Anthony Réveillac (INSA Toulouse)
Oliver Lindblad Petersen
Any closed Riemannian manifold which has vanishing scalar curvature is a solution to the relativistic vacuum constraint equations. Examples include the flat torus and certain Berger spheres. If the Ricci curvature is zero, the solutions are given by the so called TT-tensors. In the first part of the talk I will generalize this result to the case where the Ricci curvature does not necessarily vanish everywhere.
In the second part of the talk I will show that there are solutions to the linearised Einstein equations (that are not gauge solutions) that are arbitrarily irregular. The example is given on a generalised Kasner spacetime with spatially compact or non-compact topology.