A charged interior solution with cosmological constant Λ in general relativity

A new interior solution of the field equation of general relativity with cosmological constant Λ has been obtained for a static and spherically symmetric charged body. Recent charged generalizations of a class of solutions by Florides are discussed here as special cases of our solution. Robson's junction condition is extended to discuss the smooth joint of the interior solution to the Reissner-Nordström solution with nonzero Λ.     

A charged generalization of Florides' interior Schwarzschild solution

The new class of interior Schwarzschild solutions found by Florides is generalized to the charged case. A particular solution within this class is found, which represents an electromagnetic mass-model of a neutral spherically symmetric system. The pressure is isotropic, decreasing monotonously with increasing radius and vanishes at the surface of the matter distribution. The solution is regular everywhere inside a radiusR, and is joined continuously to the exterior Schwarzschild solution at this radius.     

Black holes with toroidal horizons in ($$$$)-dimensional space-time

We investigate black holes with toroidal horizons in (\(d+1\))-dimensional space-time. Using the solution phase space method, we calculated conserved charges for these black holes before exploring some features of this metric including its entropy and thermodynamic quantities. Another aspect of the study involves obtaining a general exact static interior solution for uncharged black holes with toroidal horizons in (\(d+1\))-dimensional space-time. Finally, an interior solution for charged black holes is obtained.     

A class of static charged dust spheres in general relativity

Using static spherically symmetric space-times with associated 3-spaces obtained as hypersurfacest= const as 3-spheroidal, a class of physically viable relativistic models for spherical distributions of uniformly charged dust in equilibrium is obtained. The charged analog of Schwarzschild interior solution given by Cooperstock and de la Cruz follows as a particular case of this class.     

Gravitational collapse of a charged and radiating fluid ball in the diffusion limit

The collapse of a charged and radiating ball in the diffusion limit is studied using a method reported by Herrera and collaborators. The interior solution is matched with the exterior Reissner-Nordström-Vaidya metric to obtain a system of differential equations at the surface of the distribution, which can be integrated numerically for some set of initial data. For one model, the profiles of the physical variables are obtained at any piece of the material in terms of Schwarzschild-like coordinates.     

The $$SO(3,1) \times U(1)$$-gauge covariant Dirac equation in relativistic magnetars

Using a perturbative method, we investigate solutions of the Dirac equations for a charged massive spinor field in the background of a magnetar, both in the interior solution and outside the star. A special attention is given to cases where the variables can be separated and the wave function is expressed in terms of the Heun’s general or confluent functions.     

Spherically symmetric charged perfect fluid distributions executing shear-free motion

A method to obtain exact solutions characterizing spherically symmetric charged perfect fluid distributions undergoing shear-free motion has been discussed. This method makes use of the criterion that the solution be free from movable critical points as has been employed earlier by Shah and Vaidya. Two solutions have been obtained, one of which is new and the other is the recent solution due to Sussman.     

Entropy Evolution in the Interior Volume of a Charged $f(R)$ Black Hole *

Based on the 4-dimensional black hole solution of $f(R)$ theory coupled to a nonlinear Maxwell field, we calculate the interior volume of a charged $f(R)$ black hole using the method proposed by Christodoulou and Rovelli. Considering massless scalar field in the interior volume and Hawking radiation carrying only energy, we calculate the entropy of the scalar field inside a charged $f(R)$ black hole and investigate the evolution of the entropy under Hawking radiation. In the meantime, the evolution of the Bekenstein-Hawking entropy under Hawking radiation has also been calculated. Based on these results, the proportional relation is obtained between the evolution of the scalar field entropy and the evolution of Bekenstein-Hawking entropy under Hawking radiation. According to the result, we investigate and discuss how the modified coefficient $b$ in $f(R)$ gravity theory affects the evolution relation between the two types of entropy. It is shown that the radiation rate for Hawking radiation of a charged $f(R)$ black hole can increase with the modified coefficient $b$.     

A superdense star model as charged analogue of Schwarzschild’s interior solution

A charged analogue of Schwarzschilds interior solution has been derived by considering the non-gravitational energy density to be constant along with a special choice of electric intensity. The charged fluid sphere so obtained is seen to be more general than that of P.S. Florides and joins smoothly with the Reissner-Nordström metric at the pressure-free interface. Also the new charged fluid sphere is capable of representing a superdense star with surface density of 2×10¹⁴ g cm^–3 which can occupy maximum mass 1.502408 times the solar mass. In the process of deriving the solution, the authors have also come across A. L. Mehras gaseous charged fluid model which is found to be unphysical as it has negative pressure at least at the center of the model.This revised version was published online in April 2005. The publishing date was inserted.     

Self–similar and charged spheres in the free–streaming approximation

We evolve nonadiabatic charged spherical distributions of matter. Dissipation is described by the free–streaming approximation. We match a self–similar interior solution with the Reissner–Nordstr?m–Vaidya exterior solution. The transport mechanism is decisive to the fate of the gravitational collapse. Almost a half of the total initial mass is radiated away. The transport mechanism determines the way in which the electric charge is redistributed.     

