International Journal of Modern Physics D

In this paper, we present the general properties of dynamic dissipative fluid distribution endowed with hyperbolical symmetry. All the equations required for its analysis are exhibited and used to contrast the behavior of the system with the spherically symmetric case. Several exact solutions are exhibited and prospective applications to astrophysical and cosmological scenarios are discussed.

This paper deals with stability analysis of anisotropic-charged cylindrical geometry coupled with $f(R,T)$ modified gravity theory (${ℳ}{𝒢}{𝒯}$). In this ${ℳ}{𝒢}{𝒯}$, the Lagrangian is a varying function of traces of Ricci and stress tensors. In order to examine the stable behavior of the anisotropic cylindrical cosmic object under the electromagnetic effects, we calculated the modified equations of motion and equations of continuity. in the background of $f(R,T)$ theory. By utilizing the perturbation technique, we constitute a modified collapse equation (${ℳ}{𝒞}{ℰ}$), which contains geometrical and physical variables in the charged scenario. Our investigation continues under the nonminimally coupled function of ${ℳ}{𝒢}{𝒯}$. Furthermore, we investigate the dynamically stable phases of charged geometry at Newtonian $({𝒩})$ and post-Newtonian ($p{𝒩}$) epochs with the help of the rigidity parameter of fluid ($\mathrm{\Gamma }$) by imposing some constraints on physical parameters.

In this work, we focus on constructing two analogs of an anisotropic seed solution via the decoupling technique. For this purpose, we add a new matter source alongside the anisotropic fluid in a static sphere. A transformation in the radial metric component is applied to split the field equations into two sets such that the influence of each source is limited to one array. The anisotropic solution constructed by employing the embedding class-one condition is used to specify the set corresponding to the seed source. We obtain two solutions of the second set (related to the additional source) by applying constraints on the anisotropy and complexity of the self-gravitating system. A smooth junction between the interior and exterior spacetimes determines the unknown constants. Various physical characteristics, such as viability and stability, are graphically analyzed by utilizing the radius and mass of the star PSR J1614-2230. It is found that the extended solutions agree with the energy conditions as well as stability criteria for selected values of the parameters.

Testing gravity theories and constraining their parameters using data from astrophysical observations of quasiperiodic oscillations (QPOs) is a powerful approach to study the features of black holes (BHs) and gravity theories in the strong field regime. To this end, we investigate the dynamics of the test particles in the vicinity of some charged BHs such as Reissner–Nordström (RN), regular Bardeen and Ayon–Beato–Garcia (ABG). In particular, we calculate harmonic oscillations and the innermost stable circular orbits (ISCOs) of test particles around these BHs. As an astrophysical application, we discuss the twin peak QPOs in relativistic precession (RP) model and give the possible values of the upper and lower frequencies of the QPOs at the distance from ISCO to infinity around the extremely charged BHs. Moreover, we also investigate the position of the orbit, where twin peak QPO may take place around central (charged) BH in the microquasar GRS 1915-105. We also study the dependence of the distance between the QPO position and ISCO from the BH charge. Using the upper and lower frequencies of the QPO, we obtain the relationship between the mass and charge of the central BH in the microquasar. Finally, we compare the effects of the spin of the Kerr BH and BH charges on the QPO in microquasar GRS 1915-105. We find that the BH charge can mimic the spin up to $a/M=0.2927$ in the Bardeen model and up to $a/M=0.7687$ in the case of special regular BH, admitting the same QPO frequencies.

General relativistic spacetimes in which at every point $p$ in some neighbourhood $W$ the tangent space $T_p$ is invariant under the same continuous subgroup $g$ of the Lorentz group are considered. Some previously open problems for such spacetimes are discussed and solved, and a comprehensive survey of such spacetimes is provided. For most cases, invariance of the curvature and its first covariant derivative under $g$ imply the existence of an isometry group in $W$ containing $g$ as an isotropy group. In the remaining cases, invariance of second and third derivatives may be required for this implication, and in particular, the necessity of invariance of the third derivative is proved for the locally rotationally symmetric spacetimes discussed by Ellis and by Stewart and Ellis.

