A Comprehensive Analysis of Hyperbolical Fluids in Modified Gravity

Abstract

This paper is devoted to understanding a few characteristics of static irrotational matter content that assumes hyperbolical symmetry. For this purpose, we use metric f(R) gravity to carry out our analysis. It is noticed that the matter distribution cannot fill the region close to the center of symmetry, thereby implying the existence of an empty core. Moreover, the evaluation of the effective energy density reveals that it is inevitably negative, which could have utmost relevance in understanding various quantum field events. To derive the structure scalars, we perform the orthogonal splitting of the Riemann tensor in this modified gravity. Few relationships among matter variables and both Tolman and Misner Sharp are determined. Through two generating functions, some hyperbolically symmetric cosmological models, as well as their physical interpretations, are studied. To delve deeply into the role of f(R) terms, the model of the less-complex relativistic system of Einstein gravity is presented.

Study of Charged Anisotropic Karmarkar Stars in f(R,T2)$f(\mathcal {R},\mathbb {T}^{2})$ Theory

“…Bhatti et al [ 42 ] explored few anisotropic spherically symmetric solutions to show significance of structure scalars in the background of $$f(\mathcal {R})$$ gravity. Yousaf et al [ 43 ] discussed physical characteristics of static irrotational matter content that assumes hyperbolical symmetry in the same theory.…”

“…It is worthwhile to mention here that the range of physical quantities in EMSG increases and provides more viable as well as stable compact stars as compared to GR [ 19,60,62 ] and other modified theories. [ 39–46 ] For example, in $$f(\mathcal {R})$$ theory, it is found that physical quantities such as effective matter variables, energy conditions, EoS parameters and speed of sound are satisfied for very small range and the compact star Her X‐1 under the effects of the second gravity model does not remain stable. [ 39 ] In $$f(\mathcal {G},\mathrm{T})$$ theory, the evolution of compact stars (SAXJ1808.4‐3658 and 4U1820‐30) are supported by all three gravity models while for HerX ‐ 1, there are some restrictions asserted by the second model to be completely physically viable.…”

Significance of Charge on the Dynamics of Hyperbolically Distributed Fluids

“…Equation (53) shows that in non-dissipative system there is also no influence of charge on the complexity factor, in order to keep it zero.…”

“…Yousaf et al [51][52][53][54] examined the anisotropic static fluid distributed hyperbolically in the framework of different modified theories. They carried out this analysis both in the presence as well as in the absence of charge.…”

Gaussian curvature of spherical shells: a geometric measure of complexity

“…Also, the energy conditions for a composite matter distribution (combination of a viscous matter, null dust and null strings) exhibit complex behaviour [27]. Recent studies in complexity include gravitational collapse, embedding, gravitational coupling and static irrotational matter [13,[28][29][30], in radiating stars in general relativity. Some other recent works on complexity in self-gravitaing systems are contained in the works [31][32][33][34][35].…”