Statistics – Computation
Scientific paper
Aug 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000phdt.........7a&link_type=abstract
Thesis (PhD). THE UNIVERSITY OF UTAH, Source DAI-B 61/02, p. 889, Aug 2000, 92 pages.
Statistics
Computation
Scientific paper
This thesis presents a study of two kinds of sources of gravitational waves: black hole collisions and pulsating compact objects (either a black hole or a star) The computational solution of the Einstein field equations for the coalescence of two black holes is of great interest for both theoretical and astrophysical reasons. Despite the strong motivation for results, outstanding mathematical and numerical problems have prevented a complete analysis of two black hole systems. Workers in the field have resorted to approximate techniques that make the study of such systems tractable. In Chapter 2 we use the close limit approximation to compute the gravitational energy radiated, and the recoil velocity acquired, by a system of two unequal mass black holes colliding head-on. A recent independent comparison of our approximate result with a full numerical analysis of the problem shows excellent agreement. Until recently, vibrations even of relativistically compact stars were studied using Newtonian physics and the weak field limit of general relativity. The study of the problem in the framework of general relativity revealed the existence of modes of vibration (w modes) characteristic of the spacetime geometry and therefore modes not predicted by Newtonian physics. Chapter 3 addresses the question of whether these modes can be excited in a natural astrophysical process. A small particle with a given energy and angular momentum is scattered by a compact star or black hole and in the process excites, although weakly, the w modes. Chapter 4 compares the study of pulsating stars in a Newtonian framework and in a fully relativistic setting. To excite the vibrations of the stellar model we use time dependent surface mass density and surface stress in a thin spherical shell surrounding the star. Even for stars as compact as typical neutron stars (radius ~ 5G/ c2 × mass), the two theories predict essentially the same level of excitation of the f (fluid) modes of the star. The w modes are not excited for these stars. All of the chapters in this thesis, except the introductory chapter, have been published or have been submitted for publication.
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