Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equation of motion in a scalar model of gravity   A scalar model of gravity is considered. We propose Lorentz invariant field
equation $\square f = k\eta_{ab}f_{,a}f_{,b}$. The aim of this model is to get,
approximately, Newton's law of gravity. It is shown that $f=-\frac
1k\ln(1-k\frac mr)$ is the unique spherical symmetric static solution of the
field equation. $f$ is taken to be the field of a particle at the origin,
having the mass $m$. The field of a particle moving with a constant velocity is
taken to be the appropriate Lorentz transformation of $f$. The field $F$ of $N$
particles moving on trajectories ${\psi_j(t)}$ is taken to be, to first order,
the superposition of the fields of the particles, where the instantaneous
Lorentz transformation of the fields pertaining to the $j$-th particle is
${\dot\psi_j(t)}$. When this field is inserted to the field equation the
outcome is singular at $({\psi_j(t)},t)$. The singular terms of the l.h.s. and
of the r.h.s. are both $O(R^{-2})$. The only way to reduce the singularity in
the field equation is by postulating Newton's law of force. It is hoped that
this model will be generalized to system of equations that are covariant under
general diffeomorphism.

17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess