Einstein-Maxwell Field Equations Research Articles

Stable photon orbits in stationary axisymmetric electrovacuum spacetimes

We investigate the existence and phenomenology of stable photon orbits (SPOs) in stationary axisymmetric electrovacuum spacetimes in four dimensions. First, we review the classification of equatorial circular photon orbits on Kerr-Newman spacetimes in the charge-spin plane. Second, using a Hamiltonian formulation, we show that Reissner-Nordstr\"om di-holes (a family encompassing the Majumdar-Papapetrou and Weyl-Bach special cases) admit SPOs, in a certain parameter regime that we investigate. Third, we explore the transition from order to chaos for typical SPOs bounded within a toroidal region around a di-hole, via a selection of Poincar\'e sections. Finally, for general axisymmetric stationary spacetimes, we show that the Einstein-Maxwell field equations allow for the existence of SPOs in electrovacuum; but not in pure vacuum.

Internal composition of proto-neutron stars under strong magnetic fields

In this work, we study the effects of magnetic fields and rotation on the structure and composition of proto-neutron stars (PNS's). A hadronic chiral SU(3) model is applied to cold neutron stars (NS) and proto-neutron stars with trapped neutrinos and at fixed entropy per baryon. We obtain general relativistic solutions for neutron and proto-neutron stars endowed with a poloidal magnetic field by solving Einstein-Maxwell field equations in a self-consistent way. As the neutrino chemical potential decreases in value over time, this alters the chemical equilibrium and the composition inside the star, leading to a change in the structure and in the particle population of these objects. We find that the magnetic field deforms the star and significantly alters the number of trapped neutrinos in the stellar interior, together with strangeness content and temperature in each evolution stage.

Solution of the Einstein–Maxwell equations with anisotropic negative pressure as a potential model of a dark energy star

We have obtained a new class of solutions for the Einstein–Maxwell field equations for static spherically symmetric space–times by considering the negative anisotropic pressures, which represents a potential model of a dark energy star. We take the equation of state pr = −ρ, where pr is the radial pressure and ρ is the density. We have also checked that for these solutions metric coefficients, mass density, radial pressure, transverse pressure, electric field, and current density are well defined for suitable values of the parameters involved in the solution. These exact solutions can be used to develop models of dark energy stellar interiors satisfying all physical constraints except for the causality condition, which cannot be satisfied for the equation of state considered here, and which is arguably not an applicable physical constraint for dark matter–energy.

New charged anisotropic compact models

We find new exact solutions to the Einstein-Maxwell field equations which are relevant in the description of highly compact stellar objects. The relativistic star is charged and anisotropic with a quark equation of state. Exact solutions of the field equations are found in terms of elementary functions. It is interesting to note that we regain earlier quark models with uncharged and charged matter distributions. A physical analysis indicates that the matter distributions are well behaved and regular throughout the stellar structure. A range of stellar masses are generated for particular parameter values in the electric field. In particular the observed mass for a binary pulsar is regained.

Test particles in a magnetized conformastatic spacetime

A class of exact conformastatic solutions of the Einstein-Maxwell field equations is presented in which the gravitational and electromagnetic potentials are completely determined by a harmonic function. We derive the equations of motion for neutral and charged particles in a spacetime background characterized by this class of solutions. As an example, we focus on the analysis of a particular harmonic function, which generates a singularity-free and asymptotically flat spacetime that describes the gravitational field of a punctual mass endowed with a magnetic field. In this particular case, we investigate the main physical properties of equatorial circular orbits. We show that due to the electromagnetic interaction, it is possible to have charged test particles which stay at rest with respect to a static observer located at infinity. Additionally, we obtain an analytic expression for the perihelion advance of test particles and the corresponding explicit value in the case of a punctual magnetic mass. We show that the analytical expressions obtained from our analysis are sufficient for being confronted with observations in order to establish whether such objects can exist in nature.

