Author(s)

Jan Helm

Technical University of Berlin, Berlin, Germany.

The Tolman-Oppenheimer-Volkov (TOV) equation is solved with a new ansatz: the external boundary condition with mass M₀ and radius R₁ is dual to the internal boundary condition with density ρ_bc and inner radius r_i, and the two boundary conditions yield the same result. The inner boundary condition is imposed with a density ρ_bc and an inner radius r_i, which is zero for the compact neutron stars, but non-zero for the shell-stars: stellar shell-star and galactic (supermassive) shell-star. Parametric solutions are calculated for neutron stars, stellar shell-stars, and galactic shell-stars. From the results, an M-R-relation and mass limits for these star models can be extracted. A new method is found for solving the Einstein equations for Kerr space-time with matter (extended Kerr space-time), i.e. rotating matter distribution in its own gravitational field. Then numerical solutions are calculated for several astrophysical models: white dwarf, neutron star, stellar shell-star, and galactic shell-star. The results are that shell-star star models closely resemble the behaviour of abstract black holes, including the Bekenstein-Hawking entropy, but have finite redshifts and escape velocity v < c and no singularity.

General Relativity, Tolman-Oppenheimer-Volkov Equation, Neutron Stars, Shell Stars

Helm, J. (2022) New Solutions of Tolman-Oppenheimer-Volkov-Equation and of Kerr Spacetime with Matter and the Corresponding Star Models. Journal of High Energy Physics, Gravitation and Cosmology, 8, 724-767. doi: 10.4236/jhepgc.2022.83052.