Generalized geodesic deviation equations and an entanglement first law for rotating BTZ black holes

Understand

The change in Holographic entanglement entropy (HEE) for small fluctuations about pure AdS is given by a perturbative expansion of the area functional in terms of the change in the bulk metric and the embedded extremal surface.

• However it is known that change in the embedding appear at second order or higher.
• In this paper we show that these changes in the embedding can be systematically calculated in the 2+1 dimensional case by accounting for the deviation of the spacelike geodesics between a spacetime and perturbations over it.
• Here we consider rotating BTZ as perturbation over $AdS_3$ and study deviations of spacelike geodesics in them.