Starobinsky gravitasyon modelinde relativistik yıldızlar

The strong gravity regime of neutron stars provide a good opportunity to test general relativity and constrain modified models of gravity. In this thesis the hydrostatic equilibrium of neutron stars in Starobinsky model of gravity is studied. The field equations and hydrostatic equilibrium equations are obtained for a spherically symmetric metric in the Starobinsky model. The trace of the field equations contains second order derivative of Ricci scalar and poses a singular perturbation problem. Accordingly, the matched asymptotic expansion (MAE) method is used to solve the set of differential equations for the Ricci scalar, mass within radial coordinate and pressure distribution for a uniform density object. It is found that the solution for the Ricci scalar can not match the Schwarzchild solution at the surface. This leads to the conclusion that uniform density neutron star solutions matching the Schwarzschild solution do not exist in the Starobinsky model of gravity. This does not exclude the possible existence of solutions that match an appropriate vacuum solution in this gravity model.