346 DOC.
71
PRINCETON LECTURES
THE GENERAL THEORY
tem. If,
as
in the
special
theory
of
relativity,
we
take the
fourth
co-ordinate
imaginary,
this
means
that
we
must
put
(98)
guv
=
-guv
+
yuv
in which the
Yuv
are so
small
compared to
1
that
we can
neglect
the
higher
powers
of the
Yuv
and their derivatives.
If
we
do
this,
we
learn
nothing
about the
structure
of
the
gravitational field,
or
of
metrical
space
of cosmical
dimen-
sions,
but
we
do
learn about the
influence of
neighbouring
masses
upon physical
phenomena.
[104]
Before
carrying through
this
approximation
we
shall
transform
(96).
We
multiply (96)
by
guv,
summed
over
the
u
and
v;
observing
the relation which
follows
from the
definition
of
the
guv,
guvguv
=
4
we
obtain the
equation
R
= kguvTuv =
kT.
If
we
put
this value
of R in
(96)
we
obtain
(96a)
Ruv
=
-k(Tuv
-
1/2guvT)
=
-kT*uv.
When the
approximation
which
has been
mentioned
is
carried
out,
we
obtain
for
the left-hand
side,
or
swar
a4q63v q35 32523
24rwqw3
stzrw
314ZSDFGWE35V W3423
36236
in which
has
been
put
(99)
y'uv
=
yuv
-
1/2yooguv.
[86]