Warped Entanglement Entropy

We study the applicability of the covariant holographic entanglement entropy proposal to asymptotically warped AdS$_3$ spacetimes with an SL(2,R) x U(1) isometry. We begin by applying the proposal to locally AdS$_3$ backgrounds which are written as a real-line fibration over AdS$_2$. We then perturb away from this geometry by considering a warping parameter $a=1+\delta$ to get an asymptotically warped AdS$_3$ spacetime and compute the dual entanglement entropy perturbatively in $\delta$. We find that for large separation in the fiber coordinate, the entanglement entropy can be computed to all orders in $\delta$ and takes the universal form appropriate for two-dimensional CFTs. The warping-dependent central charge thus identified exactly agrees with previous calculations in the literature. Performing the same perturbative calculations for the warped BTZ black hole again gives universal two-dimensional CFT answers, with the left-moving and right-moving temperatures appearing appropriately in the result.