Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schwarzschild Solution of the Generally Covariant Quaternionic Field
  Equations of Sachs   Sachs has derived quaternion field equations that fully exploit the
underlying symmetry of the principle of general relativity, one in which the
fundamental 10 component metric field is replaced by a 16 component four-vector
quaternion. Instead of the 10 field equations of Einstein's tensor formulation,
these equations are 16 in number corresponding to the 16 analytic parametric
functions {\partial}x^{{\mu}'}/{\partial}x^{{\nu}} of the Einstein Lie Group.
The difference from the Einstein equations is that these equations are not
covariant with respect to reflections in space-time, as a consequence of their
underlying quaternionic structure. These equations can be combined into a part
that is even and a part that is odd with respect to spatial or temporal
reflections. This paper constructs a four-vector quaternion solution of the
quaternionic field equation of Sachs that corresponds to a spherically
symmetric static metric. We show that the equations for this four-vector
quaternion corresponding to a vacuum solution lead to differential equations
that are identical to the corresponding Schwarzschild equations for the metric
tensor components.

9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics