Exact Results in Quantum Theory & Gravity

In our talk, we systematically investigate axisymmetric extremal isolated horizons (EIHs)defined by vanishing surface gravity. In the first part of our talk, using the Newman-Penrose formalism, we derive the most general metric function for such EIHs in the Einstein-Maxwell theory, which extends the previous result of Lewandowski and Pawlowski. We prove that it depends on 5 independent parameters, namely deficit angles on thenorth and south poles of a spherical-like section of the horizon, its radius (area), and total electric and magnetic charges of the black hole. In the second part of our talk, we identify this general axially symmetric solution for EIH with extremal horizons in exact electrovacuum Plebański-Demiański spacetimes, using the convenient parametrization of this family by Griffiths and Podolský. They represent all (double aligned) black holes of algebraic type D without a cosmological constant. Apart from a conicity, they depend on 6 physical parameters (mass, Kerr-like rotation, NUT parameter, acceleration, electric and magnetic charges) constrained by the extremality condition. We were able to determine their relation to the EIH geometrical parameters in full generality as well as in several interesting subclasses, such as accelerating extremely charged Reissner-Nordström black hole (C-metric) or extremal accelerating Kerr-Newman etc. ZoomMeeting ID: 861 0663 2208 Passcode: 673023