Nordstrom Metric Research Articles

Stability analysis of anisotropic stellar structures in Rastall theory of gravity utilizing cracking technique

In this manuscript, we employ the cracking technique in the Rastall gravity framework to assess how local density perturbations affect the stability of anisotropic stellar structures. To achieve this, we developed field equations for spherically symmetric spacetime with the charge inclusion in the context of Rastall gravity and then employed the krori Barua approach and barotropic equation of state while considering Reissner–Nordstrom metric as exterior spacetime, to develop the solution of the field equations. Further, we formulated the Tolman–Oppenheimer–Volkoff (TOV) equation by considering the non-conservation of energy–momentum tensor in the context of Rastall gravity. The stability of configuration is then disrupted by incorporating local density perturbations. Subsequently, our proposed approach is employed on the following compact stars: Her X-1, SAX J1808.4-3658, 4U 1820-30, PSR J1614-2230, Vela X-1, Cen X-3, and RXJ1856-37 to demonstrate its viability. The findings demonstrate that all stars under consideration experience cracking. This work particularly emphasizes the crucial role of cracking method in offering insightful information on the stability analysis of anisotropic stellar structures.

Shadows around Sgr A* and M87* as a tool to test gravity theories

In the framework of Randall–Sundrum theory with extra dimension Reissner–Nordstrom black hole solutions with a tidal charge have been found. The shadow around the supermassive black hole in M87 was reconstructed in 2019 based on observations with the Event Horizon Telescope (EHT) in April 2017. In May 2022 the EHT Collaboration presented results of a shadow reconstruction for our Galactic Center. Earlier, for Reissner–Nordstrom metric we derived analytical expressions for shadow size as a function of charge and later generalized these results for a tidal charge case. We discuss opportunities to evaluate parameters of alternative theories of gravity with shadow size estimates done by the EHT Collaboration, in particular, a tidal charge could be estimated from these observations.

The charged Zipoy–Voorhees metric with astrophysical applications

Starting from an integral of the interaction region of colliding Einstein–Maxwell waves and by applying a coordinate transformation, we obtain the charged version of the static Zipoy–Voorhees (ZV) metric valid for all values of the distortion parameter gamma . In Schwarzschild coordinates, we investigate the effect of the charge in the newly found spacetime, stress the analogy with Reissner–Nordstrom metric and discuss some of its features. It is shown that from the expression of Weyl curvature, directional singularities become manifest. For astrophysical importance, we find lensing of null geodesics from the Gauss–Bonnet theorem in such non-spherically charged objects. To prepare the ground for our null, circular geodesics we consider the angular equation linearized about the symmetry plane theta =pi /2. This, in turn, suggests the distortion parameter (the ZV parameter) must be in the interval 1/2<gamma <1. It is found that the lensing angle is highly dependent on the distortion parameter, and becomes decisive on the effect of the charge. For a class of charged compact stars, we plot the deflection angle versus the ratio of impact parameter to the radius of the star. Plots have revealed that for perfectly spherical compact stars, it is hard to identify the effect of electric/magnetic charge, but for non-spherical compact stars the effect of electric charge becomes apparent. For comparison, the same lensing angle has also been found for the stationary ZV metric in the equatorial plane. Our analysis indicates that depending on the value of gamma , the stationary state induces counter effect on the bending angle and thus, when compared with the uncharged static ZV case, the bending angle decreases. The influence of the parameter gamma on the gravitational redshift is also displayed.

Relativistic modeling of the neutron star in Vela X-1 via Bardeen space-time satisfying the embedding condition

In this paper, we present two new exact and analytic solutions of the Einstein–Maxwell field equations describing compact anisotropic charged stars satisfying the Karmarkar condition in the background of Bardeen black hole geometry. The solutions are composed of two parts: The inner region of the star is described by class I Karmarkar space-time, while exterior of the star is characterized by both the Bardeen and the Reissner–Nordstrom space-times. Physical analysis of the matter and thermodynamical variables show that the models are well-behaved. For our parametric set of values, we conclude that the Bardeen black hole metric can be used as an alternate to the exterior Reissner–Nordstrom metric.

Analysis of the Topology of the Kerr Metric

The equations of motion of a test particle are integrated for the field of a rotating Kerr black hole (BH) (in accordance with [1]). Due to the lack of analytical transformations for the Carter–Penrose diagrams (CPDs) for the Kerr metric, the topology of the Kerr BH is studied by analytical investigation of the equations of motion. Transformations for the CPDs for the Reisner–Nordstrom metric are analyzed. The problem of boundary conditions for the Reisner–Nordstrom topology is analyzed. A solution to this problem of boundary conditions is proposed. It is proved that, in the Reisner–Nordstrom topology, only one way to go to another universe is possible. For the Kerr topology, the possibility of the existence of an alternative transition to another universe that does not coincide with the universe for the ordinary transition is found. This alternative transition is performed through a surface with a zero radial coordinate (zero radius). Initial conditions for the falling particle are found that correspond to an alternative transition to another universe. The tidal forces acting on a falling body in the Kerr metric are estimated, and the possibility of the transition of the body to other universes without being destroyed by tidal forces is proved.

