Static Spherical Spacetimes Research Articles

Role of Rastall gravity in constructing new spherically symmetric stellar solutions

This paper formulates new stellar solutions corresponding to a static spherical spacetime through the minimal gravitational decoupling in the context of Rastall theory. For this, we initially adopt a seed source to be the isotropic and then add a new gravitating matter source whose impact is controlled by the decoupling parameter. The addition of the later source enhances the degrees of freedom in the corresponding equations of motion. To reduce them, we apply the geometric transformation only to a radial metric potential that divides the field equations into two sets, each of them govern the impact of only one source. Afterwards, we take into account the Schwarzschild solution to make the metric potentials known. Moreover, different constraints on the components of newly added source are employed to develop some suitable solutions of the second system. We construct three different solutions to the total fluid distribution and check their graphical behavior for certain parametric values. Finally, we conclude all our resulting models to be agree with the energy conditions in this extended theory.

Stability analysis of static spherical spacetime in extended symmetric teleparallel gravity

Our manuscript aims to analyze the viability and stability of anisotropic stellar objects in the modified symmetric teleparallel gravity. A particular model of this extended theory is considered to formulate explicit field equations that govern the interaction between matter and geometry. The configuration of static spherical symmetric structures is examined through the Finch-Skea solution. However, the values of unknown constants in the metric potentials are evaluated by the Darmois junction conditions. For the viability of the proposed stellar objects, physical parameters including density, pressure, anisotropy, mass, energy constraints, compactness function, and redshift are analyzed. Furthermore, the stability of the proposed stellar objects is investigated by the causality condition, Herrera cracking approach, and adiabatic index. Our findings indicate that the proposed stellar objects are viable as well as stable in the presence of correction terms.

Anisotropic extensions of isotropic Finch–Skea metric in the charged modified gravity

In this study, we explore the Finch–Skea perfect fluid solution and extend its domain to three distinct anisotropic interior models within the framework of the f(R,T) theory, incorporating the influence of an electromagnetic field. We assume a static spherical spacetime initially coupled with an isotropic matter distribution. We then introduce a Lagrangian corresponding to an additional gravitating source, taking into account its role in inducing pressure anisotropy within the original fluid source. By deriving the field equations for the combined matter setup, we applied a radial component transformation, which yielded two distinct systems of equations. In addition, we consider a charged exterior spacetime to determine the three constants associated with the Finch–Skea solution at the boundary. Our findings suggest that under certain parametric choices, all three resulting models exhibited physical relevance within this modified theory.

Extending Finch-Skea isotropic model to anisotropic domain in modified f(, T ) gravity

This paper considers the Finch-Skea isotropic solution and extends its domain to three different anisotropic interiors by using the gravitational decoupling strategy in the context of f(R,T) gravitational theory. For this, we consider that a static spherical spacetime is initially coupled with the perfect matter distribution. We then introduce a Lagrangian corresponding to a new gravitating source by keeping in mind that this new source produces the effect of pressure anisotropy in the parent fluid source. After calculating the field equations for the total matter setup, we apply a transformation on the radial component, ultimately providing two different systems of equations. These two sets are solved independently through different constraints that lead to some new solutions. Further, we consider an exterior spacetime to calculate three constants engaged in the seed Finch-Skea solution at the spherical interface. The estimated radius and mass of a star candidate LMC X-4 are utilized to perform the graphical analysis of the developed models. It is concluded that only the first two resulting models are physically relevant in this modified theory for all the considered parametric choices.

Implications of vanishing complexity condition in f(R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f({\ extbf{R}})$$\\end{document} theory

This paper introduces the concept of complexity for a static spherical spacetime and extends it to the modified f(R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f({\ extbf{R}})$$\\end{document} framework. The formulation of the corresponding field equations is then carried out to describe the anisotropic interior. The spherical mass function is defined in both geometric as well as matter terms. Utilizing the orthogonal splitting of the curvature tensor, specific scalars are developed, with one of them denoted as YTF,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {Y}}_{TF},$$\\end{document} identified as the complexity factor for the considered fluid setup. In addressing the system of field equations admitting some extra degrees of freedom, the complexity-free condition is introduced. In conjunction with this condition, three other constraints are applied, leading to the development of different models. We also provide a graphical representation of the resulting solutions, using specific parametric values. From this analysis, we conclude that our all three models exhibit the properties required for the existence of physically viable and stable structures for certain values of the model parameter.

A Brief analysis of isotropic Karmarkar models in modified gravity theory

This investigation explores the nature of charged compact stars within the modified theory whose functional depends on the Ricci scalar, Lagrangian density of the matter and trace of the energy–momentum tensor. The methodology involves starting with a static spherical spacetime filled with the isotropic fluid. The field equations are then formulated corresponding to a specific minimal model of this extended theory. While developing these equations, we also take into account different choices of the fluid Lagrangian density. Further, we use the Karmarkar condition to deal with the extra degrees of freedom in the equations of motion and construct their corresponding solutions. The metric components obtained from the Karmarkar condition possess three constants which are evaluated through the matching conditions of the interior spherical geometry with the exterior vacuum spacetime. Further, we explore the obtained models for different values of the parameters through a comprehensive graphical analysis. Conclusively, our results agree well with the physical conditions and thus advance our understanding of the impact of the considered gravity theory on the internal composition of stellar objects.

