Surface Stress Tensor and Junction Conditions on a Rotating Null Horizon

Understand

The general form of the surface stress tensor of an infinitesimally thin shell located on a rotating null horizon is derived, when different interior and exterior geometries are joined there.

• Although the induced metric on the surface must be the same approached from either side, the first derivatives of the metric need not be.
• Such discontinuities lead to a Dirac $\delta$-distribution in the Einstein tensor localized on the horizon.
• For a general stationary axisymmetric geometry the surface stress tensor can be expressed in terms of two geometric invariants that characterize the surface, namely the discontinuities $[\kappa]$ and $[\cal J]$ of the surface gravity $\kappa$ and angular momentum density $\cal J$.