🚀 go-pugleaf

In article <1992Oct1.020651.10696@nuscc.nus.sg> matmcinn@nuscc.nus.sg (Mcinnes B T (Dr)) writes:
>[...]
>I hope that the eventual entry will discuss what happens when the
>gravitational waves are propagating in a background which is not
>approximately flat. Does "gravity" propagate at the speed of light near
>a black hole?

For a partial answer, see chapter 35.13 of Misner, Thorne, and Wheeler,
``The Shortwave Approximation.''  To answer this question, you need to
assume that
(1)  the amplitude of the gravitational wave is small; and
(2)  the wavelength of the gravitational wave is short compared to the
     radius of curvature of the background.
Without assumptions like these, the nonlinearities make things too hard
--- you'll have a hard time defining the ``wave'' as something distinct
from the ``background.''  With these assumptions, the answer is basically
that a gravitational wave moves at the local speed of light, as set by
the background spacetime, but with slightly different interactions with
the background geometry (rotation of the polarization, backscatter from
background curvature).  (See exercize 35.15 for ``geometric optics''
for gravitational waves.)

Steve Carlip
carlip@dirac.ucdavis.edu