Numerical Simulations of Black-Hole Spacetimes

Citation

Chu, Tony (2012) Numerical Simulations of Black-Hole Spacetimes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/MKD2-1N95. https://resolver.caltech.edu/CaltechTHESIS:07292011-012517485

Abstract

This thesis covers various aspects of the numerical simulation of black-hole spacetimes according to Einstein's general theory of relativity, using the Spectral Einstein Code developed by the Caltech-Cornell-CITA collaboration. The first topic is improvement of binary-black-hole initial data. One such issue is the construction of binary-black-hole initial data with nearly extremal spins that remain nearly constant during the initial relaxation in an evolution. Another concern is the inclusion of physically realistic tidal deformations of the black holes to reduce the high-frequency components of the spurious gravitational radiation content, and represents a first step in incorporating post-Newtonian results in constraint-satisfying initial data. The next topic is the evolution of black-hole binaries and the gravitational waves they emit. The first spectral simulation of two inspiralling black holes through merger and ringdown is presented, in which the black holes are nonspinning and have equal masses. This work is extended to perform the first spectral simulations of two inspiralling black holes with moderate spins and equal masses, including the merger and ringdown. Two configurations are considered, in which both spins are either anti-aligned or aligned with the orbital angular momentum. Highly accurate gravitational waveforms are computed for all these cases, and are used to calibrate waveforms in the effective-one-body model. The final topic is the behavior of quasilocal black-hole horizons in highly dynamical situations. Simulations of a rotating black hole that is distorted by a pulse of ingoing gravitational radiation are performed. Multiple marginally outer trapped surfaces are seen to appear and annihilate with each other during the evolution, and the world tubes they trace out are all dynamical horizons. The dynamical horizon and angular momentum flux laws are evaluated in this context, and the dynamical horizons are contrasted with the event horizon. The formation of multiple marginally outer trapped surfaces in the Vaidya spacetime is also treated.

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