408
DOC.
400 NOVEMBER
1917
more
convenient in
the
calculation. In
any event,
this matter
is
worth
publication,
especially
if
you
work
out
a
special
case
according
to
your
method,
that
of
a
point
of
mass,
for
ex.
We
do not have to be
surprised
at
the
fact
that
the
curvature does not
neces
sarily
become infinitesimal with
the
vanishing
of the matter’s
energy components,
as long as no
boundary
conditions have been
set.
It
is
analogous
for
Newton;
as
long as
the
behavior
of
p
at
oo
has
not
been laid
down, p
#
0 is
possible,
even
if
throughout
finitude
Ap
=
0.
(As
a
solution
we
have
p
=
xy,
for
ex.).
It
is just
this
situation
which forces
me
to consider
boundary
conditions,
if
I
do not
want
to
admit
a
disturbing
ambiguity.[2]
2)
The second
term
k
(Tuv

1/2guvT)
on
the
righthand
side of
the
field
equa
tion
is
necessary
so
that,
through
the
field
equations,
the
energymomentum
law
(equation
(56)
in
the
booklet)[3]
r^
+
r;)_Q
"
dxa
applies.
A
result
in
agreement
with
this
is
obtained from
Hamilton’s
principle,
whereby
one
is
led
directly
to
the form
of
the
field
equations
where
kTuv appears
by
itself
on
the
righthand
side.
You will
draw this from
the
paper
I
am
sending
you by
the
same post.[4]
3)
In
the
equations
G/Ll/
A
g¡xv
=
k
(Tuv
1/2guvT)
under
no
condition
is
A
taken to be constant
so
that
a
solution
in which
p
is
constant
can
exist. If
A
were an
invariant function of
the
coordinates,
it would
need
another additional
differential
equation
that
A
would have
to
satisfy as
a
function of
x1
...
x4.
The gravitational field
would then be described
by
the
guv's
and
A.
So
if
one
wants to
maintain
that the
guv
quantities
alone
determine the
gravitational
field,
then
A
must
be
a
universal
constant.
It
is
correct
that the
periodicity
conditions
(condition
of spatial
closure)
take
the
place
of
the
boundary
conditions
at
infinity.
What
speaks
for
the
former
and
against
the latter
possibility
is
the
fact that
boundary
conditions
satisfying
the
postulate of
relativity
cannot
be postulated
for
infinity.
On
the other
hand,
the
closure condition is
relative. Added to this
is
the
physical
argument
elucidated
already by Seeliger,
which
is
also
presented
in
my
Acad.
paper
of
8 February
1917.[5]
4)
The
goal
of
unifying
gravitation
and
electromagnetism
by
tracing
both
groups
of
phenomena
back to
the
guv's
has
already
cost
me
much
frustrated
effort.
Maybe