Abstract
The gravitational radiation produced by systems which collapse from a very large initial size (R/sub i/) is investigated. A general expression is derived for the energy spectrum at low frequencies, and is applied to various astrophysical situations. The expression is valid for frequencies ..omega../sub i/ very-much-less-than ..omega.. very-much-less-than ..omega../sub asterisk/, where ..omega../sub i/ = (GMR/sub i//sup -3/)/sup 1/2/ and ..omega../sub asterisk/ is the characteristic frequency of the compact phase (size R/sub asterisk/ very-much-less-than R/sub i/). For instance, for any two-body system whose final state is coalesced and arbitrarily relativistic, d/sup 2/E/d..omega..d..cap omega.. = 6/sup -4/3/..pi../sup -2/ x (GAMMA (1/3) ..mu..)/sup 2/sin/sup 4/THETA (M..omega..)/sup 4/3/, where ..mu.. is their reduced mass, M is their total mass, and THETA is the angle measured from the direction of their initial separation vector. Results for rotating collapsing stars are also obtained.
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