Linear and Riccati equations in generating functions for stellar models in general relativity
arXiv:2004.00907 · doi:10.1140/epjp/s13360-020-00380-1
Abstract
It is shown that the expressions for the tangential pressure, the anisotropy factor and the radial pressure in the Einstein equations may serve as generating functions for stellar models. The latter can incorporate an equation of state when the expression for the energy density is also used. Other generating functions are based on the condition for the existence of conformal motion (conformal flatness in particular) and the Karmarkar condition for embedding class one metrics. In all these cases the equations are linear first order differential equations for one of the metric components and Riccati equations for the other. The latter may be always transformed into second order homogenous linear differential equations. These conclusions are illustrated by numerous particular examples from the study of stellar models.
accepted for publication in Eur. Phys. J. Plus
References in corpus (21)
- All static spherically symmetric anisotropic solutions of Einstein's equations
- A class of relativistic stars with a linear equation of state
- Anisotropic models for compact stars
- Generalized model for anisotropic compact stars
- Conformally flat polytropes for anisotropic matter
- Analytical study of anisotropic compact star models
- A family of well-behaved Karmarkar spacetime describing interior of relativistic stars
- The role of pressure anisotropy on the maximum mass of cold compact stars
- A new deterministic model of strange stars
- Possibility of higher dimensional anisotropic compact star
- Modified Finch and Skea stellar model compatible with observational data
- Exact power series solutions of the structure equations of the general relativistic isotropic fluid stars with linear barotropic and polytropic equations of state
- The Dark Energy Star and Stability analysis
- A class of solutions for anisotropic stars admitting conformal motion
- A generalized Finch-Skea class one static solution
- A comparative study between EGB gravity and GTR by modelling compact stars
- Compact stars with specific mass function
- Anisotropic static solutions in modelling highly compact bodies
- Anisotropic extension of Finch and Skea stellar model
- Revisiting Vaidya-Tikekar stellar model in the linear regime
- Analytical model of Strange star in Durgapal spacetime
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- Stability of the isotropic pressure condition
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- Integration of the Lane-Emden equation for relativistic anisotropic polytropes through Gravitational Decoupling: a novel approach
- Strange star with Krori-Barua potential in presence of anisotropy
- A new class of viable and exact solutions of EFE's with Karmarkar conditions: An application to cold star modeling
- New charged anisotropic solution on paraboloidal spacetime
- Arrow of time and gravitational entropy in collapse