (B-house, entrance 25).

10.15-10.55 Ingemar Bengtsson, Stockholms universitet: Anti-de Sitter quotients: when are they black holes?
11.00-12.00 Paul Tod, University of Oxford: Extending the conformal metric through cosmological singularities

Lunch

13.15-13.55 Michael Bradley, Umeå universitet: Slowly Rotating Fluid Balls of Petrov Type D
14.00-14.40 Alfonso García-Parrado, Linköpings universitet: Killing spinor initial data sets

Coffee

15.00-15.30 Narit Pidokrajt, Stockholms universitet: Thermodynamics of Dilaton Black Holes through Ruppeiner geometry
15.35-16.00 GR Sweden meeting


Abstracts:
I Bengtsson, Anti-de Sitter quotients: when are they black holes?:
The BTZ black holes were originally defined (in 2+1 dimensions) as quotients of open sets in anti-de Sitter space by some discrete isometries. Looking through the list of possible 3+1 spacetimes that can be obtained in this way, one sees that the original definition is not quite right. It is easily corrected though, and it will then be seen that some of the BTZ black holes are geodesically complete black hole spactimes. If time allows I will end with some remarks on 3+1 dimensional "bubbles of nothing".

P Tod, Extending the conformal metric through cosmological singularities :
According to Penrose's Weyl Tensor Hypothesis, initial singularities in GR are distinguished from final singularities in having finite or zero Weyl tensor. It is possible to produce many cosmological models with finite Weyl tensor curvature singularities by posing an initial value problem for the rescaled, unphysical metric with data at the singularity. Here we consider the converse problem: what conditions on the Weyl tensor imply the possibility of extending a rescaled metric through a cosmological singularity? Based on arXiv:0710.5552.

M Bradley, Slowly Rotating Fluid Balls of Petrov Type D :
The second order perturbative field equations for slowly and rigidly rotating perfect fluid balls of Petrov type D  are solved numerically. It is found that all the slowly and rigidly rotating perfect fluid balls up to second order, irrespective of Petrov type, may be matched to a possibly non-asymptotically flat stationary axisymmetric vacuum exterior. A subspace of the parameter space  is identified for which the solutions can be matched to an asymptotically flat exterior vacuum region.  The physical properties like equations of state, shapes and speeds of sound are determined for a number of solutions.

A García-Parrado, Killing spinor initial data sets :
A 3+1 decomposition of the twistor and valence-2 Killing spinor equation is made using the space spinor formalism. Conditions on initial data sets for the Einstein vacuum equations are given so that their developments contain solutions to the twistor and/or Killing equations. These lead to the notions of twistor and Killing spinor initial data. These notions are used to obtain a characterisation of initial data sets whose development are of Petrov type N or D.

N Pidokrajt, Thermodynamics of Dilaton Black Holes through Ruppeiner geometry :
In this talk I present the latest results from our ongoing work on thermodynamic (Ruppeiner) geometry of dilaton black holes (DBHs) in 4D. We investigate the Ruppeiner geometry of the DBHs in both Einstein and string frames and obtain some new results on the state space structure and perhaps some new insight into the extremality properties of these DBHs. At the end I will report results from the Ruppeiner approach to DBHs in 2D which are consistent with the existing ones in the literature upon dimensional reduction.



Göran Bergqvist  (gober_at_mai.liu.se)
Brian Edgar (bredg_at_mai.liu.se)