Einstein's field equations in empty space i.e. R_ik = 0
agree with observations.
Can we say the same for the equations in the
presence of matter i.e. G_ik = 8 pi T_ik ?
Do you know some astrophysical (= not
cosmological) test supporting them ?
Thanks in advance.
---------------------------------
[[Mod. note -- Good places to look might include tests of Newtonian
gravitation (= the slow-motion weak-field limit of Einstein's equations)
and observations of binary pulsar systems (where non-Einstein theories
of relativistic gravity often have extra dynamical effects due to the
individual neutron stars' strong internal gravitational fields).
Some good references include:
@incollection
{
Damouor-1987-in-300-years-of-gravitation,
author = "Thibault Damour",
title = "The problem of motion in Newtonian and Einsteinian gravity",
pages = "128--198",
editor = "Stephen W. Hawking and Werner Israel",
booktitle = "Three Hundred Years of Gravitation",
publisher = "Cambridge University Press",
address = "Cambridge (UK)",
year = 1987,
isbn = "0-521-34312-7",
snote = "++good discussion of how to go from Einstein eqns
to N-body equations of motion; the effacement of the
internal structure of a freely falling subsystem",
}
Kramer et al
"Tests of General Relativity from Timing the Double Pulsar"
Science 6 October 2006:
Vol. 314 no. 5796 pp. 97-102
DOI: 10.1126/science.1132305
http://www.sciencemag.org/content/314/5796/97.short
preprint: arXiv:astro-ph/0609417
Stairs
"Testing General Relativity with Pulsar Timing"
Living Reviews in Relativity volume 6 (2003), 5
http://relativity.livingreviews.org/Articles/lrr-2003-5/
-- jt]]