Field Equations Research Articles

Closed time-like curves in [formula omitted] modified gravity theory

In this manuscript, we investigate solutions that allow closed time-like curves (CTCs) in general relativity (GR) within the framework of a modified gravity theory. We consider here an alternative theory recently proposed in gravity theories known as f(R,A)=(R+αA) gravity or Ricci-inverse (RI) gravity, α is the coupling constant. This theory incorporates modifications into the Einstein-Hilbert action through a coupling with an anti-curvature scalar derived from the anti-curvature tensor. We investigate a family of Petrov type-N solutions that are non-vacuum solutions of the field equations, characterized by a negative cosmological constant. The matter-energy content is Vaidya radiation, and its energy density may either remain constant or vary with axial distance. One distinctive feature of the considered solutions is the formation of CTCs, which violate the causality condition. Another observation is that the determinant of the Ricci tensor, Rμν, differs from zero, confirming the existence of an anti-curvature tensor, Aμν, the inverse of the Ricci tensor, defined as Aμν=Rμν−1, and hence, the anti-curvature scalar A=gμνAμν. We demonstrate that the family of cosmological models serves as valid solutions within the framework of Ricci-inverse gravity model, with Vaidya radiation as the matter-energy content whose energy density is modified by the coupling parameter. Thus, our results affirm that the Ricci-inverse gravity theory allows for the existence of CTCs, similar to the case in general relativity.

A worldsheet description of flux compactifications

We demonstrate how recent developments in string field theory provide a framework to systematically study type II flux compactifications with non-trivial Ramond-Ramond profiles. We present an explicit example where physical observables can be computed order by order in a small parameter which can be effectively viewed as string coupling constant. We obtain the corresponding background solution of the string field equations of motions up to the second order in the expansion. Along the way, we show how the tadpole cancellations of the string field equations lead to the minimization of the F-term potential of the low energy supergravity description. String field action expanded around the obtained background solution furnishes a “worldsheet” description of the flux compactifications.

Dark energy nature of logarithmic f(R,Lm)-gravity models with observational constraints

This work explores the dark energy nature of logarithmic [Formula: see text]-gravity models with observational constraints, where [Formula: see text] represents the matter Lagrangian for perfect fluid and R is the Ricci-scalar curvature. With a matter Lagrangian [Formula: see text], a flat FLRW space–time metric and an arbitrary function [Formula: see text], where [Formula: see text] is a positive model parameter, we have derived the field equations of this model. By using the Hubble function, we have been able to solve the energy conservation equation and create a relationship between [Formula: see text], [Formula: see text] and [Formula: see text]. Using the most recent two observational datasets as 32 [Formula: see text] and 1048 Pantheon SNe Ia datasets, we conducted MCMC analysis. We have obtained best fit values of model parameters with [Formula: see text] errors and using these values, we have explored the cosmological properties of the model. We have performed om diagnostic analysis for the model and estimated the present age of the universe. Thus our derived model presents a transit phase decelerating to accelerating model without dark energy term [Formula: see text]. We found that the effective equation of state parameter is in the range [Formula: see text] over [Formula: see text] with present value [Formula: see text].

Static Spherically Symmetric Perfect Fluid Solutions in Teleparallel F(T) Gravity

In this paper, we investigate static spherically symmetric teleparallel F(T) gravity containing a perfect isotropic fluid. We first write the field equations and proceed to find new teleparallel F(T) solutions for perfect isotropic and linear fluids. By using a power-law ansatz for the coframe components, we find several classes of new non-trivial teleparallel F(T) solutions. We also find a new class of teleparallel F(T) solutions for a matter dust fluid. After, we solve the field equations for a non-linear perfect fluid. Once again, there are several new exact teleparallel F(T) solutions and also some approximated teleparallel F(T) solutions. All these classes of new solutions may be relevant for future cosmological and astrophysical applications.