Integrability of Dirac equations in static spherical space-times

We consider the Dirac equations in static spherically-symmetric space-times, and we present a type of spinor field whose structure allows the separation of elevation angle and radial coordinate in very general situations. We demonstrate that after such a separation of variables the Dirac equations reduce to two equations that can always be integrated, at least in principle. To prove that ours is a fully-working method, we find an explicit exact solution in the special case of the de Sitter universe.

Spherically symmetric wormhole solutions admitting Karmarkar condition

This paper investigated the viable traversable wormhole solutions through Karmarkar condition in the context of f(G,T) theory. A static spherical spacetime with anisotropic matter configuration is used to study the wormhole geometry. Karmarkar condition is used to develop a viable shape function for a static wormhole structure. A wormhole geometry is constructed using the resulting shape function that satisfies all the required conditions and connects the asymptotically flat regions of the spacetime. To assess the viability of traversable wormhole geometries, the energy conditions are analyzed by various models of this theory. Further, their stable state is investigated through sound speed and adiabatic index. This investigation demonstrates the presence of viable traversable wormhole solutions in the modified theory.

Conformal vectors and stellar models

The relationship between conformal symmetries and relativistic spheres in astrophysics is studied. We use the nonvanishing components of the Weyl tensor to classify the conformal symmetries in static spherical spacetimes. It is possible to find an explicit connection between the two gravitational potentials for both conformally flat and nonconformally flat cases. We show that the conformal Killing vector admits time dependence in terms of quadratic, trigonometric and hyperbolic functions. The Einstein and Einstein-Maxwell field equations can be written in terms of a single potential, any choice of which leads to an exact solution. Previous results of conformally invariant static spheres are contained in our treatment.

The Schwarzschild metric: It's the coordinates, stupid!

Every general relativity textbook emphasizes that coordinates have no physical meaning. Nevertheless, a coordinate choice must be made in order to carry out real calculations, and that choice can make the difference between a calculation that is simple and one that is a mess. We give a concrete illustration of the maxim that “coordinates matter” using the exact Schwarzschild solution for a vacuum, static spherical spacetime. We review the standard textbook derivation, Schwarzschild's original 1916 derivation, and a derivation using the Landau-Lifshitz formulation of the Einstein field equations. The last derivation is much more complicated, has one aspect for which we have been unable to find a solution, and gives an explicit illustration of the fact that the Schwarzschild geometry can be described in infinitely many coordinate systems.

Influence on the entropic force by the virtual degree of freedom on the holographic screen

We generalize the study of entropic force to a general static spherical spacetime and examine the acceleration, temperature, equation of gravity and the energy associated with the holographic screen in this general background. We show that the virtual degree of freedom on the holographic screen plays a crucial role in interpreting field equations of gravity based on thermodynamical perspective.

State equations for massless spin fields in static spherical spacetime filled with quintessence

The entropy density, energy density, pressure and equation of state for the gases of massless particles with spin s ≤ 2 around the static spherical black hole with quintessence are investigated by using the brick-wall method. It is shown that the state equations for spin fields in curved spacetime do not take the same forms as that in flat spacetime and contain additional terms with spin dependence. Then the character of the terms and the effect of quintessence and spin on them are discussed.

General solution and classification of conformal motions in static spherical spacetimes

We find the complete and explicit general solution of the conformal Killing equation in static spherically symmetric spacetimes, thus unifying and generalizing previous special cases. For non-conformally-flat spacetimes, there are at most two proper conformal motions. There are three classes of such spacetimes, and one or both of the conformal Killing vectors is non-inheriting. One of the classes includes self-similar spacetimes (i.e. with a homothetic motion). The conformally flat spacetimes (including the Schwarzschild interior metric) fall into three classes, and their eleven proper conformal Killing vectors are given in full. The only spacetimes with conformal motion that are regular at the centre are conformally flat. An addendum for this article has been published in 1996 Class. Quantum Grav. 13 317

Additivity of the entropies of black holes and matter in equilibrium.

We consider static spherical spacetimes in which a black hole is in equilibrium with surrounding matter. The grand canonical ensemble is defined by the geometry of the boundary of a region of spacetime and the chemical potential evaluated on this boundary. Additivity of the actions of gravity and matter and the principle of equivalence then jointly imply that the total entropy is the simple sum of the accepted black-hole entropy and the ordinary matter entropy. However, energy and thermodynamic potentials exhibit interaction terms and are not simply additive..