Anisotropic generalization of isotropic models via hypergeometric equation

Abstract

We study Einstein's field equations to describe static spherically symmetric relativistic compact objects with anisotropic matter distribution, and generate two classes of exact solutions by choosing a generalized form for one of the gravitational potentials and a particular form for the measure of anisotropy. This is achieved by transforming the Einstein's field equation to a hypergeometric equation. The generated models generalize the isotropic models of Durgapal-Bannerji, Tikekar and Vaidya-Tikekar. The physical viability of the model is examined and compared with observational results of strange star candidates.

Electromagnetic and anisotropic extension of a plethora of well-known solutions describing relativistic compact objects

“…R 2 ), and A 2 , B 2 are constants. The solution (31) was the second class of solutions obtained by Nasheeha et al (2020). Note that our solution (31) corrects a minor misprint in the result obtained by (Nasheeha et al 2020).…”

“…where a and b are nonzero arbitrary constants and R is the boundary of the star. A similar form of the metric potential was earlier used by Nasheeha et al (2020) for the modelling of a neutron star and also by Komathiraj and Sharma (2018) for a superdense charged star. For particular choices of the parameters a and b, it is possible to identify the metric ansatz with the following solutions: (i) charged stellar model of for b = 1; (ii) stellar model of developed by Maharaj and Leach (1996) for b = 1; (iii) superdense stellar model developed by Tikekar (1990) for a = −7, b = 1; (iv) Vaidya and Tikekar superdense stellar model (Vaidya and Tikekar 1982) for a = −2, b = 1 and (v) Durgapal and Bannerji neutron star model (Durgapal and Bannerji 1983) for a = 1, b = 1/2.…”

“…R 2 ), and A 1 , B 1 are constants. The solution (30) was the first of its class solutions found by Nasheeha et al (2020). The exact solution (30) has been comprehensively studied (Nasheeha et al 2020) and it has been shown the solution corresponds to an uncharged and anisotropic fluid sphere satisfying all the necessary conditions of a physically acceptable stellar model.…”

Non-Riemannian gravity actions from double field theory

“…It was not until recently that successful attempts have been made [2,8,9] for certain classes and limits of non-relativistic geometries. Importance of understanding dynamics of non-Riemannian gravity is underpinned by the far-reaching possibilities this entails: theories based on Galilean symmetry play a role on truncations of string theory [10][11][12], post-Newtonian physics [13][14][15][16], and provide a natural setting to study response in condensed matter systems with Galilean symmetry [17][18][19][20]. Carrollian symmetry, on the other hand, is relevant to description of excitations in the near horizon geometry of black holes [21][22][23], and is instrumental in flat space holography [24,25].…”

Linear and Riccati equations in generating functions for stellar models in general relativity

“…The differential equations for y and u are linear. Eq (46) has been used in [56], [57], [58], [59], [60], [61], [62], [63], [64], [65], [66]. It is well-known that the Newtonian polytropes satisfy the non-linear Lane-Emden equation for perfect or anisotropic fluids [67].…”