The impact of viscosity and anisotropy on cosmic expansion in [formula omitted] gravity

In modified gravity theories, such as f(Q,T) gravity, the concept of dark energy arises from alterations to the gravitational field equations, often manifesting as purely geometrical effects. This perspective opens up intriguing possibilities, suggesting that a universe undergoing cosmic acceleration could be explained by a bulk viscous fluid coupled with a modified gravity theory. In this paper, we introduce a model describing the LRS Bianchi type-I spacetime filled with a viscous fluid within the framework of f(Q,T) gravity. By assuming that the universe is dominated by non-relativistic viscous matter, we derive an exact solution to the field equations for the Hubble parameter H(z) as a function of redshift z. We assess the viability of the proposed f(Q,T) model by fitting it to observational datasets and explore several key physical properties of our cosmological model, including the deceleration parameter, jerk parameter, anisotropy parameter, and Om(z) diagnostics. For the present-day values of the parameters, we obtain: zt=0.80−0.003+0.004, q0=−0.45±0.01, j0=0.63±0.12, and Δ=0.38±0.09 at the 1−σ confidence level. In addition, our findings indicate that our f(Q,T) model, dominated by bulk viscous dark energy, displays quintessence-like behavior according to the Om(z) diagnostic, with a negative slope across all redshift values. We conclude that our study contributes to a deeper understanding of cosmic dynamics and the role of viscosity in cosmological models.

Characterization of continuous homomorphisms on entire slice monogenic functions

Abstract This paper is inspired by a class of infinite order differential operators arising in quantum mechanics. They turned out to be an important tool in the investigation of evolution of superoscillations with respect to quantum fields equations. Infinite order differential operators act naturally on spaces of holomorphic functions or on hyperfunctions. Recently, infinite order differential operators have been considered and characterized on the spaces of entire monogenic functions, i.e. functions that are in the kernel of the Dirac operators. The focus of this paper is the characterization of infinite order differential operators that act continuously on a different class of hyperholomorphic functions, called slice hyperholomorphic functions with values in a Clifford algebra or also slice monogenic functions. This function theory has a very reach associated spectral theory and both the function theory and the operator theory in this setting are subjected to intensive investigations. Here we introduce the concept of proximate order and establish some fundamental properties of entire slice monogenic functions that are crucial for the characterization of infinite order differential operators acting on entire slice monogenic functions.

An Approximate Kerr-Newman-like Metric Endowed with a Magnetic Dipole and Mass Quadrupole

Abstract Approximate all-terrain spacetimes for astrophysical applications are presented. The metrics possess five relativistic multipole moments,
namely mass, rotation, mass quadrupole, charge, and magnetic dipole moment. All these spacetimes approximately satisfy the Einstein-
Maxwell field equations. The first metric is generated by means of the Hoenselaers-Perjés method from given relativistic multipoles. The
second metric is a perturbation of the Kerr-Newman metric, which makes it a relevant approximation for astrophysical calculations. The
last metric is an extension of the Hartle-Thorne metric that is important for obtaining internal models of compact objects perturbatively.
The electromagnetic field is calculated using Cartan forms for locally nonrotating observers. These spacetimes are relevant to infer properties of compact objects from astrophysical observations. Furthermore, the numerical implementations of these metrics are straightforward, making them versatile for simulating the potential astrophysical applications.

Topological interpretation of extremal and Davies-type phase transitions of black holes

Topological arguments are currently being used as a novel scheme to discern the properties of black holes while ignoring their detailed structure and specific field equations. Among various avenues of black hole physics, where this novel approach is being utilized, the phase transition in black hole thermodynamics lies at the forefront. There are several types of phase transition in black holes; such as the van der Waals type phase transition, Davies-type phase transition, extremal phase transition, and Hawking-Page (HP) transition. So far, the topological interpretation, where the critical point has been identified with the non-zero topological charge, has been obtained only for the van der Waals type phase transition and HP transition in different spacetimes. To complete the picture, here we provide the same interpretation for two other phase transitions: Davies-type phase transition and extremal phase transition. The entire analysis is general and is valid for any spacetime where these types of phase transitions are observed. More importantly, our analysis suggests that amid the apparent differences in these phase transitions, they share the same topological characteristics, i.e. non-zero topological charge arising from different thermodynamic potentials in different types of phase transition.

