Solution generating theorems for the Tolman-Oppenheimer-Volkov equation

The Tolman-Oppenheimer-Volkov (TOV) equation constrains the internal structure of general relativistic static perfect fluid spheres. We develop several "solution generating" theorems for the TOV equation, whereby any given solution can be deformed into a new solution. Because the theorems we develop work directly in terms of the physical observables-pressure profile and density profile-it is relatively easy to check the density and pressure profiles for physical reasonableness. This work complements our previous article [Phys. Rev. D 71, 124037 (2005)] wherein a similar algorithmic analysis of the general relativistic static perfect fluid sphere was presented in terms of the spacetime geometry-in the present analysis the pressure and density are primary and the spacetime geometry is secondary. In particular, our deformed solutions to the TOV equation are conveniently parametrized in terms of delta rho(c) and delta p(c), the finite shift in the central density and central pressure. We conclude by presenting a new physical and mathematical interpretation for the TOV equation-as an integrability condition on the density and pressure profiles.