Charged spheres in general relativity

1969 ◽  
Vol 47 (18) ◽  
pp. 1989-1994 ◽  
Author(s):  
M. C. Faulkes
Keyword(s):  
General Relativity ◽  
Total Energy ◽  
General Equation ◽  
Maxwell Equations ◽  
Equilibrium Configuration ◽  
Rate Of Change ◽  
Spherically Symmetric ◽  
Charged Matter ◽  
Spherically Symmetric Distribution ◽  
Charged Spheres

The Einstein–Maxwell equations for a spherically symmetric distribution of charged matter are studied. A general equation is derived for the rate of change of the "total energy" of the sphere in terms of the 4–4 component of the electromagnetic and matter tensors. It is shown that, subject to certain conditions, the spheres of charged matter can oscillate, and further that the static configuration is uniquely given by the relation m2 = 4πe2α, where [Formula: see text]. Finally, it is demonstrated that the equilibrium configuration is unstable to small radial perturbations.

Exact solution of a static charged sphere in general relativity

1969 ◽  
Vol 47 (21) ◽  
pp. 2401-2404 ◽  
Author(s):  
S. J. Wilson
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Gravitational Constant ◽  
The Self ◽  
Spherically Symmetric ◽  
Charged Sphere ◽  
Field Equations ◽  
First Order ◽  
Self Energy ◽  
Spherically Symmetric Distribution

An exact solution of the field equations of general relativity is obtained for a static, spherically symmetric distribution of charge and mass which can be matched with the Reissner–Nordström metric at the boundary. The self-energy contributions to the total gravitational mass are computed retaining only the first order terms in the gravitational constant.

scholarly journals Nonstatic Spherically Symmetric Solutions for a Perfect Fluid in General Relativity

1976 ◽  
Vol 29 (2) ◽  
pp. 113 ◽  
Author(s):  
N Chakravarty ◽  
SB Dutta Choudhury ◽  
A Banerjee
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Perfect Fluid ◽  
Dynamical Behaviour ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Spherically Symmetric Solutions ◽  
Spherically Symmetric Distribution ◽  
General Method

A general method is described by which exact solutions of Einstein's field equations are obtained for a nonstatic spherically symmetric distribution of a perfect fluid. In addition to the previously known solutions which are systematically derived, a new set of exact solutions is found, and the dynamical behaviour of the corresponding models is briefly discussed.

SPHERICALLY SYMMETRIC SCALAR FIELD IN GENERAL RELATIVITY

1996 ◽  
Vol 11 (30) ◽  
pp. 2409-2415 ◽  
Author(s):  
FERNANDO KOKUBUN
Keyword(s):  
Exact Solution ◽  
General Relativity ◽  
Scalar Field ◽  
Field Distribution ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Ordinary Matter ◽  
Spherically Symmetric Distribution

We analyze the presence of a scalar field around a spherically symmetric distribution of an ordinary matter, obtaining an exact solution for a given scalar field distribution.

Evolution of radiating charged spheres in general relativity

1988 ◽  
Vol 66 (11) ◽  
pp. 981-986 ◽  
Author(s):  
V. Medina ◽  
L. Núñez ◽  
H. Rago ◽  
A. Patiño
Keyword(s):  
General Relativity ◽  
Energy Density ◽  
Radial Velocity ◽  
Maxwell Equations ◽  
Charged Fluid ◽  
Vaidya Solution ◽  
Physical Variables ◽  
Electric Charge Distribution ◽  
Fluid Spheres ◽  
Charged Spheres

A method reported by Herrera et al. is extended to study radiating, charged, fluid spheres. A heuristic assumption relating pressure, energy density, the radial velocity of matter, and the electric-charge distribution is introduced. This ansatz, together with matching the boundaries with those of the Reissner–Nordstrom–Vaidya solution, leads to a system of ordinary differential equations for quantities evaluated at the surface. The integration allows one to obtain the profile of the physical variables for any piece of material via the Einstein–Maxwell equations. As an example of the procedure, a particular model is worked out in some detail.

scholarly journals ENERGY OF SPHERICALLY SYMMETRIC SPACE–TIMES ON REGULARIZING TELEPARALLELISM

2010 ◽  
Vol 25 (14) ◽  
pp. 2883-2895 ◽  
Author(s):  
GAMAL G. L. NASHED
Keyword(s):  
General Relativity ◽  
Symmetric Space ◽  
Total Energy ◽  
Gravitational Energy ◽  
Spherically Symmetric ◽  
Tetrad Formulation ◽  
Spherically Symmetric Solutions