Anisotropy Induced by Electric Charge: A Computational Analytical Approach

This paper presents a novel class of interior solutions for anisotropic stars under the imposition of a self-similar symmetry. This means proposing exact solutions to the Einstein field equations to describe charged matter distribution with radiation flow. The Einstein–Maxwell system by employing specific choices of mass function is formulated to describe the gravitational collapse of charged, anisotropic, spherically symmetric distributions using the Schwarzschild metric. Two ordinary differential equations governing the dynamics are derived by matching a straightforward solution of the symmetry equations to the charged exterior (Reissner–Nordström–Vaidya). Models with satisfactory physical behavior are constructed by extensively exploring self-similar solutions for a set of parameters and initial conditions. Finally, the paper presents the evolution of physical variables and the collapsing radius, demonstrating the inevitable collapse of the matter distribution.

Cosmological implications of the Weyl geometric gravity theory

We consider the cosmological implications of the Weyl geometric gravity theory. The basic action of the model is obtained from the simplest conformally invariant gravitational action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and a matter term, respectively. The total action is linearized in the Weyl scalar by introducing an auxiliary scalar field. To maintain the conformal invariance of the action the trace condition is imposed on the matter energy–momentum tensor, thus making the matter sector of the action conformally invariant. The field equations are derived by varying the action with respect to the metric tensor, the Weyl vector field, and the scalar field, respectively. We investigate the cosmological implications of the theory, and we obtain first the cosmological evolution equations for a flat, homogeneous and isotropic geometry, described by Friedmann–Lemaitre–Robertson–Walker metric, which generalize the Friedmann equations of standard general relativity. In this context we consider two cosmological models, corresponding to the vacuum state, and to the presence of matter described by a linear barotropic equation of state. In both cases we perform a detailed comparison of the predictions of the theory with the cosmological observational data, and with the standard Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} CDM model. By assuming that the presence of the Weyl geometric effects induce small perturbations in the homogeneous and isotropic cosmological background, and that the anisotropy parameter is small, the equations of the cosmological perturbations due to the presence of the Weyl geometric effects are derived. The time evolution of the metric and matter perturbations are explicitly obtained. Therefore, if Weyl geometric effects are present, the Universe would acquire some anisotropic characteristics, and its geometry will deviate from the standard FLRW one.

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.

Wormhole inducing exponential expansion in R2 gravity

Wormholes are considered both from the Wheeler deWitt equation, as well as from the field equations in the Euclidean background of Robertson Walker mini-superspace in [Formula: see text] gravity. Quantum wormhole satisfies Hawking Page wormhole boundary condition in the Euclidean background of mini-superspace, however, in the Lorentzian background wave functional turns to the usual oscillatory function. The Euclidean field equations for [Formula: see text] lead to the wormhole configuration, as well as oscillating universe in Euclidean time [Formula: see text]. The oscillating universe in Euclidean time [Formula: see text] transforms to an expanding universe only for [Formula: see text] in Lorentz time [Formula: see text] under analytic continuation [Formula: see text] and asymptotically leads to an exponential solution. An Euclidean wormhole in the very early era evolves to an oscillating universe in [Formula: see text], thereafter crossing deSitter radius transition to an inflationary era is evident at later epoch only for [Formula: see text].

Exploring the physical properties of strange star SAXJ1808.4–3658 in rainbow gravity

This study investigated the formation and evolution of a strange star known as SAX.J1808.4–3658 in the Krori–Barua Rainbow spacetime, resulting from the collapse of string fluid. The study examined the dynamical variables derived from the field equations, taking into consideration the influence of the particle’s energy on the mass density, pressure, and string tension. Additionally, various techniques were employed to analyze the physical properties, including gradients, energy conditions, anisotropy, stability, the Tolman–Oppenheimer–Volkoff equation, mass function, compactness, and red-shift. The study’s findings revealed that the strange star SAX.J1808.4–3658 satisfies all the conditions necessary for its evolution from an anisotropic string fluid. This discovery suggests that strange stars might have emerged during the string-oriented quark era of the Universe. The researchers presented all the physical quantities within the frameworks of both rainbow gravity and general relativity, while also utilizing graphical representations to aid in comprehending the study’s findings. The energy conditions and anisotropy were found to be fulfilled, indicating the stability of the strange star. Furthermore, the Tolman–Oppenheimer–Volkoff equation was employed to determine the maximum mass of the strange star, which was found to align with observational data.