Class of Charged Fluid Balls in General Relativity

In the present study, we have obtained a new analytical solution of combined Einstein-Maxwell field equations describing the interior field of a ball having static spherically symmetric isotropic charged fluid within it. The charge and electric field intensity are zero at the center and monotonically increasing towards the boundary of the fluid ball. Besides these, adiabatic index is also increasing towards the boundary and becomes infinite on it. All other physical quantities such as pressure, density, adiabatic speed of sound, charge density, adiabatic index are monotonically decreasing towards the surface. Causality condition is obeyed at the center of ball. In the limiting case of vanishingly small charge, the solution degenerates into Schwarzchild uniform density solution for electrically neutral fluid. The solution joins smoothly to the Reissner-Nordstrom solution over the boundary. We have constructed a neutron star model by assuming the surface density . The mass of the neutron star comes with radius 14.574 km.

Effective Perihelion Advance and Potentials in a Conformastatic Background with Magnetic Field

Exact solutions of the Einstein-Maxwell field equations for a conformastatic metric with magnetized sources are investigated. In this context, effective potentials are studied in order to understand the dynamics of the magnetic field in galaxies. We derive the equations of motion for neutral and charged particles in a spacetime background characterized by this class of solutions. In this particular case, we investigate the main physical properties of the equatorial circular orbits and related effective potentials. In addition, we obtain an effective analytic expression for the perihelion advance of test particles. Our theoretical predictions are compared with the observational data calibrated with the ephemerides of the planets of the solar system and the Moon (EPM2011). In general, we show that the magnetic punctual mass predicts values that are in better agreement with observations than the values predicted in Einstein’s gravity alone.

Singularity free charged anisotropic solutions of Einstein–Maxwell field equations in general relativity

In this paper, we present generalization of anisotropic analogue of charged Heintzmann’s solution of the general relativistic field equations in curvature coordinates. These exact solutions are stable and well behaved in all respect for a wide range of anisotropy parameter and charge parameter. We have found that these new solutions are suitable for the modeling of super dense stars like neutron stars and quark stars because they yield a wide range of masses and radii with simple mathematical expressions. By tuning different values of the few parameters, we can model various neutron stars and quark stars which are compatible with the experimentally observed values of masses and radii. Therefore, we have synchronized our solution with the observed values of some of the compact stars XTE J1739 − 217, EXO 0748 − 676, PSR J1614 − 2230, PSR J0348 + 0432 and PSR B0943 + 10.

Some new Wyman–Leibovitz–Adler type static relativistic charged anisotropic fluid spheres compatible to self-bound stellar modeling

In this work some families of relativistic anisotropic charged fluid spheres have been obtained by solving the Einstein–Maxwell field equations with a preferred form of one of the metric potentials, and suitable forms of electric charge distribution and pressure anisotropy functions. The resulting equation of state (EOS) of the matter distribution has been obtained. Physical analysis shows that the relativistic stellar structure for the matter distribution considered in this work may reasonably model an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself (e.g., electrically charged bare strange stars). Furthermore these models permit a simple method of systematically fixing bounds on the maximum possible mass of cold compact electrically charged self-bound stars. It has been demonstrated, numerically, that the maximum compactness and mass increase in the presence of an electric field and anisotropic pressures. Based on the analytic models developed in this present work, the values of some relevant physical quantities have been calculated by assuming the estimated masses and radii of some well-known potential strange star candidates like PSR J1614-2230, PSR J1903+327, Vela X-1, and 4U 1820-30.

Anisotropic charged fluids with Chaplygin equation of state in ( 2 + 1 ) $(2+1)$ dimension

Present paper provides a new non-singular model for anisotropic charged fluid sphere in (\(2+1\))-dimensional anti de-Sitter spacetime corresponding to the exterior BTZ spacetime (Banados et al., Phys. Rev. Lett. 69:1849, 1992). The model is obtained by assuming Krori and Barua (KB) ansatz (Krori and Barua, J. Phys. A, Math. Gen., 8:508, 1975). To solve the Einstein-Maxwell field equations we choose modified Chaplygin gas. Various physical quantities have been discussed and from our analysis we show that our model satisfies all required physical conditions for representing compact stars.

