Singularity-free Solutions Research Articles

Charged stellar structure in f(R,ϕ) gravity admitting Chaplygin equation of state

The aim of this paper is to examine the singularity-free solutions for anisotropic stellar structures in [Formula: see text] theory of gravity, where [Formula: see text] denotes the Ricci scalar and [Formula: see text] represents the scalar field. For this purpose, we consider the spherically symmetric spacetime to discuss the stellar structures with anisotropic fluid. Moreover, the Einstein field equations are solved by using Chaplygin equation of state, and the Karori–Barua metric. To analyze the charged stellar structure, we use the matching conditions of spherically symmetric spacetime with the Reissner–Nordstrom exterior metric and develop some expressions for finding the unknown parameters. We further investigate the graphical behavior of energy density, pressure components, anisotropic component, equation of state parameters, equilibrium condition, stability analysis, adiabatic index and energy conditions. Conclusively, our considered stellar structures under observations are realistic, stable, and are free from any singularities.

Impact of f(ℜ,𝒯2) theory on stable Finch–Skea gravastar model

This paper examines the structure of a gravitational vacuum star (also known as gravastar) in the background of [Formula: see text] theory. This hypothetical object can be treated as a substitute of a black hole, with three regions: (i) the internal region, (ii) the intrinsic shell and (iii) the outer region. We examine these geometries using Finch–Skea metric for the radial metric component along with the particular [Formula: see text] model. We determine singularity-free solutions for both the inner as well as thin-shell domains. The smooth matching of the interior region with external Schwarzschild spacetime is obtained through Israel matching constraints. Finally, we study various characteristics of gravastar domains including the equation-of-state parameter, proper length, entropy, energy as well as surface redshift. It is found that the compact gravastar structure is a viable alternate to the black hole in the perspective of this gravity.

Geodesic completeness of effective null geodesics in regular space-times with non-linear electrodynamics

We study the completeness of light trajectories in certain spherically symmetric regular geometries found in Palatini theories of gravity threaded by non-linear (electromagnetic) fields, which makes their propagation to happen along geodesics of an effective metric. Two types of geodesic restoration mechanisms are employed: by pushing the focal point to infinite affine distance, thus unreachable in finite time by any sets of geodesics, or by the presence of a defocusing surface associated to the development of a wormhole throat. We discuss several examples of such geometries to conclude the completeness of all such effective paths. Our results are of interest both for the finding of singularity-free solutions and for the analysis of their optical appearances e.g. in shadow observations.

Study of gravastars in 4D Einstein-Gauss-Bonnet gravity

In the present work, we investigate the configuration of gravastar in the framework of Einstein-Gauss-Bonnet (EGB) gravity. A gravastar is conceptually an alternative model for black holes, which has three distinct layers with different equations of state. Under these specifications, we find out a set of exact and singularity free solutions of the gravastar in EGB gravity. The interior and exterior layers are matched by considering the Israel and Darmois junction conditions. The mass of the thin intermediate shell is formulated and various physical aspects of gravastar, specifically, energy of the shell, entropy inside the shell, intermediate thin shell and proper length of the shell is examined. It is noted that the Gauss-Bonnet term strongly affects the physical properties of gravastar in EGB gravity.

Shadow of a charged black hole with scalar hair

Seeking singularity free solutions are important for further understanding black holes in quantum level. Recently, a five-dimensional singularity free black hole/topological star was constructed (Bah and Heidmann in Phys Rev Lett 126:151101, 2021). Through the Kaluza–Klein reduction, an effective four-dimensional static spherically symmetric charged black hole with scalar hair can be obtained. In this paper, we study shadow of this charged black hole with scalar hair in terms of four kinds of observers, i.e., static observers, surrounding observers, freely falling observers, and escaping observers in four-dimensional spacetime. For a spherically symmetric black hole, the shadow is circular for any observer, but the shadow size depends on the motion status of the observer. On the other hand, the effect of plasma is also investigated by a simple model. The radius of the photon sphere depends on the plasma model. Most importantly, we find that the shadow sizes do not monotonically decrease with r in some cases.

A study of charged stellar structure in modified f (R,ϕ,χ) gravity

The aim of this paper is to investigate and analyze the behavior of charged compact stars in the modified [Formula: see text] theory of gravity. When solving the field equations, we assume that Krori– Barua space-time describes the geometry of the inner space [K. Krori and J. Barua, A singularity-free solution for a charged fluid sphere in general relativity, J. Phys. A Math. Gen. 8 (1975) 508]. We further analyzed various physical characteristics for our model, including energy density, pressure components, anisotropy parameter, mass function, compactness element, and redshift through their graphical representations. Additionally, we have checked the equilibrium position by taking Tolman–Oppenheimer–Volkoff equation and stability by using Abreu’s criterion [H. Abreu, H. Hernandez, and L. Nunez, Sound speeds, cracking and the stability of self-gravitating anisotropic compact objects, Class. Quantum Grav. 24 (2007) 4631] and relativistic adiabatic index. For our study, we choose Hercules XI, Centaurus XIII, EXO 1785-248, LMC XIV stars for analysis.