Reissner–Nordstrom metric in unimodular theory of gravity

We study the modified Reissner–Nordstrom (RN) metric in the unimodular gravity. So far the spherical symmetric Einstein field equation in unimodular gravity has been studied in the absence of any source. We consider static electric and magnetic charge as source. We solve for Maxwell equations in unimodular gravitational background. We show that in unimodular gravity, the electromagnetic field strength tensor is modified. We also show that the solution in unimodular gravity differs from the usual RN metric in Einstein gravity with some corrections. We further study the thermodynamical properties of the RN black hole solution in this theory.

Nonsingular black hole with a nonlinear electric source

A modified version of the Reissner–Nordstrom (RN) metric is proposed on the grounds of the nonlinear electrodynamics model. The source of curvature is an anisotropic fluid with pr = -ρ which resembles the Maxwell stress tensor at r ≫ q2/2m, where q and m are the mass and charge of the particle, respectively. We found the black hole (BH) horizon entropy obeys the relation S = ∣W∣/2T = AH/4, with W the Komar energy and AH the horizon area. The electric field around the source depends not only on its charge but also on its mass. The corresponding electrostatic potential Φ(r) is finite everywhere, being -m/2q at the origin and nonzero asymptotically, with Φ∞ = m/q.

Dynamics of a Charged Scalar Field Thin Shell

This paper deals with the motion of a charged spherically symmetric thin shell composed of a scalar field. The equations of motion resulting from the matching conditions of the two surrounding spacetimes which are described by the Reissner Nordstrom metric are derived. I evaluate the case of massless scalar field, where the scalar field potential is zero, also I evaluate the case of massive scalar field.

The geometric nature of approximate Noether gauge symmetries

We find the geometrical set of equations corresponding to the approximate Noether gauge symmetry conditions of the perturbed geodesic Lagrangian for spacetimes. Using the obtained new set of approximate Noether symmetry equations which involves exact, first-order and second-order metrics, we calculate exact, first-order and second-order approximate Noether gauge symmetry vectors of the geodesic Lagrangian for the potential function defining the dynamical system in spacetimes. We apply our geometrical method to each of the Schwarzschild metric and Reissner–Nordstrom metric.

A family of charge analogue of Durgapal solution

We obtain a new parametric class of exact solutions of Einstein–Maxwell field equations which are well behaved. We present a charged super-dense star model after prescribing particular forms of the metric potential and electric intensity. The metric describing the super dense stars joins smoothly with the Reissner–Nordstrom metric at the pressure free boundary. The electric density assumed is \(\frac{E^{2}}{c_{1}} = \frac{Kx}{2}(1 + x)^{n}(1 + 6x)^{\frac{2}{3}}\) where n may take the values 0,1,2,3,4 and so on and K is a positive constant. For n=0,1 we rediscover the solutions by Gupta and Maurya (Astrophys. Space Sci. 334(1):155, 2011) and Fuloria et al. (J. Math. 2:1156, 2011) respectively. The solution for n=2 have been discussed extensively keeping in view of well behaved nature of the charged solution of Einstein–Maxwell field equations. The solution for n=3 and n=4 can be also studied likewise. In absence of the charge we are left behind with the regular and well behaved fifth model of Durgapal (J. Phys. A 15:2637, 1982). The outmarch of pressure, density, pressure-density ratio and the velocity of sound is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. For this class of solutions the mass of a star is maximized with all degree of suitability, compatible with Neutron stars and Pulsars.

Charged Analogues of Henning Knutsen Type Solutions in General Relativity

In the present article, we have found charged analogues of Henning Knutsen’s interior solutions which join smoothly to the Reissner–Nordstrom metric at the pressure free interface. The solutions are singularity free and analyzed numerically with respect to pressure, energy-density and charge-density in details. The solutions so obtained also present the generalization of A.L. Mehra’s solutions.

Charged fluid sphere in bimetric general theory of relativity

Static and spherical symmetric solutions of the field equations in the bimetric general theory of gravitation are obtained for perfect and anisotropic charged fluids under the assumption that the physical metric admits a one-parameter group of conformal motion. All solutions are matched to the Reissner–Nordstrom metric and possess positive energy density larger than the stresses, everywhere within the sphere. The solution agrees with Einstein’s general relativity for a physical system comparable to the size of the universe, such as the solar system.