We calculate the total energy of an exact spherically symmetric solutions, i.e. Schwarzschild and Reissner–Nordström, using the gravitational energy–momentum 3-form within the tetrad formulation of general relativity. We explain how the effect of the inertial makes the total energy unphysical. Therefore, we use the covariant teleparallel approach which makes the energy always physical one. We also show that the inertial has no effect on the calculation of momentum.

scholarly journals Janis–Newman–Winicour and Wyman Solutions are the Same

1997 ◽  
Vol 12 (27) ◽  
pp. 4831-4835 ◽  
Author(s):  
K. S. Virbhadra
Keyword(s):  
Exact Solution ◽  
Scalar Field ◽  
Total Energy ◽  
Space Time ◽  
Massless Scalar ◽  
Spherically Symmetric ◽  
Scalar Equations

We show that the well-known most general static and spherically symmetric exact solution to the Einstein-massless scalar equations given by Wyman is the same as one found by Janis, Newman and Winicour several years ago. We obtain the energy associated with this space–time and find that the total energy for the case of the purely scalar field is zero.

scholarly journals Spherically Symmetric Tensor Fields and Their Application in Nonlinear Theory of Dislocations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 830
Author(s):  
Evgeniya V. Goloveshkina ◽  
Leonid M. Zubov
Keyword(s):  
Nonlinear Theory ◽  
Hollow Sphere ◽  
Tensor Field ◽  
Exact Analytical Solution ◽  
Symmetric Tensor ◽  
Symmetric Distribution ◽  
Spherically Symmetric ◽  
Tensor Fields ◽  
Spherically Symmetric Distribution ◽  
Nonlinear Elastic

The concept of a spherically symmetric second-rank tensor field is formulated. A general representation of such a tensor field is derived. Results related to tensor analysis of spherically symmetric fields and their geometric properties are presented. Using these results, a formulation of the spherically symmetric problem of the nonlinear theory of dislocations is given. For an isotropic nonlinear elastic material with an arbitrary spherically symmetric distribution of dislocations, this problem is reduced to a nonlinear boundary value problem for a system of ordinary differential equations. In the case of an incompressible isotropic material and a spherically symmetric distribution of screw dislocations in the radial direction, an exact analytical solution is found for the equilibrium of a hollow sphere loaded from the outside and from the inside by hydrostatic pressures. This solution is suitable for any models of an isotropic incompressible body, i. e., universal in the specified class of materials. Based on the obtained solution, numerical calculations on the effect of dislocations on the stress state of an elastic hollow sphere at large deformations are carried out.

scholarly journals Off-Shell Noether Currents and Potentials for First-Order General Relativity

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 348
Author(s):  
Merced Montesinos ◽  
Diego Gonzalez ◽  
Rodrigo Romero ◽  
Mariano Celada
Keyword(s):  
General Relativity ◽  
Vector Fields ◽  
Killing Vector ◽  
Spherically Symmetric ◽  
Killing Vector Fields ◽  
Arbitrary Vector ◽  
Four Dimensions ◽  
First Order ◽  
Direct Form ◽  
Definition Of

We report off-shell Noether currents obtained from off-shell Noether potentials for first-order general relativity described by n-dimensional Palatini and Holst Lagrangians including the cosmological constant. These off-shell currents and potentials are achieved by using the corresponding Lagrangian and the off-shell Noether identities satisfied by diffeomorphisms generated by arbitrary vector fields, local SO(n) or SO(n−1,1) transformations, ‘improved diffeomorphisms’, and the ‘generalization of local translations’ of the orthonormal frame and the connection. A remarkable aspect of our approach is that we do not use Noether’s theorem in its direct form. By construction, the currents are off-shell conserved and lead naturally to the definition of off-shell Noether charges. We also study what we call the ‘half off-shell’ case for both Palatini and Holst Lagrangians. In particular, we find that the resulting diffeomorphism and local SO(3,1) or SO(4) off-shell Noether currents and potentials for the Holst Lagrangian generically depend on the Immirzi parameter, which holds even in the ‘half off-shell’ and on-shell cases. We also study Killing vector fields in the ‘half off-shell’ and on-shell cases. The current theoretical framework is illustrated for the ‘half off-shell’ case in static spherically symmetric and Friedmann–Lemaitre–Robertson–Walker spacetimes in four dimensions.

Static spherically symmetric stiff matter in general relativity

1994 ◽  
Vol 11 (4) ◽  
pp. L69-L72 ◽  
Author(s):  
Salah Haggag ◽  
Joseph Hajj-Boutros
Keyword(s):  
General Relativity ◽  
Spherically Symmetric ◽  
Stiff Matter
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