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 ${\mathit{h}}_{\mathit{j}\mathit{k}}^{\mathrm{TT}}$. 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 ${\mathrm{\tau }}_{\mathrm{bwm}}$ 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.