In the literature, several spherically symmetric static solutions of the Einstein–Maxwell field equations (EMFEs) have been obtained by taking assumptions/ansatz on the parameters involved, like electric field intensity, gravitational potential, equation of state, etc. In this paper, using the Segre classification, we present a systematic scheme that limits the number of assumptions/ansatz required to be taken. It is found that the static spherically symmetric solutions of the EMFEs can only be of Segre types $[(1111)]$, $[(11)(11)]$, $[1(111)]$, or $[1(11)1]$. It is also shown that the type $[(1111)]$ leads to the Schwarzschild de-Sitter/anti de-Sitter solutions.

I had worked with John Wheeler on York-time foliation of a black hole in a closed Universe (1978–1993), on my own, and with my students, Amjad Parvez and Azad Siddiqui, on that and foliation of asymptotically flat black hole spacetimes from then till 2013. In July 2021, the work by Gerard ’t Hooft and others, presented in MG16, seemed to have “rediscovered” what we had found much earlier. The work of Roy Kerr and others displayed confusion that could be cleared up by those insights. I review this material.

This paper examines the structure of gravastar (gravitationally vacuum star) in the background of $f(\Re ,{{𝒯}}^2)$ theory. The gravastar can be regarded as a substitute for a black hole comprising of three regions (i) the interior domain, (ii) the intrinsic shell and (iii) the exterior domain. We investigate these domains by employing Karmarkar’s condition by assuming a specific $f(\Re ,{{𝒯}}^2)$ model. The field equations are solved to evaluate nonsingular solutions of both the interior and intermediate regions. Inner as well as outer spacetimes are matched together using Israel formalism to obtain density and pressure at the joining surface. Different attributes of gravastar like the equation of state parameter, proper length, entropy and energy are analyzed through graphical behavior. It is found that the gravastar model is a viable alternative to the black hole in the context of this gravity.

Albert Einstein referred to gravitational microlensing as a “most curious effect”, and while its underlying principles are intriguingly simple, their universality makes a powerful tool for inferring information about a wide range of astronomical bodies. Much has happened since the first observation of a gravitational microlensing event in 1992, and the frontiers have shifted. What we did not dare dreaming about just a few decades ago turned into reality, and we have not reached the end of the journey. New challenges and opportunities lie ahead. Where might we be able to go and how can we get there?

In this paper, we review modified theories of gravity with a curvature–matter coupling between an arbitrary function of the scalar curvature and the Lagrangian density of matter. This explicit nonminimal coupling induces a nonvanishing covariant derivative of the energy–momentum tensor, that implies nongeodesic motion and consequently leads to the appearance of an extra force. Here, we explore the physical and cosmological implications of the nonconservation of the energy–momentum tensor by using the formalism of irreversible thermodynamics of open systems in the presence of matter creation/annihilation. The particle creation rates, pressure, and the expression of the comoving entropy are obtained in a covariant formulation and discussed in detail. Applied together with the gravitational field equations, the thermodynamics of open systems lead to a generalization of the standard $\mathrm{\Lambda }$CDM cosmological paradigm, in which the particle creation rates and pressures are effectively considered as components of the cosmological fluid energy–momentum tensor. Furthermore, we also briefly present the coupling of curvature to geometry in conformal quadratic Weyl gravity, by assuming a coupling term of the form $L_m{\tilde{R}}^2$, where $L_m$ is the ordinary matter Lagrangian, and $\tilde{R}$ is the Weyl scalar. The coupling explicitly satisfies the requirement of the conformal invariance of the theory. Expressing ${\tilde{R}}^2$ with the use of an auxiliary scalar field and of the Weyl scalar, the gravitational action can be linearized in the Ricci scalar, leading in the Riemann space to a conformally invariant $f(R,L_m)$-type theory, with the matter Lagrangian nonminimally coupled to geometry.

