Christodoulou's nonlinear gravitationalwave memory: Evaluation in the quadrupole approximation
Abstract
Christodoulou has found a new nonlinear contribution to the net change in the wave form caused by the passage of a burst of gravity waves (``memory of the burst''). We argue that this effect is nothing but the gravitational wave form generated by the stress energy in the burst itself. We derive an explicit formula for this effect in terms of a retardedtime integral of products of time derivatives of wavezone gravitational wave forms. The resulting effect corresponds in size to a correction 2.5 postNewtonian orders [O((Gm/rc^{2})^{5/2}) =(O(v/c)^{5})] beyond the quadrupole approximation, and is therefore negligible for all but the most relativistic of systems. For gravitational bremsstrahlung from two stars moving at 300 km s^{1}, the effect is much less than 10^{10} of the usual linear quadrupole wave form, while for a system of coalescing binary compact objects we estimate that the effect is of order 10^{1} for two neutron stars.
 Publication:

Physical Review D
 Pub Date:
 November 1991
 DOI:
 10.1103/PhysRevD.44.R2945
 Bibcode:
 1991PhRvD..44.2945W