Recent years have witnessed a rise in interest in the geometrical trinity of General Relativity and its extensions. This interest has been fuelled by novel insights into the nature of gravity, the possibility to address computational and conceptual questions—such as the determination of black hole entropy or the definition of gravitational energy–momentum—from a new perspective. In particular, f(Q) gravity has also inspired numerous works on black holes, wormholes, and cosmology. In the latter case, f(Q) models have the potential to elucidate phenomena in both early and late-time cosmology without necessitating the inclusion of dark energy, the inflaton field, or dark matter. Particularly noteworthy is the role of f(Q) theories in addressing cosmological tensions, presenting exciting possibilities for reshaping our understanding of gravity and its manifestations in cosmology. The emergence of intriguing new black hole solutions and the potential existence of wormhole solutions suggest the presence of novel physics within the realm of strong gravity. These phenomena have become increasingly measurable only in recent times, opening up exciting avenues for further exploration and discovery. This review is tailored to students and researchers alike. It offers a self-contained and pedagogical introduction to metric-affine geometry—The mathematical foundation and indispensable tool upon which the geometrical trinity of General Relativity as well as its various extensions are built. 

Review on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e2262" altimg="si5.svg"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="double-struck">Q</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> gravity

Abstract In this manuscript, we use the conformal killing vectors to solve the Einstein–Maxwell field equations in the background of modified $$f({\mathcal {G}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> gravity. We consider the observational data for four different stars namely $$PSR~J1614-2230$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mi>S</mml:mi> <mml:mi>R</mml:mi> <mml:mspace /> <mml:mi>J</mml:mi> <mml:mn>1614</mml:mn> <mml:mo>-</mml:mo> <mml:mn>2230</mml:mn> </mml:mrow> </mml:math> , $$PSR ~J1930+327$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mi>S</mml:mi> <mml:mi>R</mml:mi> <mml:mspace /> <mml:mi>J</mml:mi> <mml:mn>1930</mml:mn> <mml:mo>+</mml:mo> <mml:mn>327</mml:mn> </mml:mrow> </mml:math> , $$Cen~X-3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mi>e</mml:mi> <mml:mi>n</mml:mi> <mml:mspace /> <mml:mi>X</mml:mi> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> and $$Vela~X-1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>V</mml:mi> <mml:mi>e</mml:mi> <mml:mi>l</mml:mi> <mml:mi>a</mml:mi> <mml:mspace /> <mml:mi>X</mml:mi> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> respectively. By using the data, we derive the physical parameters from the matching criteria using conformal killing vectors and the exterior Bardeen geometry. Furthermore, several physical properties of compact stellar structures are examined in order to achieve the physical validity and stability for considered models. The graphical analysis including energy density, pressure components, equation of state parameters, and energy conditions are examined. Moreover, the equilibrium conditions through Tolman–Oppenheimer–Volkoff equation and stability criteria through adiabatic index for the charged stellar structure study are investigated. It is worth noting that all of these compact objects are physically viable and stable under conformal motion in context of Bardeen geometry for two different models of $$f({\mathcal {G}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>G</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> theory of gravity. Conclusively, the results show that f ( G ) gravity with Bardeen model may provide more massive stellar objects as compared to general relativity. 

A comprehensive study of Bardeen stars with conformal motion in f(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f(

Charged anisotropic compact stars in Ricci-inverse gravity

In this article, we use the prominent Karmarkar condition to investigate some novel features of astronomical objects in the f(R, ϕ) gravity; R and ϕ represent the Ricci curvature and the scalar field, respectively. It is worth noting that we classify the exclusive set of modified field equations using the exponential type model of the f(R, ϕ) theory of gravity f(R, ϕ) = ϕ(R + α(e β R − 1)). We show the embedded class-I approach via a static, spherically symmetric spacetime with an anisotropic distribution. To accomplish our objective, we use a particular interpretation of metric potential (g rr ) that has already been given in the literature and then presume the Karmarkar condition to derive the second metric potential. We employ distinct compact stars to determine the values of unknown parameters emerging in metric potentials. To ensure the viability and consistency of our exponential model, we execute distinct physical evolutions, i.e. the graphical structure of energy density and pressure evolution, mass function, adiabatic index, stability, equilibrium, and energy conditions. Our investigation reveals that the observed anisotropic findings are physically appropriate and have the highest level of precision.

