Following from the seminal work of Dain, a great deal is now known concerning geometric inequalities relating the area, charge, and angular momentum of axisymmetric black hole horizons in (possibly dynamical) spacetimes. A key feature of these results is that they are quasi-local: they depend on spacetime only near the horizon itself and so are not sensitive to the asymptotic behaviour of the geometry.
For Einstein-Maxwell theory the celebrated uniqueness theorems tell us under certain conditions, that the Kerr-Newman (KN) family of solutions are the only stationary, axisymmetric and asymptotically flat black hole spacetimes. These are the model geometries that originally motivated the inequalities. However if we relax the condition of asymptotic flatness there are many other families of black hole solutions. While in general these will not contain event horizons (whose standard definitions require flat or AdS asymptotics) they still contain singularities and Killing horizons. In this paper we focussed Continue reading
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