Abstract
Abstract
A new approach to construct relativistic stellar models is presented. The problem is formulated as an optimal control problem, with an objective function to be optimized. As illustration, the problem is formulated and solved, with the rest mass as the objective function to be minimized, in three cases. First, if the density is piece-wise continuous the optimal solution is the spherical shell. Second, if the density gradient is piece-wise continuous the optimal solution has constant density. Third, if the speed of sound does not exceed that of light, the optimal solution has a linear equation of state. Thus, using this new approach, the equation of state is determined by a physical motivation. Results support the suggestion that the linear equation of state could represent a relativistic incompressible fluid. Extensions to some other configurations are explored.
Subject
Condensed Matter Physics,Mathematical Physics,Atomic and Molecular Physics, and Optics