Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An exact solution of the orbit equation for a massive particle in
  Schwarzschild metric   In this paper, we consider a spherically curved symmetric spacetime to exact
solving the orbit equation of a massive particle by using Jacobi's elliptic
functions. Generally, the solution of the orbit equation provides the
relativistic effects on the massive particle, absents in Newtonian mechanics.
Besides, we investigate the additional physical information introduced by the
exact solution to the orbit equation that is not visible in the approximate
solutions traditionally presented in literature. Here, we exactly solve the
problem by the use an analytical methodology step by step in order to provide
detailed solutions as well as demonstrate with mathematical rigour the geodesic
solution in terms of Jacobi's elliptic functions. We find oscillatory movements
of the orbit of the massive particle at the expected regimes without to
consider any heuristic argument. Bound regions to the solution of the equation
of motion is presented, finding the aspect of the geodesic when the massive
particle is trapped in the gravitational field of the source.

37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys