Exact solutions based on Segre classification in the f(R) modified theory of gravity

Abstract

In this article, the Segre classification approach is used to obtain some new solutions for spherically symmetric static spacetime metric corresponding to Segre types [(1, 111)], [1, (111)], [(1, 1)(11)], or [1, 1(11)]. The eigenvalue degeneracy in these situations correlates to timelike and spacelike eigenvectors and their primary null direction, which identify the kind of matter distribution in space and aid in the consideration of novel solutions for the corresponding energy momentum tensor. The isotropic Segre type [(1, 111)] in modified theory provides the Schwarzschild de-Sitter/anti-de-Sitter solutions, whereas in types [1, (111)] and [1, 1(11)] depending upon matter distribution new obtained solutions adhere all the physical conditions and present the viable trends of energy and causality conditions. Moreover, the profiles of the adiabatic index, surface, and gravitational redshift are observed along with the hydrostatic equilibrium using the Tolman–Oppenheimer–Volkoff equation. Additionally, for these types the solution is compared with observational data, and numerical values are calculated for central and surface densities and central pressure of compact star candidates KS1731-260\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$KS 1731-260$$\\end{document} and PSRJ1614-2230\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$PSR J1614-2230$$\\end{document}. Segre type [(1, 1)(11)] relates to a non-null electromagnetic field that corresponds to models with anisotropy in dark energy, which is demonstrated by graphical analysis. Dark energy does not behave as an ordinary matter resulting in the violation of strong energy condition and the causality condition.