Williams. Curved space (CERN lectures)(T)(50s).djvu: eKnigu

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Williams. Curved space (CERN lectures)(T)(50s).djvu

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Date Jul 4, 2004

The speed of light determined by them is still a limiting speed, so the light-
cones and associated particle paths and light-rays still determine what parts of the
space-time can influence the other parts...
Asymptotic behaviour
For very large r, 2m/r becomes negligible, and we obtain
ds2 ~ -dt2 + dr2 + r2(dd2 + sin2 0 d<j>2) ,
the flat-space metric in spherical polars...
Applicability of the Schwarzschild solution
According to BirkhofTs theorem, the Schwarzschild solution represents the
gravitational field of any spherically symmetric star, not only if it is static but also
if it is collapsing, expanding, or pulsating...
For large r, they behave as though space were flat,
but as r decreases, they tilt over towards the spatial origin; they are parallel to the
t-axis for r = 2m and approach v = const as r decreases to zero...
Note that the speed at which the surface of the star crosses the
horizon is not necessarily large (and is certainly less than c) so the infinite red-shift is
purely a gravitational effect...
IV.11 An observer at t = to can see matter
up to a radial coordinate value u by light emitted
at t — te
t=t...
OTHER UNIVERSE MODELS
In this final section, we consider some other models of the universe, which are
related to the FLRW models already described...
Finally, the apparent
homogeneity and isotropy of the universe are explained in the simplest possible way...