15 June 2021

Current trends in gravitation Seminar

Location: University Oldenburg - Online
When: 15.6.2021, 16:15 h

Speaker: Raul Vera (University of the  Basque Country, Bilbao, Spain)

Title: Existence and uniqueness of rigidly rotating stars in GR in second order perturbation theory

Abstract:

Static and spherically symmetric perfect fluid stars in General Relativity (GR) are known to (exist and) be unique given an equation of state satisfying some mild conditions and the value of the central pressure (Rendall & Schmidt 1991). However, much less is known in the rotating case, for which we do not even have a single explicit solution describing a rotating finite object with its corresponding asymptotically flat exterior. In the rotating case we only have results on existence of solutions sufficiently close to Newtonian configurations (Heilig 1995, Makino 2017). On the other hand, of course, the problem has been very succesfully tackled resorting to numerical integration and perturbation methods. The most widely used perturbation framework is the Hartle-Thorne model, which describes slowly rigidly rotating stars in the strong field regime by using perturbation theory up to second order, under a number of explicit and implicit assumptions. Amongst the explicit, equatorial symmetry is assumed, as well as that the perturbation parameter is the angular velocity. And implictly, in particular, the way the perturbed matching is performed, which was dealt with in (Reina, Vera 2015), and the structure and regularity of the perturbation tensors.

In this talk I present the two works in collaboration with Mars and Reina where slowly, rigidly rotating fluid balls are analyzed consistently in second order perturbation theory by imposing only basic differentiability requirements. We prove in particular that, at this level of approximation, the spacetime must be equatorially symmetric and is fully determined by two parameters, namely the central pressure and the rotation of the fluid.