Cosmographic and matter bounce scenario in modified torsion gravity

In this manuscript, we investigate the matter bounce cosmological implications in the context of f(T,τ) gravity (T represents the torsion scalar whereas τ is the trace of the energy–momentum tensor). We construct the field equations for spatially flat homogeneous and isotropic space–time with perfect fluid configuration. We consider the two particular forms of scale factor inspired by loop-quantum cosmology to investigate the matter bounce mechanism. In this regard, we examine the graphical behavior of cosmological as well as dynamical parameters at and in the neighborhood of bounce point. Furthermore, the stability via perturbation technique and energy conditions are also discussed. It is concluded that all the cosmographic tests favor the bouncing cosmology for an appropriate choice of model parameters. It is worth mentioning that considered models are stable and energy conditions are violated at the bouncing point as well as in its vicinity leading to a successful bouncing scenario.

The instability of the inner horizon of the quantum-corrected black hole

We analyse the stability of the inner horizon of the quantum-corrected black hole which is proposed in loop quantum gravity as the exterior of the quantum Oppenheimer–Snyder and Swiss Cheese models. It is shown that the flux and energy density of a test scalar field measured by free-falling observers are both divergent near the Cauchy horizon. By considering the generalized Dray–’t Hooft–Redmond relation which is independent of the field equation, we find that the mass inflation always happens and the scalar curvature and Kretschmann scalar are also divergent on the inner horizon. These suggest that the inner horizon is unstable and will probably turn into a null singularity.The results support the strong cosmic censorship hypothesis.However, this also implies that the quantum corrected model may not be the definitive endpoint as a regular black hole.Besides, it further proposes that it may be challenging to observe the astronomical phenomenon which depends on the existence of the inner horizon of the black hole

Signature of f(R) gravity via Lemaître–Tolman–Bondi inhomogeneous perturbations

We analyze inhomogeneous cosmological models in the local Universe, described by the Lemaître–Tolman–Bondi (LTB) metric and developed using linear perturbation theory on a homogeneous and isotropic Universe background. Focusing on the different evolution of spherical symmetric inhomogeneities, we compare the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}LTB model, in which the cosmological constant Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} is included in the LTB formalism, with inhomogeneous cosmological models based on fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} modified gravity theories viewed in the Jordan frame. We solve the system of field equations for both inhomogeneous cosmological models adopting the method of separation of variables: we integrate analytically the radial profiles of local perturbations, while their time evolution requires a numerical approach. The main result of the analysis concerns the different radial profiles of local inhomogeneities due to the presence of a non-minimally coupled scalar field in the Jordan frame of fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} gravity. While radial perturbations follow a power-law in the Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}LTB model, Yukawa-like contributions appear in the fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} theory. Interestingly, this latter peculiar behavior of radial profile is not affected by the choice of the fR\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f\\left( R\\right) $$\\end{document} functional form. The numerical solution of time-dependent perturbations exhibits a non-diverging profile. This work suggests that investigations about local inhomogeneities in the late Universe may allow us to discriminate if the present cosmic acceleration is caused by a cosmological constant term or a modified gravity effect.

New algorithm based on Hermite wavelets and Green’s function to solve Thomas-Fermi type differential equations

This article introduces a novel method using Hermite wavelets and Green’s function to solve Thomas-Fermi-type equations with specific boundary conditions. The equation is first transformed into an integral form and then expanded using Hermite wavelets to create an algebraic expression. The collocation technique generates a set of nonlinear equations, solved iteratively by methods like Newton-Raphson. Several examples demonstrate the method’s effectiveness and accuracy. It is useful for a range of linear and nonlinear differential equations in various fields. Comparative analysis shows it is more accurate and computationally efficient than traditional methods. All computations are performed using MAT LAB.

