DOC.
398
NOVEMBER
1917 405
=
1
9
J29aß(f^f*ß
~
fv*Uß).
aß
If
furthermore
one
forms
Bao
=
TgaTBTa
then
Bko
=

£9aß9yk{UßU,

fc«fße),
and
9
aßy
B
=
Y.Bt
=

E
gaßg9\faßfyö

UM
k
9
aßyö
result. Thus
the
mixed
energy
tensor of matter
according
to
the
field
equations
of
1916[4]
becomes
n
=

e
9aß97i(f*ßfyk

um
gaßgiS(UßUs

um
•
K9
[aßy
2
aß7S
Example 2:
Arbitrary
class.
s1 =
x1,
s2
+
x2;
dgik/dx1
=
dgik/dx2
=
0:
(Special
class of twodimensional
static
or
onedimensional
dynamic
fields.)
The above
portrayal
shows
immediately
that
all
Bik's
except
for
B33, B34,
B44
vanish. The
line element becomes
ds2
=
dx\
+
dx
2
+ edu2 +
2
ƒ
dudv
+
gdv2
B33
:
B34
:
B44
:
1
=
e
:
ƒ
:
g+
: 1/k,
where k
is
the Gauss curvature of
the
line
element edu2 +
2f
dudv +
gdv2.
Furthermore,
B33
=
B44
=
k;
B34
=
0.
But
unfortunately
Tao
=
0
for all the indices.
2)
Hence
the
space
can
be curved
even
without
the
presence
of matter! Some
thing is
evidently wrong
here. For from
Toa
=
0,
although
not
ds2,
the
curvature
ought
to be
established,
if I
have
understood
the matter
correctly.
At
the
same
time,
I
venture
to
request being
informed
about
how
the second term
on
the
righthand
side of
your
field
equations k(Tuv

1/2
guv
.
T)
is
justified.
3)
Regarding
your
field
equations
of
1917
(February
8):[5]
Guv 
Aguv =
k(Tuv

1/2
guv
.
T). (a)
Surely you
assume
A
as
the
universal constant
only
because
p
is
supposed
to be constant?
(b)
You have
disposed
of
the
boundary
conditions
at
infinity,
but
in
exchange
the
periodicity
conditions result.
4)
Re
your
gravitational
wave
theory.[6]
One
still tends to
say
gravitation is
propagated
with the
velocity
of
light.
Atomic
physicists
still
tend
to
attribute