DOC. 2 COVARIANCE PROPERTIES
7
accelerated three-dimensional coordinate system-can be viewed
as a
"real"
gravitational
field;
in other
words,
if acceleration-transformations
(i.e.,
nonlinear
transformations)
become
permissible
transformations
in
the
theory.
At first
glance
it
appears
desirable
to
look for
gravitational equations
that
are
covariant toward
arbitrary
transformations.
However,
in
§2
of the
present
paper2 we
will
show
by a simple
consideration that the
quantities
guv
which characterize the
gravitational
field cannot
completely
be
determined
by generally-covariant equations.
In
the
following
we
shall demonstrate
that
the
gravitational equations
established
by us are
generally
covariant
just
to
the
degree imaginable
under the condition that
the
fundamental
tensor
guv
must be
completely
determined.
It
follows
in particular
that the
gravitational
equations
are
covariant with
respect
to
quite
varied
accelera-
tion
transformations (i.e.,
nonlinear
transformations).
[5]
§1.
The Basic
Equations of the
Theory
We characterized the
energetic response
of
a
physical process by means
of
a
covariant tensor
Tuv
or
its
reciprocal
contravariant tensor
©uv,
respectively.
This
tensor satisfies
equations (10)
of the
"Outline," viz.,
[6]
or respectively
.9

___
4uv
`Lv,
_
I
c~z
4uv/
S
a
dx~
go
_
I-
/4
2
Ftp
09pv
die0
S,sv,
and
they represent
the
energy-momentum equations
of the material
process.
All [p.
217]
equations
of the
theory
take
a particularly comprehensive
form
if
one
introduces the
quantities
(1)
Lav=-gyauTuv=-ggauQuv,4"
which differ from the
components
of
a
mixed
tensor3
only by
a
factor of \pg.
Conceptually
we
call them the
complex
of
energy-density
of
the
physical process.
Our
equations
above
can now
be rewritten
as
2Compare
also the remark in the
appendix
of
the
reprint
in Zeitschr.
f.
Math.
u. Phys., [4]
vol. 62.
3Compare
§1
of
part
II
of
the "Outline."
[7]
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