Einstein-Maxwell Field Equations Research Articles

An approximate Kerr–Newman-like metric endowed with a magnetic dipole and mass quadrupole

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 using 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 non-rotating observers. These spacetimes are relevant for inferring properties of compact objects from astrophysical observations. Furthermore, the numerical implementations of these metrics are straightforward, making them versatile for simulating potential astrophysical applications.

Charged compact star with Gaussian density profile showing spin retardation

A charged compact star is modelled within the framework of general relativity and electromagnetism to investigate the intricate complexities arising from charge accumulation through the accretion of surrounding charged baryonic matter, charged dark matter, or both. The Einstein-Maxwell field equations are solved for the compact star PSRJ0740+6620 in anisotropic regime by employing a Gaussian type density profile over a coherent background. A radially modulated exponential function is used as a seed ansatz for coherently connecting the class-one type metric. The structural stability and feasibility are then probed through physical bounds on stellar parameters at equilibrium. The key findings associated with charge accretion emphasised: (i). the existence of a transition zone close to mass M∈[1.262,1.271]M⊙ and radius R∈[12.497,12.505]km, indicating the formation of a core–shell type stellar structure (ii). the plane shifting of intrinsic force fields and (iii) the spin retardation, both suggest a non-vanishing spin-charge coupling between the stellar spin and the accreted charge, whether it be from baryonic matter, dark matter, or both.

Particle motion and tidal force in a non-vacuum-charged naked singularity

We investigate the gravitational field of a charged, non-vacuum, non-rotating, spherically symmetric body of mass M assuming a static solution to the Einstein–Maxwell field equations. We show the characteristics of perihelion precession of orbits in the case of charged naked singularity (CNS) spacetime. Here we discuss some novel features of light-like geodesics in this spacetime. We also discuss the comparative study of tidal force in the null singularity spacetime and charged naked singularity spacetime.

Some new relativistic charged models with anisotropic pressure

In this paper, we found new classes of solutions to the Einstein-Maxwell field equations with matter anisotropic distribution incorporating a particular form of electric field intensity within the framework of general relativity. We use a metric potential or ansatz that depends on an adjustable parametern in order to get the new solutions. We generated new models of compact stars with n=1 and n=2. Graphical analysis allows us to conclude that the new models satisfy all the physical characteristics for astrophysical objects and can be very useful in the study and description of compact structures. We obtained models consistent with the pulsars PSR J1311-3430 and PSR J0952–0607.

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}$$f({\\mathcal {G}})$$\\end{document} gravity

In this manuscript, we use the conformal killing vectors to solve the Einstein–Maxwell field equations in the background of modified f(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f({\\mathcal {G}})$$\\end{document} gravity. We consider the observational data for four different stars namely PSRJ1614-2230\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$PSR~J1614-2230$$\\end{document}, PSRJ1930+327\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$PSR ~J1930+327$$\\end{document}, CenX-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Cen~X-3$$\\end{document} and VelaX-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Vela~X-1$$\\end{document} 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(G)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f({\\mathcal {G}})$$\\end{document} 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.

Electromagnetic effects on anisotropic expansion-free fluid content

The major goal of this work is to find solutions of Einstein–Maxwell field equations for anisotropic, expansion-free, non-static, spherically distributed matter content. The analytical models that highlight the major benefit of simplicity are shown and this makes it possible to use them as a toy model to illustrate how cavities evolve. Furthermore, the transport equations, quasi-homologous constraints and the junction conditions are also evaluated along with their useful implications. Eventually, the consequences of electric force on this system are summed up in the last section.

Physical quark star model with generalized logarithmic anisotropy

A new quark star model for a charged anisotropic stellar object is generated using the Einstein–Maxwell field equations. We use a metric function, linear equation of state, and a new measure of anisotropy in form of logarithmic function to formulate the model. For particular choices of parameters in the anisotropic measure, some anisotropic and isotropic models are regained as a special case. Physical analysis indicates that matter variables and gravitational potentials in the model are well behaved. The generated model satisfies the energy, regularity, causality, and stability conditions. The speed of sound is consistent with quark stars.