Gradient models of moving heat sources for powder bed fusion applications

In this paper, we derive closed form solutions for the quasi-stationary problems of moving heat sources within the gradient theory of heat transfer. This theory can be formally deduced from the two-temperature model and it can be treated as a generalized variant of the Guyer–Krumhansl model with the fourth order governing equation. We show that considered variant of the gradient theory allows to obtain useful singularity-free solutions for the moving point and line heat sources that can be used for the refined analysis of the melt pool shape in the laser powder bed fusion processes. Derived solutions contain single additional length scale parameter that can be related to the mean size of the powder particles . Namely, we show that developed gradient models allow to describe the decrease of the melt pool depth with the increase of the powder’s particles size that was observed previously in the experiments. We also derived the dimensionless relations that can be used for the experimental identification of the model’s length scale parameter for different materials. Semi-analytical solution for the Gaussian laser beam is also derived and studied based on the Green function method within the considered theory.

Impact of charge on gravastars in f(ℜ,𝒯2) gravity

This paper studies the influence of charge on a compact stellar structure also regarded as vacuum condensate star in the background of [Formula: see text] gravity. This object is considered the alternate of black hole whose structure involves three distinct regions, i.e. interior, exterior and thin-shell. We analyze these domains of a gravastar for a particular model of this modified theory. In the inner region of a gravastar, the considered equation of state defines that energy density is equal to negative pressure which is the cause of repulsive force on the spherical shell. In the intermediate shell, pressure and energy density are equal and contain ultra-relativistic fluid. The inward-directed gravitational pull of thin-shell counterbalances the force exerted by the inner region of a gravastar allowing the formation of a singularity-free object. The Reissner–Nordström metric presents the outer vacuum spherical domain. Moreover, we discuss the impact of the charge on physical attributes of a gravastar such as the equation of state parameter, entropy, proper length and energy. We conclude that singularity-free solutions of charged gravastar are physically consistent in this modified theory.

Cylindrical Gravastar Like-Structures in f(G) Gravity

The aim of this manuscript is to explore singularity-free solution for a specific self-gravitating highly dense object known as gravastar suggested by Mazur and Mottola, in the context of f(G) gravity theory. Gravastars are regarded as a possible alternate to black hole. To derive modified field equations and law of conservation related to Gauss-Bonnet gravity, we assume cylindrically symmetric irrotational configuration. Particular equation of states are used for the illustration of three sectors of gravastar model. Furthermore, we are intended to obtain a regular solution for our model and graphs will be used to elaborate various substantial characteristics of it.

Analysis of charged gravastar in f(R,G) gravity

This paper is dedicated to inspecting the appearance of electromagnetic field, which is caused by the presence of charge in the highly compact object named gravastar in the background of [Formula: see text] theory. According to conjecture introduced by Mazur and Mottola gravastar must be consisted of three sectors. We have interpreted these sectors by using specific equations of states. Spherically static metric, perfect fluid and the isotropic pressure have been used in order to calculate a singularity free solution. Gravitational mass present in the inner sector of gravastar is changed into electromagnetic mass in the existence of charge. The electromagnetic mass model of inner sector is responsible for stability by providing balance to the repulsive pressure, which is caused by the presence of charge. It is observed that the presence of electrical charge has a significant effect on energy content, entropy and proper length of the shell that is demonstrated with the help of graphs.

Quantum and Classical Cosmology in the Brans–Dicke Theory

In this paper, we discuss classical and quantum aspects of cosmological models in the Brans–Dicke theory. First, we review cosmological bounce solutions in the Brans–Dicke theory that obeys energy conditions (without ghost) for a universe filled with radiative fluid. Then, we quantize this classical model in a canonical way, establishing the corresponding Wheeler–DeWitt equation in the minisuperspace, and analyze the quantum solutions. When the energy conditions are violated, corresponding to the case ω<−32, the energy is bounded from below and singularity-free solutions are found. However, in the case ω>−32, we cannot compute the evolution of the scale factor by evaluating the expectation values because the wave function is not finite (energy spectrum is not bounded from below). However, we can analyze this case using Bohmian mechanics and the de Broglie–Bohm interpretation of quantum mechanics. Using this approach, the classical and quantum results can be compared for any value of ω.