Charged analogue of Vlasenko–Pronin superdense star with variable cosmological term

The set of three static spherically symmetric solutions of the Einstein–Maxwell field equations by Maurya and Gupta, Astrophys. Space Sci.333, 149 (2011) are modified by introducing the variable cosmological term. Motivated by Tiwari et al, Indian J. Pure Appl. Math.31, 1017 (2000), some particular values of the cosmological term are taken to obtain well-behaved solutions of the Einstein–Maxwell field equations. All the results given by Maurya and Gupta can be obtained as particular cases of our solutions by choosing a cosmological term equal to zero.

Spherically symmetric charged compact stars

In this article we consider the static spherically symmetric metric of embedding class 1. When solving the Einstein-Maxwell field equations we take into account the presence of ordinary baryonic matter together with the elec- tric charge. Specific new charged stellar models are obtained where the solutions are entirely dependent on the electromag- netic field, such that the physical parameters, like density, pressure etc. do vanish for the vanishing charge. We system- atically analyze altogether the three sets of Solutions I, II, and III of the stellar models for a suitable functional relation of ν(r ). However, it is observed that only the Solution I pro- vides a physically valid and well-behaved situation, whereas the Solutions II and III are not well behaved and hence not included in the study. Thereafter it is exclusively shown that the Solution I can pass through several standard physical tests performed by us. To validate the solution set presented here a comparison has also been made with that of the compact stars, like RX J 1856 − 37, Her X − 1, PSR 1937 + 21, PSRJ 1614 − 2230, and PSRJ 0348 + 0432, and we have shown the feasibility of the models.

An Analysis of Charged Anisotropic Star with de Sitter Spacetime

We propose a model for charged anisotropic star in de Sitter spacetime. We have taken Krori and Barua (J. Phys. A, Math. Gen. 8, 508, 1975) metric in de Sitter spacetime with non-zero cosmological constant. The model is free from singularity. We incorporate the existence of the cosmological constant on a small scale to study the structure of anisotropic charged star. To solve the Einstein-Maxwell field equations we assume the relation between the radial and transverse pressure as p t −p r =g q(r)2 r 2 (where g is a non-zero positive constant). The physical conditions inside the stellar model are also discussed.

Dynamic of charged planar geometry in tilted and non-tilted frames

We investigate the dynamics of charged planar symmetry with an anisotropic matter field subject to a radially moving observer called a tilted observer. The Einstein-Maxwell field equations are used to obtain a relation between non-tilted and tilted frames and between kinematical and dynamical quantities. Using the Taub mass formalism and conservation laws, two evolution equations are developed to analyze the inhomogeneities in the tilted congruence. It is found that the radial velocity (due to the tilted observer) and the electric charge have a crucial effect on the inhomogeneity factor. Finally, we discuss the stability in the non-tilted frame in the pure diffusion case and examine the effects of the electromagnetic field.

Gravitational collapse and expansion of charged anisotropic cylindrical source

In this paper, we have discussed the gravitational collapse and expansion of charged anisotropic cylindrically symmetric gravitating source. To this end, the generating solutions of Einstein-Maxwell field equations for the given source and geometry have been evaluated. We found the auxiliary solution of the filed equations, this solution involves a single function which generates two kinds of anisotropic solutions. Every solution can be expressed in terms of arbitrary function of time that has been chosen arbitrarily to fit the various astrophysical time profiles. The existing solutions predict gravitational collapse and expansion depending on the choice of initial data. Instead of base to base collapse, in the present case, wall to wall collapse of the cylindrical source has been investigated. We have found that the electromagnetic field is responsible for the enhancement of anisotropy in collapsing system.