A charged star with geometric Karmarkar condition

In this paper, we analyse an analytical solution of the Einstein–Maxwell field equations that considers matter with anisotropic pressures in a static and spherically symmetric geometry. We report the manner in which we obtained the solution, which is by means of the Karmarkar condition. For the model, we assume a state equation that describes the interaction of matter from quarks P = (c 2 ρ − 4B g )/3 and we consider the presence of electric charge, which can generate that the radial and tangential pressures are not equal. In a graphic manner, we analyse the physical properties of the model, taking as the observational data those of mass 1M ⊙ and radius 7.69 km which were reported for the star Her X-1. The charge values are found between 5.57 × 1018C ≤ Q ≤ 1.31 × 1020C and the interval of the Bag constant B g ∈ [118.7, 122.13]MeV/fm3. Also, we show the stability of the configuration by means of the static stability criteria of Harrison–Zeldovich–Novikov , as well as in regards to infinitesimal radial adiabatic perturbation, since the adiabatic index γ > 3.3 which guarantees the stability of the solution.

Role of decoupling measure on the complexity factor and isotropization of the charged anisotropic spheres

An electromagnetic field is a consequential aspect of the space carried by moving electric charges. The contemporaneous interaction of Einstein–Maxwell field could be provoked by the dispersing electro-magnetic waves owing to the warping of the spacetime. Within the complete geometric deformation scenario, current work is devoted to exploring the substantial impact of an electromagnetic field on the anisotropic spherically symmetric structures that are taken to be the seed source, and then augment to the additional source. In this case, the gravitational decoupling strategy and embedding Class-I constraint will be used as two techniques to address the issue. We compute the Einstein–Maxwell field equations for the desired configuration. The transformed metric potentials corresponding to the temporal and radial components are then applied to formulate the two distinct sets of field equations. Through the Kuchowicz-ansatz for the seed metric potential, we enforce the Karmarkar constraint to grasp the entire gravitational aspect of a static compact sphere together with the effects of charged anisotropic pressure. The uniqueness of our study is that we used isotropization and disappearing complexity requirements to derive the deformation function within the bounds of a charged scenario. Thereby, two solutions to the associated relativistic equations are then presented for physical validity. We address the fact that the existence of charged pressure anisotropy in the bounded sphere has a consequential influence on governing its stability. Furthermore, it is identified that the decoupling-constant magnitude controls the energy flow within both the generically charged fluid and the fluid matter composition.

Krori–Barua Bardeen compact stars in [formula omitted] gravity

The current study emphasizes the impact of electric charge for static spherically symmetric stellar structures using isotropic distribution in f(R,T) theory of gravity. For this purpose, we assume the Krori–Barua metric potential, ν(r)=Br2+C and λ(r)=Ar2, where A,B and C are the unknowns constants. The simplified phenomenological MIT bag equation of state, p=13(ρ−4Bg), and a precise form of electrical charge distribution q(r)=Q(rR)3=χr3 to be evaluated for the solution of Einstein–Maxwell field equations. To get the value of unknown parameters of the compact structures, we compare the Krori–Barua spacetime to external Bardeen geometry. Moreover, we examine the physical attributes of compact objects by presuming three viable f(R,T) models. We analyze the graphical behavior of density and pressure, the Tolman–Oppenheimer–Volkov equation, energy conditions, mass function, surface redshift, and adiabatic index. It is recognized that all the obtained results deliver emphatic evidence for the stability of our considered realistic stars.

Charged anisotropic models with complexity-free condition

This paper uses the definition of complexity for a static spherically symmetric spacetime and extends it to the case of charged distribution. We formulate the Einstein–Maxwell field equations corresponding to the anisotropic interior and calculate two different mass functions. We then take Reissner–Nordström metric as an exterior spacetime to find the matching conditions at the spherical boundary. Some scalars are developed from the orthogonal splitting of the curvature tensor, and we call one of them, i.e., YTF as the complexity factor for the considered setup. Further, the three independent field equations are not enough to close the system, therefore, we adopt the complexity-free condition. Along with this condition, we consider three constraints that lead to different models. We also present the graphical interpretation of the resulting solutions by choosing some particular values of parameters. We conclude that the models corresponding to pr=0 and a polytropic equation of state show viable and stable behavior everywhere.