Charged compact star in f(R,\xa0T) gravity in Tolman\u2013Kuchowicz spacetime

In this current study, our main focus is on modeling the specific charged compact star SAX J 1808.4-3658 (M = 0.88 M_{odot }, R = 8.9 km) within the framework of f(R,,T) modified gravity theory using the metric potentials proposed by Tolman–Kuchowicz (Tolman in Phys Rev 55:364, 1939; Kuchowicz in Acta Phys Pol 33:541, 1968) and the interior spacetime is matched to the exterior Reissner–Nordström line element at the surface of the star. Tolman–Kuchowicz metric potentials provide a singularity-free solution which satisfies the stability criteria. Here we have used the simplified phenomenological MIT bag model equation of state (EoS) to solve the Einstein–Maxwell field equations where the density profile (rho ) is related to the radial pressure (p_{mathrm{r}}) as p_{mathrm{r}}(r) = (rho - 4B_{mathrm{g}})/3. Furthermore, to derive the values of the unknown constants a,, b,, B,, C and the bag constant B_{mathrm{g}}, we match our interior spacetime to the exterior Reissner–Nordström line element at the surface of stellar system. In addition, to check the physical validity and stability of our suggested model we evaluate some important properties, such as effective energy density, effective pressures, radial and transverse sound velocities, relativistic adiabatic index, all energy conditions, compactness factor and surface redshift. It is depicted from our current study that all our derived results lie within the physically accepted regime which shows the viability of our present model in the context of f(R,,T) modified gravity.

Modeling of compact stars: an anisotropic approach

We present here a new class of singularity free interior solutions relevant for the description of realistic anisotropic compact stellar objects with spherically symmetric matter distribution. In this geometric approach, specific choices of one of the metric functions and a selective anisotropic profile allow us to develop a stellar model by solving Einstein Field equations. The interior solutions thus obtained are matched with the Schwarzschild exterior metric over the bounding surface of a compact star. These matching conditions together with the condition that the radial pressure vanishes at the boundary are used to fix the model parameters. The different physical features for the developed model explicitly studied from the aspect of the pulsar 4U $$1820-30$$ with its current estimated data (mass $$=1.46 \pm 0.21~M\odot $$ and radius $$=11.1 \pm 1.8$$ km (Ozel et al.: ApJ 820(1): 28, 2016) ). Analysis has shown that all the physical aspects are acceptable demanded for a physically admissible star and satisfy all the required physical conditions. The stability of the model is also explored in the context of causality conditions, adiabatic index, generalized Tolman–Oppenheimer–Volkov (TOV) equation, Buchdahl Condition and Herrera Cracking Method. To show that the developed model is compatible with a wide range of recently observed pulsars, various relevant physical variables are also highlighted in tabular form. The data studied here are in agreement with the observation of gravitational waves from the first binary merger event. Assuming a particular surface density ( $$7.5 \times 10^{14}\text { gm cm}^{-3}$$ ), the mass-radius ( $$M - b$$ ) relationship and the radius-central density relationship ( $$b - \rho (0)$$ ) of the compact stellar object are analyzed for this model. Additionally, comparing the results with a slow rotating configuration, we have also discussed moment of inertia and the time period using Bejger-Haensel idea.

Does emergent scenario in Hořava–Lifshitz gravity demand a ghost field?

The non-singular model of the Universe i.e. emergent scenario is now very well known in cosmology. In Einstein gravity such type of singularity free solution is possible in the context of non-equilibrium thermodynamical prescription (both in first and 2nd order theory) with particle creation mechanism. Also there are various models of emergent scenario in different gravity theories. The present work is a twofold attempt namely (i) it has been examined whether it is possible to have singularity free solution in Hořava–Lifshitz modified gravity theory, (ii) if such singularity free solution exists then whether such solution is thermodynamically viable. It is found that perfect fluid matter distribution with phantom nature can generate such type of solution for closed and flat model. Finally thermodynamical analysis has been studied both at the apparent horizon and at any arbitrary horizon.

Singularities in quantum corrected space-times

In this paper we consider a static and regular fluid generating a locally spherically symmetric and time-independent space-time and calculate the leading quantum corrections to the metric to first order in curvature. Starting from a singularity free classical solution of general relativity, we show that singularities can be introduced in the curvature invariants by quantum gravitational corrections calculated using an effective field theory approach to quantum gravity. We identify non-trivial conditions that ensure that curvature invariants remain singularity free to leading order in the curvature expansion of the effective action.

