Gravitational-wave bursts with memory: the Christodoulou effect

The "memory" of a gravitational-wave burst is the permanent relative displacement that it imposes on free test masses, or more precisely, the permanent change in the burst's gravitational-wave field hjkTT. This memory, in general, is equal to the change, from before the burst to afterward, in the transverse-traceless (TT) part of the "1/r, Coulomb-type" gravitational field generated by the four-momenta of the source's various independent pieces. Christodoulou has recently identified a contribution to a burst's memory that arises from nonlinearities in the vacuum Einstein field equation. This paper shows that the Christodoulou memory is precisely the TT part of the "1/r, Coulomb-type" gravitational field produced by the burst's gravitons, and it therefore gets built up over the same length of time τbwm as it takes for the source to emit the gravitons. The sensitivity of broad-band gravitational-wave detectors such as LIGO to the Christodoulou memory is analyzed and discussed.