DOC.
420
DECEMBER
1917
429
Audxp
+
[ S/ju,
+
-^
ßA
+
rflI/\sAT)dxp6x’'+
. ï
&A
ß
i
pft
^A-h
pft
dAh
h
dA"
\ji
iß
+
IV*
+
dvda I“
in'
11.1,
da
^
T
^
^
(Iff
du
ft
r
1
(T.. dxh
dT!*
+Ah P1*
Qg.
i
'
pr
1
p/i
/xcr1
,
rv
pr
'
p,
1
gvl
\it
Î.ÏÏ
dx'1
b\xvbixa
+
.
.
.
Addendum
to
(2a):
If
one
sets
guvdAa/dv
+
gav.dAa/du
+
Aadguv/da =
0,
then
dguv/dx
=
0
results
as
above
(with
the
special
coordinate
choice Aa
=
0, 0, 0,
1).
If
a
four
potential is
introduced:
pa
= gBaAB =
g4a,
then the
electromagnet.
six
tensor becomes:
Fia
=
- -
a
(¿,
i
a A
4);
Fl0l
-
-
-.
2
i
a = Fdgws
#
4).
Here it
is
advisable
to
limit oneself
to
the
symmetric
tensor suv.
Then
2 a
=
Fai
also
results; furthermore, 2
i
=
Fi4
=
-Fa
(i
#
4).
In
the
gravitational
energy
tensor[6]
tuo
(or
rather
in its
part)
-suvTauBTBva,
terms
then
appear:
-1/4
s44EßepsaEFße.sßpFap that
suspiciously
resemble
the
Maxwell
tensor.
Other
terms also
appear,
however:
-1/2Eveßs4v{vaB}saeFeB
that
must
correspond to
a
reciprocal
energy
of
matter and
electricity.
If,
for
instance,
one now
attempts to
develop
Schwarzschild’s
solution[7]
g11 =
f1(x1);
g22 =
-
{-rij-;
g33 =
-/2(x1)
•
(1
-
^);
g44
=
h(x1)\
fxflf4
= 1
on
this
point
a
bit further
along
his
lines,
then
A1
=
A2
=
A3
=
0;
da4/dx4
=
0
results;
thus
pa =
(0, 0, 0, f4
.
A4); F12
=
F23
=
F13
=
F24
=
F34
= 0;
F14
=
-dp4/dx1,
and
the
entire
fine
correlation
is
lost because
f4
merges completely
with
A4.
4)
Normal forms of
the
line element.
(a)
At
variance
with
spaces
with
low
num-
bers
of
dimensions,
in
general,
the
orthogonal
form
ds2
=
Eigii(dxi)2
cannot
be
obtained,
only
when
B12,34
=
B13,24
=
B14,23
=
0
(:2 equations:).
This
is
probably
known
to
some,
but
could be
emphasized
once.[8]
(b)
The
geodesic
form
that
can
be found in
the
old Bianchi:[9]
gi4
=
0,
g44 =
1.
(c)
“Light ray
coor-
dinates.” The
equation
gikdpdp/dxidxk
=
0
(giK =
gKi)
[:
in
the
case
of
the
special