Approximate Noether symmetries of the geodesic equations for the charged-Kerr spacetime and rescaling of energy

Using approximate symmetry methods for differential equations we have investigated the exact and approximate symmetries of a Lagrangian for the geodesic equations in the Kerr spacetime. Taking Minkowski spacetime as the exact case, it is shown that the symmetry algebra of the Lagrangian is 17 dimensional. This algebra is related to the 15 dimensional Lie algebra of conformal isometries of Minkowski spacetime. First introducing spin angular momentum per unit mass as a small parameter we consider first-order approximate symmetries of the Kerr metric as a first perturbation of the Schwarzschild metric. We then consider the second-order approximate symmetries of the Kerr metric as a second perturbation of the Minkowski metric. The approximate symmetries are recovered for these spacetimes and there are no non- trivial approximate symmetries. A rescaling of the arc length parameter for consistency of the trivial second-order approximate symmetries of the geodesic equations indicates that the energy in the charged-Kerr metric has to be rescaled and the rescaling factor is r-dependent. This re-scaling factor is compared with that for the Reissner–Nordstrom metric.

Creation of fundamental particles in Wesson’s IMT

Fundamental particles, regarded as possible constituents of quarks and leptons, are described classically in the framework of the Weyl-Dirac version of Wesson’s Induced Matter Theory (IMT). There are neutral particles and particles having charge \(\pm \frac{1}{3}e\). The particles appear on the 4D brane, our universe, and are filled with an induced by the 5D bulk substance. This substance is taken to have mass density, pressure, and (if charged) charge density, and is characterized by the equation of state ρ + P = 0. The interior is separated from the surrounding vacuum by a spherical boundary surface where the components of the 4D metric tensor h00 = 1/h11 = 0. Outside of the boundary holds the Schwarzschild, or the Reissner–Nordstrom metric, while the particles are characterized by Mass, Radius, Charge.

BLACK HOLES AND SOLITONS OF THE NONLINEAR ISOVECTOR MODEL

We formulate the nonlinear isovector model in a curved background and calculate the spherically symmetric solutions for weak and strong coupling regimes. The question whether gravity has appreciable effects on the structure of solitons will be examined, in the framework of the calculated solutions, by comparing the flat-space and curved-space solutions. It turns out that in the strong coupling regime, gravity has essential effects on the solutions. It is also shown that the asymptotic form of the metric conforms with that of the charged Reissner–Nordstrom metric. The dimensionless coupling constant of the model has a limit, beyond which a horizon appears in the solutions, indicating the presence of black hole solutions.

On Charged Analogues of Buchdahl’S Type Fluid Spheres

In this article the charged analogues of recently derived Buchdahl’s type fluid spheres have been obtained by considering a particular form of electric field intensity. In this process, Einstein–Maxwell field equations yield eight different classes of solutions, joining smoothly with the exterior Reissner–Nordstrom metric at the pressure free intersurface. Out of the eight solutions only seven could be utilized to represent superdense star models with ultrahigh surface density of the order 2×1014 gm cm−3. The maximum masses of the star models were found to be 8.223931MΘ and 8.460857MΘ subject to strong and weak energy conditions, respectively, which are much higher than the maximum masses 3.82MΘ and 4.57MΘ allowed in the neutral cases. The velocity of sound seen to be less than that of light throughout the star models.

A new way of solving the Wheeler-Dewitt equation as applied to point sources

A new way of solving the Wheeler–DeWitt equation is proposed which is based on quantization over free parameters of metrics satisfying the Einstein equations. This technique is applied to two point sources described in the classical case by the Tangherlini metric (in an n-dimensional space) and the Reissner–Nordstrom metric (in the case of the presence of a charge). The results obtained clarify the sense of the Wheeler hypothesis about statistical weights of small dimensionalities and make possible a new approach to the problem of variation of fundamental constants.

Nonstatic charged spheres admitting a conformal Killing vector

Exact, nonstatic, spherically symmetric solutions of the Einstein–Maxwell equations are found for self-gravitating charged spheres under the assumption of the existence of a conformal Killing vector. Solutions are matched to the Reissner–Nordstrom metric and it is found that as a consequence of the junction conditions, the material must be anisotropic. The radius of the sphere for static distributions corresponds to the radius of the unstable null circular orbit of the Reissner–Nordstrom geometry.

On the solution of the equations governing the coupled emission of gravitational and electromagnetic radiation

ABS>Some of the analytic properties of the system of differential equations governing the emission of electromagnetic and gravitational radiation due to the radial infall of an unchanged particle of mass m in a Reissner- Nordstrom metric are examined, and the integration technique is amplified. (LBS)