Seminarium Teorii Względności i Grawitacji

In Einstein’s general relativity, extremely strong gravity can trap light. In a spacetime admitting a singularity, we say that light (or a“photon”) is trapped if it neither escapes to spatial infinity nor falls into the singularity. Null geodesics govern the trajectories oflight. In the Schwarzschild spacetime with positive mass M, there exist (unstable) circular orbits of trapped photons at theSchwarzschild radius r = 3M, outside the black hole horizon at r=2M. These orbits fill a three-dimensional submanifold of topologyS^2\times R called the photon sphere of the Schwarzschild spacetime. In general, a region in spacetime that is a union of all trapped nullgeodesics is called the Trapped Photon Region (TPR) of spacetime. In this talk, we will consider a particular stationary space-time classconstructed by the Newman-Jenis algorithm. We will see that, unlike the TPR of Schwarzschild spacetime, the TPR in such spacetimes is nota submanifold of the spacetime in general. However, the lift of TPR in the phase space is a five-dimensional submanifold. This result hasapplications in various problems in mathematical relativity (This work is an extension of a similar result but in sub-extremal Kerr spacetimeby Cederbaum and Jahns- 2019). This is a joint work with Carla Cederbaum.