Compact stars with non-uniform relativistic polytrope

Area of Science:

• Astrophysics
• General Relativity
• Stellar Structure

Background:

• Compact stars, such as neutron stars, require relativistic models due to strong gravitational fields.
• Polytropic equations of state are commonly used to approximate stellar matter, but relativistic composite models offer enhanced accuracy.

Purpose of the Study:

• To develop and analyze new relativistic composite polytropic models for compact stars.
• To simulate spherically symmetric, static matter distributions by solving Einstein field equations.
• To investigate the internal structure, mass, and radius of neutron star candidates.

Main Methods:

• Simultaneously solving Einstein field equations with a polytropic state equation.
• Deriving and numerically solving the composite Tolman-Oppenheimer-Volkoff (CTOV) equation.
• Computing Emden and mass functions for various relativistic parameters and polytropic indices.

Main Results:

• The models successfully simulate compact star structures, with relativistic parameters approaching zero recovering Newtonian polytropic models.
• Calculated core radii for neutron star candidates Cen X-3 and PSR J1614-22304 are 50-60% of their total radii.
• The core radius for SAXJ1808.4-3658 is found to be approximately 30% of its total radius, consistent with observations.

Conclusions:

• The composite relativistic polytrope model provides a robust approximation for neutron star structure.
• The developed models yield masses and radii consistent with observational data for compact stars.
• This work validates the computational code by comparing Newtonian and relativistic models.