Conformastationary disk-haloes in Einstein–Maxwell gravity

An exact solution of the Einstein–Maxwell field equations for a conformastationary metric with magnetized disk-haloes sources is worked out in full. The characterization of the nature of the energy momentum tensor of the source is discussed. All the expressions are presented in terms of a solution of the Laplace’s equation. A “generalization” of the Kuzmin solution of the Laplace’s equations is used as a particular example. The solution obtained is asymptotically flat in general and turns out to be free of singularities. All the relevant quantities show a reasonable physical behaviour.

Role of Bulk Viscosity and Electromagnetic Field on the Stability of Collapsing Cylinder

This paper deals with the instability regions of charged cylindrically symmetric star with anisotropic matter distribution consisting on radial heat flux and bulk viscosity. We explore junction conditions by taking the external geometry in retarded time coordinates. The Einstein-Maxwell field and conservation equations are perturbed to formulate the collapse equation. Instability regions with Newtonian and post-Newtonian limits are then studied which indicate the importance of adiabatic index. We find that instability range depends upon anisotropic pressure, energy density, electromagnetic field and bulk viscosity. It is concluded that bulk viscosity decreases the instability range leading to stability while electromagnetic field increases the instability range.

Accelerated FRW solutions in Chern–Simons gravity

We consider a five-dimensional Einstein–Chern–Simons action which is composed of a gravitational sector and a sector of matter where the gravitational sector is given by a Chern–Simons gravity action instead of the Einstein–Hilbert action and where the matter sector is given by the so-called perfect fluid. It is shown that (i) the Einstein–Chern–Simons (EChS) field equations subject to suitable conditions can be written in a similar way to the Einstein–Maxwell field equations; (ii) these equations have solutions that describe an accelerated expansion for the three possible cosmological models of the universe, namely, spherical expansion, flat expansion, and hyperbolic expansion when \(\alpha \), a parameter of the theory, is greater than zero. This result allows us to conjecture that these solutions are compatible with the era of dark energy and that the energy–momentum tensor for the field \(h^{a}\), a bosonic gauge field from the Chern–Simons gravity action, corresponds to a form of positive cosmological constant. It is also shown that the EChS field equations have solutions compatible with the era of matter: (i) In the case of an open universe, the solutions correspond to an accelerated expansion (\(\alpha >0\)) with a minimum scale factor at initial time that, when time goes to infinity, the scale factor behaves as a hyperbolic sine function. (ii) In the case of a flat universe, the solutions describe an accelerated expansion whose scale factor behaves as an exponential function of time. (iii) In the case of a closed universe there is found only one solution for a universe in expansion, which behaves as a hyperbolic cosine function of time.

Generalizations of the Levi-Civita-Bertotti-Robinson spacetime

The Levi-Civita-Bertotti-Robinson (LBR) solution of Einstein's field equations may be interpreted to describe spacetime in a region without matter outside a charged spherical domain wall. In the present paper we investigate the physical properties of some solutions of the Einstein-Maxwell equations, and show that they are generalizations of the LBR solution. One represents a spacetime with charged dust outside a charged shell, and another one a spacetime with Lorentz-Invariant Vacuum Energy (LIVE) outside a charged shell. The uniqueness of static, spherically symmetric and conformally flat solutions of the Einstein-Maxwell field equations is also discussed.

Dynamics and stability of charged spherical star with tilted and non-tilted congruences

This paper investigates the dynamics of anisotropic viscous spherical star under the effects of electromagnetic field for a radially moving observer relative to the matter distribution, i.e. a tilted observer. We formulate relationship between tilted and non-tilted quantities using the Einstein–Maxwell field equations. The dynamical equations and equations for the Weyl tensor are constructed to examine the inhomogeneities in the fluid configuration. It is found that different factors like heat radiation, shear viscosity, electric charge and in particular congruence of the tilted observer, affect the energy density inhomogeneity of the spherical star. Finally, we study stability of the system with non-tilted frame in the presence of charge.