scholarly journals Regular and singular solutions for charged dust distributions in the Einstein-Maxwell theory

2007 ◽  
Vol 85 (9) ◽  
pp. 957-965
Author(s):  
D Horvat ◽  
S Ilijić
Keyword(s):  
Distinctive Feature ◽  
Total Mass ◽  
Singular Solutions ◽  
Charged Dust ◽  
Spherically Symmetric ◽  
Regular Solutions ◽  
Maxwell Theory ◽  
Metric Tensor ◽  
Net Charge ◽  
Adm Mass

Solutions for the static spherically symmetric extremally charged dust in the Majumdar–Papapetrou system have been found. For a certain amount of the allocated mass and (or) charge, the solutions have singularities of a type that could render them physically unacceptable, since the corresponding physically relevant quantities are singular as well. These solutions, with a number of zero-nodes in the metric tensor, are regularized through the δ-shell formalism, thus redefining the mass and (or) charge distributions. The bifurcating behaviour of regular solutions found before is no longer present in these singular solutions, but quantized-like behaviour in the total mass is observed. The spectrum of regularized solutions restores the equality of the Tolman–Whittaker and Arnowitt–Deser–Misner (ADM) mass, as well the equality of the net charge and ADM mass, which is the distinctive feature of Majumdar–Papapetrou systems.PACS No.:04.40.Nr

Black hole in balance with dark matter

2020 ◽  
Vol 35 (02n03) ◽  
pp. 2040050
Author(s):  
Boris E. Meierovich
Keyword(s):  
Black Hole ◽  
Dark Matter ◽  
Phase Equilibrium ◽  
Vector Field ◽  
Scalar Field ◽  
Total Mass ◽  
Metric Tensor ◽  
Static Solutions ◽  
Tensor Formula ◽  
Galaxy Rotation Curves

Equilibrium of a gravitating scalar field inside a black hole compressed to the state of a boson matter, in balance with a longitudinal vector field (dark matter) from outside is considered. Analytical consideration, confirmed numerically, shows that there exist static solutions of Einstein’s equations with arbitrary high total mass of a black hole, where the component of the metric tensor [Formula: see text] changes its sign twice. The balance of the energy-momentum tensors of the scalar field and the longitudinal vector field at the interface ensures the equilibrium of these phases. Considering a gravitating scalar field as an example, the internal structure of a black hole is revealed. Its phase equilibrium with the longitudinal vector field, describing dark matter on the periphery of a galaxy, determines the dependence of the velocity on the plateau of galaxy rotation curves on the mass of a black hole, located in the center of a galaxy.

scholarly journals 4D STATIC SOLUTIONS WITH INTERACTING PHANTOM FIELDS

2008 ◽  
Vol 17 (11) ◽  
pp. 2125-2142 ◽  
Author(s):  
VLADIMIR DZHUNUSHALIEV ◽  
VLADIMIR FOLOMEEV
Keyword(s):  
Scalar Fields ◽  
Spherically Symmetric ◽  
Symmetric Problem ◽  
Regular Solutions ◽  
Traversable Wormhole ◽  
Static Solutions ◽  
Static Models ◽  
Phantom Fields

Three static models with two interacting phantom and ghost scalar fields are considered: a model of a traversable wormhole, a branelike model and a spherically symmetric problem. It is shown numerically that regular solutions exist for all three cases.

Charged solutions in higher dimensions

1992 ◽  
Vol 70 (9) ◽  
pp. 752-759
Author(s):  
K. D. Krori ◽  
T. Chaudhury ◽  
P. Borgohain ◽  
Kanika Das ◽  
Chandra Rekha Mahanta
Keyword(s):  
Higher Dimensions ◽  
Spherically Symmetric ◽  
Maxwell Theory ◽  
Anisotropic Solution ◽  
Isotropic Solution ◽  
Particular Solutions

