The existence of neutron stars was suggested soon after the discovery of such particles, and it soon became clear that Newtonian physics was innapropriate to study such stars. The problem was initially addressed by Richard C. Tolman, whose results were used by J. Robert Oppenheimer and George M. Volkoff for the deduction of what is known as Tolman-Oppenheimer-Volkoff (TOV) equation. This equation represents the hydrostatic equilibrium of a sphere of perfect fluid in the relativistic regime and, when combined with a suitable equation of state, yields a mathematical model for neutron stars. This paper presents the deduction of the TOV equation in a detailed and didactic way, since the treatment of Einstein's equations of general relativity (GR) until the application to the case where the star is made up of a Fermi gas of degenerate neutrons, whence we can deduce that there is a maximum mass possible for such objects. Although today we know that the Fermi gas model is by itself unsuitable in this case, the analysis is interesting from the historic and didactic viewpoint, once it consists in a fairly simple example of application of an equation of state to the calculations of the structure of neutron stars.
Keywords
General Relativity; Neutron Stars; TOV Equation
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