Isolated horizons in numerical relativity

by 1974- Krishnan, Badri

iii The isolated horizon framework is applied to numerical relativity. This framework describes black holes which are in equilibrium in a spacetime which is otherwise fully dynamical. We introduce isolated horizons in a way which is directly applicable in numerical evolutions. In particular, we present and numerically implement a coordinate invariant method for calculating the mass and angular momentum of isolated horizons. We also show how isolated horizons can be used to study the local geometry of a black hole and extract invariant gravitational waveforms. We apply some results from the isolated horizon framework to calculate the binding energy between two black holes. This will be useful in comparing different initial data sets which represent similar physical situations. Finally, we also present a method for studying the physics of dynamical black holes. In particular, we derive balance laws relating the flux of matter fields/radiation with the change in the physical parameters of the black hole such as angular momentum and mass.