A Tolman-like Compact Model with Conformal Geometry.

Area of Science:

• Astrophysics and General Relativity
• Theoretical Physics
• Compact Star Modeling

Background:

• Anisotropic pressure and electric fields are crucial in understanding compact stars.
• Conformal symmetry provides a pathway to simplify complex Einstein-Maxwell equations.
• Existing models often require numerical approximations; exact solutions are highly valuable.

Purpose of the Study:

• To develop a new analytical model for charged anisotropic compact stars.
• To derive exact solutions to the Einstein-Maxwell field equations under specific symmetry conditions.
• To verify the physical viability of the proposed model for realistic compact objects.

Main Methods:

• Utilizing a conformal symmetry assumption to establish a relationship between metric functions.
• Formulating a first-order differential equation incorporating pressure anisotropy and electric fields.
• Employing the Tolman VII metric and specific electric field forms to solve field equations.
• Generating new classes of exact solutions expressed via elementary functions.

Main Results:

• New classes of exact solutions for charged anisotropic compact stars were successfully derived.
• The model satisfies essential physical criteria, including causality, stability, and energy conditions.
• Generated numerical values for mass, radius, density, redshift, and compactness align with observed pulsars (e.g., PSR J1614-2230) and X-ray binaries (e.g., SMC X-1).

Conclusions:

• The proposed model provides a consistent and physically realistic framework for charged anisotropic compact stars.
• The derived exact solutions offer valuable analytical insights into the structure and behavior of these extreme celestial objects.
• This work contributes to the ongoing effort to accurately model and understand the properties of neutron stars and other compact objects.