Surveys in Differential Geometry

Volume 20 (2015)

Gravitational waves and their memory in general relativity

Pages: 75 – 97



Lydia Bieri (Department of Mathematics, University of Michigan, Ann Arbor, Mich., U.S.A.)

David Garfinkle (Department of Physics, Oakland University, Rochester, Michigan, U.S.A.)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)


General relativity explains gravitational radiation from binary black hole or neutron star mergers, from core-collapse supernovae and even from the inflation period in cosmology. These waves exhibit a unique effect called memory or Christodoulou effect, which in a detector like LIGO or LISA shows as a permanent displacement of test masses and in radio telescopes like NANOGrav as a change in the frequency of pulsars’ pulses. It was shown that electromagnetic fields and neutrino radiation enlarge the memory. Recently it has been understood that the two types of memory addressed in the literature as ‘linear’ and ‘nonlinear’ are in fact two different phenomena. The former is due to fields that do not and the latter is due to fields that do reach null infinity.


gravitational radiation, Cauchy problem for Einstein equations, asymptotics, null-structure of spacetimes, isolated gravitating systems, stability, memory effect of gravitational waves, Christodoulou effect, gravitational wave experiments, Einstein equations and radiation in vacuum and coupled to other fields, corecollapse supernova, binary mergers

2010 Mathematics Subject Classification

35A01, 35L51, 35Q76, 83C05, 83C35

Published 7 July 2015