Shielding a charged black hole

We describe a shielding mechanism for a charged black hole immersed in a background involving charged matter fields, solely arising from the Einstein-Maxwell field equations. In particular, we consider a charged generalization of the Einstein cluster, that is a charged black hole surrounded by an effective fluid model for a partially charged dust cloud. We show that the shielding mechanism, arising thereof, is generic and appears in a different parametrization of the problem as well. In this process, we provide the most general electrovacuum solution in a spacetime region devoid of charges, but in the presence of a static and spherically symmetric charge distribution elsewhere. Side by side, we also introduce a convenient parametrization, providing the global solution of the Einstein-Maxwell's field equations in the presence of a charged black hole within the environment of charged fluid. We also comment on the nature of the photon sphere, shadow radius and the eikonal quasi-normal modes in the Einstein-Maxwell cluster.

Complete Evaporation of Black Holes and Page Curves

The problem of complete evaporation of a Schwarzschild black hole, the simplest spherically symmetric vacuum solution of the Einstein field equation, posed by Hawking, is that when the black hole mass M disappears, an explosion of temperature T=1/8πM takes place. We consider the Reissner–Nordstrom black hole, a static spherically symmetric solution to the Einstein–Maxwell field equations, and show that if mass M and charge Q<M satisfy the bound Q>M−CM3, C>0 for small M, then the complete evaporation of black holes without blow-up of temperature is possible. We describe curves on the surface of state equations such that the motion along them provides complete evaporation without temperature explosion. In this case, the radiation entropy follows the Page curve and vanishes at the end of evaporation. Similar results for rotating Kerr, Schwarzschild–de Sitter and Reissner–Nordstrom-(Anti)-de Sitter black holes are discussed.

Study of Compact Stars with Buchdahl Potential in 5-D Einstein-Gauss-Bonnet Gravity

The general theory of relativity has allowed a better understanding of the structure of universe. One of the fundamentals problems in the general relativity is finding exact solutions of the Einstein-Maxwell field equations. Some solutions found applications in astrophysics, cosmology and more recently in the developments inspired by string theory. In this paper, we presented a compact object model in the framework of Einstein-Gauss-Bonnet gravity (EGB) with a linear equation of state considering a metric potential proposed for Buchdahl (1959). The new obtained models satisfy all physical requirements of a physically reasonable stellar object. We analyzed the effect of the Gauss-Bonnet coupling constant α on the main physical characteristics of the model. We checked that the radial pressure, energy density and anisotropy are well defined and are regular in the interior of the star and are dependent of the values of the coupling constant.

Relativistic polytropic models of charged anisotropic compact objects

In this paper, we introduce new viable solutions to the Einstein-Maxwell field equations by incorporating the features of anisotropic matter distributions within the realm of the general theory of relativity (). To obtain these solutions, we employed the Finch-Skea spacetime, along with a generalized polytropic equation of state (). We constructed various models of generalized polytropes by assuming different values of the polytropic index, i.e., , and . Next, numerous physical characteristics of these considered models were studied via graphical analysis, and they were found to obey all the essential conditions for astrophysical compact objects. Furthermore, such outcomes of charged anisotropic compact star models could be reproduced in various other cases including linear, quadratic, and polytropic

A generalised double layered model with polytropic and quadratic equations of state

This study generates a new exact model for a massive stellar spheres by utilising the Einstein–Maxwell field equations. The model has two interior regions with distinct equations of state (EoS): the polytropic EoS at the core region, and quadratic EoS at the envelope region. Variation of the physical features in the interior of star affirms that the matter variables, gravitational potentials and other physical quantities are consistent with massive stellar bodies. Interestingly, our model can regain solutions of the two-layered model generated by Mardan, Noureen and Khalid. Matching of the layers in junctions is done with help of the Reissner–Nordstrom exterior spacetime. Using our model, stellar masses, and radii consistent with observations and well known stars are generated.