In this paper we derive spherically symmetric interior isotropic and anisotropic solutions in higher dimensions in Einstein–Maxwell theory. Some particular solutions are obtained from the general isotropic solution. The anisotropic solution is Schwarzschild-like. It reduces to the Krori–Borgohain–Das solution if the charge is zero and to the Krori–Paul solution if the number of dimensions is four.

scholarly journals Black hole and naked singularity geometries supported by three-form fields

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
Bruno J. Barros ◽  
Bogdan Dǎnilǎ ◽  
Tiberiu Harko ◽  
Francisco S. N. Lobo
Keyword(s):  
Black Hole ◽  
Killing Vector ◽  
Field Potential ◽  
Naked Singularity ◽  
Radial Coordinate ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Metric Tensor ◽  
Killing Horizon ◽  
Form Field

Abstract We investigate static and spherically symmetric solutions in a gravity theory that extends the standard Hilbert–Einstein action with a Lagrangian constructed from a three-form field $$A_{\alpha \beta \gamma }$$Aαβγ, which is related to the field strength and a potential term. The field equations are obtained explicitly for a static and spherically symmetric geometry in vacuum. For a vanishing three-form field potential the gravitational field equations can be solved exactly. For arbitrary potentials numerical approaches are adopted in studying the behavior of the metric functions and of the three-form field. To this effect, the field equations are reformulated in a dimensionless form and are solved numerically by introducing a suitable independent radial coordinate. We detect the formation of a black hole from the presence of a Killing horizon for the timelike Killing vector in the metric tensor components. Several models, corresponding to different functional forms of the three-field potential, namely, the Higgs and exponential type, are considered. In particular, naked singularity solutions are also obtained for the exponential potential case. Finally, the thermodynamic properties of these black hole solutions, such as the horizon temperature, specific heat, entropy and evaporation time due to the Hawking luminosity, are studied in detail.

Discontinuities in spherically symmetric gravitational fields and shells of radiation

1958 ◽  
Vol 248 (1254) ◽  
pp. 404-414 ◽  
Keyword(s):  
Boundary Conditions ◽  
Spherical Shell ◽  
Previous Treatment ◽  
Empty Space ◽  
Point Of View ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
Metric Tensor ◽  
Gravitational Fields

Boundary conditions at a 3-space of discontinuity ∑ are considered from the point of view of Lichnerowicz. The validity of the O’Brien—Synge junction conditions is established for co-ordinates derivable from Lichnerowicz’s ‘admissible co-ordinates’ by a transformation which is uniformly differentiable across ∑. The co-ordinates r , θ , ϕ , t , used by Schwarzschild and most later authors when dealing with spherically symmetric fields, are shown to be of this type. In Schwarzschild’s co-ordinates, the components of the metric tensor can always be made continuous across Ʃ, and simple relations are derived connecting the jumps in their first derivatives. A spherical shell of radiation expanding in empty space is examined in the light of the above ideas, and difficulties encountered by Raychaudhuri in a previous treatment of this problem are cleared up. A particular model is then discussed in some detail.

scholarly journals Self-similar Langmuir collapse at critical dimension

1991 ◽  
Vol 9 (2) ◽  
pp. 363-370 ◽  
Author(s):  
L. Bergé ◽  
PH. Dousseau ◽  
G. Pelletier ◽  
D. Pesme
Keyword(s):  
Control Parameter ◽  
Linear Time ◽  
Critical Dimension ◽  
Singular Solutions ◽  
Spherically Symmetric ◽  
Scalar Model ◽  
Contraction Rate ◽  
Self Similar ◽  
Similar Solutions ◽  
Time Contraction

Two spherically symmetric versions of a self-similar collapse are investigated within the framework of the Zakharov equations, namely, one relative to a vectorial electric field and the other corresponding to a scalar modeling of the Langmuir field. Singular solutions of both of them depend on a linear time contraction rate Ξ(t) = V(t* – t), where t* and V = – Ξ denote, respectively, the collapse time and the constant collapse velocity. We show that under certain conditions, only the scalar model admits self-similar solutions, varying regularly as a function of the control parameter V from the subsonic (V ≪ 1) to the supersonic (V ≫ 1) regime.

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