Singularity-free solutions for inverse kinematics of degenerate mobile robots

This paper describes a method for inverse kinematics that is tolerant to degenerate wheels structures, specifically to control the motion of the transformable, pseudo-omnidirectional mobile platform. This platform can expand its lateral footprint while maintaining the robot’s planar mobility. The proposed method creates an inverse kinematical solution where there previously was none due to modeling singularities from the use of degenerate wheel structures. The idea of degenerate wheel structures is introduced and a robot using only these wheels is described. The first order dynamics of the robot are derived and an analytical inverse kinematical solution to the steering angle and rate of wheel rotation for each wheel is given using closed form solutions. The bifurcating solutions are addressed and as long as the chosen solutions are consistent between the steering angle and the wheel rotation speed, there is no impact on the effectiveness of either pair of solutions. This solution proved to be accurate through simulation of both omnidirectional motion and instantaneous center of rotation-based motion. Consistent results were achieved in experiments.

Study of gravastars under [formula omitted] gravity

In the present paper, we propose a stellar model under the f(T) gravity following the conjecture of Mazur-Mottola [1,2] known in literature as gravastar, a viable alternative to the black hole. This gravastar has three different regions, viz., (A) Interior core region, (B) Intermediate thin shell, and (C) Exterior spherical region. It is assumed that in the interior region the fluid pressure is equal to a negative matter-energy density providing a constant repulsive force over the spherical thin shell. This shell at the intermediate region is assumed to be formed by a fluid of ultrarelativistic plasma and the pressure, which is directly proportional to the matter-energy density according to Zel'dovich's conjecture of stiff fluid [Zel'dovich (1972) [3]], does nullify the repulsive force exerted by the interior core region for a stable configuration. On the other hand, the exterior spherical region can be described by the exterior Schwarzschild-de Sitter solution. With all these specifications we have found out a set of exact and singularity-free solutions of the gravastar which presents several physically interesting as well as valid features within the framework of alternative gravity.

Gravastars in f(𝕋,𝒯) gravity

We propose a stellar model under the [Formula: see text] gravity following Mazur–Mottola’s conjecture[Formula: see text] known as gravastar which is generally believed as a viable alternative to black hole. The gravastar consists of three regions, viz., (I) interior region, (II) intermediate shell region, and (III) exterior region. The pressure within the interior core region is assumed to be equal to the constant negative matter-energy density which provides a constant repulsive force over the thin shell region. The shell is assumed to be made up of fluid of ultrarelativistic plasma and following the Zel’dovich’s conjecture of stiff fluid3 it is also assumed that the pressure which is directly proportional to the matter-energy density according to Zel’dovich’s conjecture, does cancel the repulsive force exerted by the interior region. The exterior region is completely vacuum and it can be described by the Schwarzschild solution. Under all these specifications, we find out a set of exact and singularity-free solutions of the gravastar presenting several physically valid features within the framework of alternative gravity, namely [Formula: see text] gravity,4 where the part of the gravitational Lagrangian in the corresponding action is taken as an arbitrary function of torsion scalar [Formula: see text] and the trace of the energy–momentum tensor [Formula: see text].

Gravastars in [formula omitted] dimensions admitting Karmarkar condition

The development of gravastar model by Mazur and Mottola (2004) is one of the most acceptable alternatives of conventional classical black hole. They have studied phase transition of the collapsing stellar objects at low temperature near event horizon which leads to the condensate phase, i.e. Bose–Einstein condensation. In the present study we have obtained a unique solution of this gravastar model under Einstein’s GR in (3+1) dimensions by incorporating the Karmarkar condition for embedding class 1. The most important motive of this work is to find an exact solution of the shell without taking the thin shell approximation. We have obtained singularity free finite solutions for the interior of the gravastar.

Singularity-free defect mechanics for polar media

We present singularity-free solution for cracks within polar media in which material points possess both position and orientation. The plane strain problem is addressed in this study for which the generalized continua including micropolar, nonlocal micropolar, and gradient micropolar elasticity theories are employed. For the first time, the variationally consistent boundary conditions are derived for gradient micropolar elasticity. Moreover, having reviewed the solution to line defects including glide edge dislocation and wedge disclination from the literature, the fields of a climb edge dislocation within micropolar, nonlocal micropolar and gradient micropolar elasticity are derived. This completes the collection of line defects needed for an inplane strain analysis. Afterward, as the main contribution, using both types of line defects (i.e., dislocation being displacement discontinuity and disclination being rotational discontinuity), the well-established dislocation-based fracture mechanics is systematically generalized to the dislocation- and disclination-based fracture mechanics of polar media for which we have three translations together with three rotations as degrees of freedom. Due to the application of the line defects, incompatible elasticity is employed throughout the paper. Cracks under three possible loadings including stress and couple stress components are analyzed, and the corresponding line defect densities and stress and couple stress fields are reported. The singular fields are obtained once using the micropolar elasticity, while nonlocal micropolar, and gradient micropolar elasticity theories give rise to singularity-free fracture mechanics.