Through this paper, I will overview the use of Noether symmetry approach in discussing the integration of geodesic equations for the geodesic Lagrangians of spacetimes. I will also give some examples to reveal the efficiency of Noether symmetry approach by finding the first integrals related for the geodesic Lagrangians of the Gödel-type, Schwarzschild, Reïssner–Nordström and Kerr spacetimes. After obtaining the approximate Noether symmetries of the Schwarzschild, Reïssner–Nordström and Kerr spacetimes, the first integrals associated with each of approximate Noether symmetries have been integrated to find a general solution of geodesic equations in terms of the arc length $s$.

In this paper, metric-affine theories in which the gravity Lagrangian is built using (projectively invariant) contractions of the Ricci tensor with itself and with the metric (Ricci-based gravity theories, or RBGs for short) are reviewed. The goal is to provide a contextualized and coherent presentation of some recent results. In particular, we focus on the correspondence that exists between the field equations of these theories and those of general relativity, and comment on how this can be used to build new solutions of physical interest. We also discuss the formalism of junction conditions in the $f(R)$ case, and provide a brief summary on current experimental and observational bounds on model parameters.

The bulk of the matter of the universe is believed to be in the form of dark energy, which makes up about 70% of the total matter content of the universe. Since its discovery around 1998, researchers have been trying to find out about the nature of this dark energy. Despite a lot of effort, there is still no proper explanation for it. Two possible candidates for dark energy are Chaplygin gas and bulk viscosity. There is a lot of similarity in these two proposed forms. The relationship between them is explored in this presentation, and it is shown that mathematically, they are in some sense, equivalent, although their physical interpretation is different.

Among the geniuses of mankind, Einstein was probably one of those who made more erroneous claims, and often changed his opinion during the years on important scientific subjects. However, it is important to bear in mind that his mistakes were always due to a misinterpretation of the results obtained from his equations, since he was often biased by his own view of the universe. Einstein’s equations have always given the correct answer and, till now, more than a century after its development, there is no evidence that it may not be correct.

We consider an extended theory of gravity with Lagrangian ${ℒ}=f(R,T^{(n)})$, with $T^{(n)}$ being a $2n$th-order invariant made of contractions of the energy–momentum tensor. When $n=1$, this theory reduces to $f(R,T)$ gravity, where $T$ accounts for the trace of the energy–momentum tensor. We study the gravitational wave polarization modes, from which it results that when the matter Lagrangian contains dynamical scalar fields minimally coupled to the geometry, further polarization modes arise with respect to General Relativity. Finally, we show that the motion for test particles is nongeodesic and we explicitly obtain the extra force.

We would first show that how the two fundamental constants, the velocity of light, $c$, and the so called, cosmological constant, $\mathrm{\Lambda }$, arise from geometric characterization of forcefree state of spacetime. They are the two most fundamental constants as they have been synthesized in the structure of spacetime, no other constant can claim this degree of fundamentalness. Next when spacetime turns inhomogeneous, Einstein gravity arises most naturally from the spacetime geometry without any prescription from outside; i.e. the inverse square law is mandated by the geometry, and not a prescription. It would then suggest that dynamics of a fundamental force should not be prescribed but should perhaps be determined by the geometry of appropriate spacetime manifold.

In this paper, we consider static spherical structure to develop some anisotropic solutions by employing the extended gravitational decoupling scheme in the background of $f({ℛ},{𝒯},{{ℛ}}_{\gamma \chi }{{𝒯}}^{\gamma \chi })$ gravity, where ${ℛ}$ and ${𝒯}$ indicate the Ricci scalar and trace of the energy–momentum tensor, respectively. We transform both radial as well as temporal metric functions and apply them on the field equations that produce two different sets corresponding to the decoupling parameter $\xi$. The first set is associated with isotropic distribution, i.e. modified Krori–Barua solution. The second set is influenced from anisotropic factor and contains unknowns which are determined by taking some constraints. The impact of decoupling parameter is then analyzed on the obtained physical variables and anisotropy. We also investigate energy conditions and some other parameters such as mass, compactness and redshift graphically. It is found that our solution corresponding to pressure-like constraint shows stable behavior throughout in this gravity for the considered range of $\xi$.