Strange Quark Star (SQS) in Tolman IV potential with density dependent B-parameter and charge

In this paper, the solutions of Einstein–Maxwell Field Equations for relativistic strange quark star in Tolman-IV potential considering MIT bag model EoS p=frac{1}{3}(rho -4B) of interior matter in presence of charge in higher dimensions is presented, where B is bag parameter. Here we consider density dependent B as it has more practical application. We note some interesting results. It is observed that interior of a strange quark star may contain bulk stable quarks as a whole having energy per baryon E_B<930.4 MeV/fm^3 or stable quark matter core enclosed by a thin metastable quark matter layer enveloped by unstable quark matter. It is also found that interior composition depends on the value of space-time dimension (D) and net charge (Q). The model presented in this paper satisfies all the necessary stability and energy conditions for a viable stellar configuration. We also note the maximum mass of stable strange quark star is 1.773 M_{odot } for density dependent B and 1.684 M_{odot } for constant B.

Study of a realistic model for electrically charged anisotropic stars with a simplest non-interacting quark matter equation of state

In this article a self bound quark star model that possesses some net electric charge is introduced. The quarks considered here are deconfined non-interacting Fermi gas. The solution has been found by solving Einstein-Maxwell field equations through MIT-bag equation of state and a metric potential. The obtained solution is further use to present a comparative studies of four compact stars 4U 1820-30, PSR J1903 + 327, Vela X-1 and PSR J1614-2230. The models are free from singularity, fulfil energy conditions, stability criteria and far within Buchdahl-Andreasson limit. Finally, we have predicted radii of these four compact objects.

Maximum mass of anisotropic charged strange quark stars in a higher dimensional approach (D ≥ 4)

In this article, a new class of solutions of Einstein-Maxwell field equations of relativistic strange quark stars obtained in dimensions , is shown. We assume that the geometry of space-time is pseudo-spheroid, embedded in Euclidean space of dimensions. The MIT bag model equation of state is employed to study the relevant properties of strange quark stars. For the causal and non-negative nature of the square of the radial sound velocity , we observe that some restrictions exist on the reduced radius , where R is a parameter related to the curvature of the space-time, and b is the radius of the star. The spheroidal parameter λ used here defines the metric potential of the component, which is pseudo-spheroidal in nature. We note that the pressure anisotropy and charge have some effects on λ. The maximum mass for a given surface density () or bag constant assumes a maximum value in dimension and decreases for other values of D. The generalized Buchdahl limit for a higher dimensional charged star is also obeyed in this model. We observe that in this model, we can predict the mass of a strange quark star using a suitable value of the electric charge (Q) and bag constant (B). Energy and stability conditions are also satisfied in this model. Stability is also studied considering the dependence of the Lagrangian perturbation of radial pressure () on the frequency of normal modes of oscillations. The tidal Love number and tidal de-formability are also evaluated.

Electrically charged isotropic stars with Tolman[formula omitted] model

The paper discusses novel solutions of Einstein–Maxwell field equations by describing the static spherically symmetric isotropic matter distributions and electrifying a well-known uncharged model in general relativity. We start by selecting a Tolman−IV type potential for the gravitational potential gtt and a physically reasonable choice for the electric field intensity E in view to exploiting isotropic sources of matter which act as a basis for generating confined compact stars. These solutions are constructed to match interior space–time geometries with exterior Reissner–Nordström solution at the pressure-free boundary. The viability of the models is compared with observational data of some heavy pulsars coming from the Neutron Star Interior Composition Explorer (NICER). In particular, Her X-1, SAX J1808.4-3658, and 4U 1538-52 are considered. We stretch our findings by measuring the mass–radius relationship for our developed model, which reveals that the predicted radii via the M–R curve are lying in the range of R≤14–16km. Moreover, the generated model satisfies all of the required major physical properties for realistic compact stars. We can also say that this approach can play a vital role in encouraging the study of the electrification of well-known neutral stellar systems.