Comprehensive analysis of relativistic embedded class-I exponential compact spheres in f(R, ϕ) gravity via Karmarkar condition

Abstract This paper investigate the impacts of local density perturbations on the stability of self-gravitating compact objects by utilizing cracking technique within the context of f ( R , T ) gravity, where R and T represent the Ricci scalar, and the trace of energy–momentum, respectively. To achieve this, we developed the hydrostatic equilibrium equation for spherically symmetric spacetime with anisotropic matter configuration and subsequently applied the Krori–Barua spacetime coefficient. Subsequently, the hydrostatic equilibrium equation of the configuration is perturbed by employing the local density perturbations to the system, while considering a barotropic equation of state. To ascertain the validity of the proposed technique, we applied it to several compact stars, including, Her X-1, SAX J1808.4-3658, 4U 1820-30, PSR J1614-2230, Vela X-1, Cen X-3, and RXJ1856-37 and found that all the considered stars exhibit cracking or overturning. This study conclusively highlights the significance of the cracking technique in providing valuable insights into the stability analysis of self-gravitating compact objects. 

Development of local density perturbation technique to identify cracking points in f(R, T) gravity

pdf/physical-characteristics-and-maximum-allowable-mass-of-2yycfc13.pdf

Physical characteristics and maximum allowable mass of hybrid star in the context of f(Q) gravity

The objective of this paper is to unveil the evolving traversable wormhole solutions within the perspective of modified f(R,G) gravity, where R is Ricci scalar and G is Gauss Bonnet term. In order to accomplish this, we develop a wormhole shape function using the Karmarkar condition for traversable static wormhole geometry, that links two asymptotically flat spacetime regions and meets the necessary requirements. The embedding diagram in two and three-dimensional Euclidean space is also discussed in order to demonstrate the wormhole configurations. For our current study, we choose two realistic and viable f(R,G) gravity models to discuss the wormhole geometry. For the traversable wormhole configurations the energy conditions must be satisfied at the throat. For this purpose, we check the energy conditions and observed that these conditions are satisfied near the throat of the wormhole space in modified f(R,G) gravity. Further, the intriguing part of this research is to perform a comparative analysis of the evolving wormhole geometries of our considered models with the help of three-dimensional graphical representation along with their regions. Moreover, we also describe the stability of obtained wormholes solutions by employing the equilibrium condition. It can be observed that our shape function acquired through the Karmarkar technique yields validated wormhole configurations with even less exotic matter correlating to the proper choice of f(R,G) gravity models. As a nutshell, we can infer that our findings fulfill all of the criterion for the presence of traversable wormhole, ensuring that our study is viable and consistent. 

Evolving embedded traversable wormholes in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e2392" altimg="si8.svg"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="script">R</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="script">G</mml:mi><

Bouncing Cosmology with 4D-EGB Gravity

Abstract This paper investigates the concept of cracking and overturning to analyze the impact of local density perturbations on the stability of self-gravitating compact objects in the framework of $$f(R,\phi , X)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>,</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>X</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> theory of gravity, where R , $$\phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ϕ</mml:mi> </mml:math> , and X denote the Ricci scalar, scalar potential, and kinetic term, respectively. In this context, we developed the hydrostatic equilibrium equation for spherically symmetric spacetime with anisotropic matter configuration and subsequently employed the Krori Barua technique. We then perturb the hydrostatic equilibrium state of the configuration by employing the local density perturbation technique, while taking into account the barotropic equation of state. To validate this technique, we employed it on different compact stars namely, Her X-1, SAX J1808.4-3658, 4U 1820-30, PSR J1614-2230, Vela X-1, and Cen X-3, and found that all stars exhibit cracking or overturning for a specific range of model parameters. Conclusively, this study emphasizes that the proposed cracking technique provides significant insights into the stability analysis of self-gravitating compact objects. 

A comprehensive discussion for the identification of cracking points in f(R) theories of gravity

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