The binding of cosmological structures by massless topological defects

ABSTRACT Assuming spherical symmetry and weak field, it is shown that if one solves the Poisson equation or the Einstein field equations sourced by a topological defect, i.e. a singularity of a very specific form, the result is a localized gravitational field capable of driving flat rotation (i.e. Keplerian circular orbits at a constant speed for all radii) of test masses on a thin spherical shell without any underlying mass. Moreover, a large-scale structure which exploits this solution by assembling concentrically a number of such topological defects can establish a flat stellar or galactic rotation curve, and can also deflect light in the same manner as an equipotential (isothermal) sphere. Thus, the need for dark matter or modified gravity theory is mitigated, at least in part.

Cosmic evolution in f(Q,T) gravity with observational constraints: A comparative analysis with ΛCDM

In this investigation, we explore the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model within the framework of the f(Q,T) modified gravitation theory. This theory was recently introduced to account for the late cosmic acceleration of our Universe. To address the modified field equations derived from the f(Q,T)=αQ+βQ2+kT form of the f(Q,T) function, we assume a redshift-dependent deceleration parameter. Our goal is to impose observational constraints on the model parameters, ensuring its viability and alignment with the observable Universe's characteristics. The observational constraints are derived from a diverse dataset, encompassing Cosmic Chronometers (CC), type Ia supernovae (SNIa), Baryon Acoustic Oscillation (BAO), Gamma Ray Burst (GRB), and Quasar (Q) measurements. Employing the Markov Chain Monte Carlo (MCMC) technique with the CC + BAO + SNIa + GRB + Q dataset, we conduct simulations to obtain constraints on the model parameters. In the subsequent segments of the study, we delve into the evolution of the constrained model from the past to the present. We utilize metrics such as deceleration and jerk parameters, statefinder pairs, the Om diagnostic, and various physical parameters of the model. This detailed analysis allows us to scrutinize the transition of the model from a decelerating phase in the past to the late accelerating phase, comparing its evolution with established dark energy models. To assess the model's goodness of fit, we employ statistical criteria, including the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), P-value, and L-statistic. Remarkably, these criteria consistently indicate that the ΛCDM model is slightly favored by the observational data compared to the proposed cosmological model.

Probing the Bardeen–Kiselev black hole with the cosmological constant caused by Einstein equations coupled with nonlinear electrodynamics using quasinormal modes and greybody bounds

In this work, we investigate a static and spherically symmetric Bardeen–Kiselev black hole (BH) with the cosmological constant, which is a solution of the Einstein-non-linear Maxwell field equations. We compute the quasinormal frequencies for the Bardeen–Kiselev BH with the cosmological constant due to electromagnetic and gravitational perturbations. By varying the BH parameters, we discuss the behavior of both real and imaginary parts of the BH quasinormal frequencies and compare these frequencies with the Reissner–Nordström–de Sitter BH surrounded by quintessence (RN-dSQ). Interestingly, it is shown that the responses of the Bardeen–Kiselev BH with the cosmological constant and the RN-dSQ under electromagnetic perturbations are different when the charge parameter q, the state parameter w and the normalization factor c are varied; however, for the gravitational perturbations, the responses of the Bardeen–Kiselev BH with the cosmological constant and the RN-dSQ are different only when the charge parameter q is varied. Therefore, compared with the gravitational perturbations, the electromagnetic perturbations can be used to understand nonlinear and linear electromagnetic fields in curved spacetime separately. Another interesting observation is that, due to the presence of Kiselev quintessence, the electromagnetic perturbations around the Bardeen–Kiselev BH with the cosmological constant damps faster and oscillates slowly; for the gravitational perturbations, the quasinormal mode decays slowly and oscillates slowly. We also study the reflection and transmission coefficients along with the absorption cross section in the Bardeen–Kiselev BH with the cosmological constant; it is shown that the transmission coefficients will increase due to the presence of Kiselev quintessence.