An interior solution for the gamma metric

Interior solutions for a static, axially symmetric family of solutions of Einstein's equations are described. The interior solutions correspond to spatially bound matter and are properly matched to an exterior vacuum solution. The family of solutions discussed include the Schwarzschild solution as a special case. A general method is exhibited for transforming any spherically symmetric interior solution to an interior for the other members of the family of solutions. The energy density remains positive for at least a finite range of the parameter that describes the family of solutions. Two solutions are explicitly exhibited. One is transformed from the constant density Schwarzschild interior solution and one from the Adler interior solution. The first solution would be expected to be unstable under adiabatic perturbations of the matter, the second would be expected to be stable.Supported in part by The National Science Foundation under Grant No. INT 782-5663.Supported in part by Consejo Nacional de Investigaciones Cientificas y Technologicas (CONICIT), Venezuela.     

An Exact Interior Solution of a Static Charged Sphere in Higher Dimensional Spacetime

By assuming "p = Aρ" and the total intrinsic energy density εr^k (k + D - 1 > 0), we strictly solve the higher dimensional Einstein-Maxwell field equations in a static charged sphere, resulting in an exact interior solution of the equations.     

Relativistic fluid sphere on pseudo-spheroidal space-time

A new exact closed form solution of Einstein's field equations is reported describing the space-time in the interior of a fluid sphere in equilibrium. The physical 3-space,t=constant of its space-time has the geometry of a 3-pseudo spheroid. The suitability of this solution for describing the model of a relativistic superdense star is discussed and the stability of the model under radial pulsations is examined.     

Rotating charged fluid in 2+1 dimensions

The (2+l)-dimensional Einstein-Maxwell equations are solved for a perfect fluid source with a positive electric charge distribution and nonzero vorticity. The solution describes the interior region of an extended charged object and is physically reasonable in the sense that the massenergy density and the pressure are both positive throughout the region. An unexpected feature is that the charged fluid produces no electric field in its proper frame of reference, so that the electromagnetic field is purely magnetic.     

Charged thin-shell gravastars in noncommutative geometry

In this paper we construct a charged thin-shell gravastar model within the context of noncommutative geometry. To do so, we choose the interior of the nonsingular de Sitter spacetime with an exterior charged noncommutative solution by cut-and-paste technique and apply the generalized junction conditions. We then investigate the stability of a charged thin-shell gravastar under linear perturbations around the static equilibrium solutions as well as the thermodynamical stability of the charged gravastar. We find the stability regions, by choosing appropriate parameter values, located sufficiently close to the event horizon.     

The $$SO(3,1) \times U(1)$$-gauge invariant approach to charged bosons in relativistic magnetars

Using a perturbative method, we investigate solutions of the Klein–Gordon equations for a charged massive field in the background of a magnetar, both in the interior solution and outside the star. A special attention is given to cases where the variables can be separated and the wave function is expressed in terms of the Heun’s general or confluent functions. By imposing various conditions on the parameters, one gets the energy quantization law and simple polynomial forms of the Heun’s functions, which can be used in computing first-order transition amplitudes.     

Collapse and rebound of a charged dust-like star

It is shown that a charged spherically symmetric star, made out of a continuous superposition of thin shells with Poincaré stresses, undergoes gravitational collapse in free fall like an uncharged star of dust. The interior solution is a Friedmann universe matching the Reissner-Nordström geometry at the boundary of the star. When the absolute value of the chargeQ does not exceed the massM, the star rebounds elastically inside the event horizon at the radial coordinateQ ²/(2M). The further history of the charged star after the bounce is analyzed. Besides, a simple mechanism which accounts for the development of Poincaré stresses in an originally charged star of dust is suggested. It is also verified that the energy density is nonnegative all along the collapse process.     

Self-similar and charged radiating spheres: an anisotropic approach

Considering charged fluid spheres as anisotropic sources and the diffusion limit as the transport mechanism, we suppose that the inner space–time admits self-similarity. Matching the interior solution with the Reissner–Nordström–Vaidya exterior one, we find an extremely compact and oscillatory final state with a redistribution of the electric charge function and non zero pressure profiles.     

The mass of a static charged sphere

The field of a static, charged sphere is investigated using general relativity. InNordström's exterior solution the parametersm ande, referring to mass and charge, are unrelated, and indeedm can be put equal to zero. It is shown that, if the interior solution is considered,m cannot be put zero unless the matter density is negative. The contribution of the electric field energy to the gravitational mass is estimated using certain special models. A model is given in which the gravitational attraction of the charged matter balances its electrical repulsion. If the radius is allowed to tend to zero, this gives a model of a point charge with finite and non-zero mass and charge.     

Modeling electrokinetic flows by the smoothed profile method

We propose an efficient modeling method for electrokinetic flows based on the smoothed profile method (SPM) 1, 2, 3 and 4 and spectral element discretizations. The new method allows for arbitrary differences in the electrical conductivities between the charged surfaces and the surrounding electrolyte solution. The electrokinetic forces are included into the flow equations so that the Poisson–Boltzmann and electric charge continuity equations are cast into forms suitable for SPM. The method is validated by benchmark problems of electroosmotic flow in straight channels and electrophoresis of charged cylinders. We also present simulation results of electrophoresis of charged microtubules, and show that the simulated electrophoretic mobility and anisotropy agree with the experimental values.