Conformally-flat metric representing a radiating fluid ball

1990 ◽  
Vol 163 (2) ◽  
pp. 223-227 ◽  
Author(s):  
D. N. Pant ◽  
B. C. Tewari
Keyword(s):  
Conformally Flat ◽  
Fluid Ball ◽  
Flat Metric ◽  
Conformally Flat Metric

scholarly journals Field of a charged particle in the presence of scalar meson fields in general relativity

1983 ◽  
Vol 24 (4) ◽  
pp. 461-465 ◽  
Author(s):  
D. R. K. Reddy ◽  
V. U. M. Rao
Keyword(s):  
Charged Particle ◽  
Point Charge ◽  
Scalar Meson ◽  
Scalar Fields ◽  
Flat Space ◽  
Spherically Symmetric ◽  
Conformally Flat ◽  
Field Equations ◽  
Conformally Flat Metric ◽  
Scalar Meson Field

AbstractField equations for coupled gravitational and zero mass scalar fields in the presence of a point charge are obtained with the aid of a static spherically symmetric conformally flat metric. A closed from exact solution of the field equations is presented which may be considered as describing the field of a charged particle at the origin surrounded by the scalar meson field in a flat space-time.

scholarly journals A Relativistic Algorithm with Isotropic Coordinates

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
S. A. Ngubelanga ◽  
S. D. Maharaj
Keyword(s):  
Spherically Symmetric ◽  
Conformally Flat ◽  
Einstein Field Equations ◽  
Elementary Functions ◽  
Field Equations ◽  
Isotropic Coordinates ◽  
New Exact Solutions ◽  
Symmetric Spacetimes ◽  
Particular Solution ◽  
Conformally Flat Metric

We study spherically symmetric spacetimes for matter distributions with isotropic pressures. We generate new exact solutions to the Einstein field equations which also contain isotropic pressures. We develop an algorithm that produces a new solution if a particular solution is known. The algorithm leads to a nonlinear Bernoulli equation which can be integrated in terms of arbitrary functions. We use a conformally flat metric to show that the integrals may be expressed in terms of elementary functions. It is important to note that we utilise isotropic coordinates unlike other treatments.

The projective geometry of simple cosmological models

1985 ◽  
Vol 397 (1813) ◽  
pp. 233-243 ◽  
Keyword(s):  
Projective Geometry ◽  
Flat Space ◽  
Conformally Flat ◽  
Flow Lines ◽  
Quadric Hypersurface ◽  
Essential Properties ◽  
Conformally Flat Metric ◽  
Friedmann Robertson Walker ◽  
Matter Flow ◽  
Selection Of

The conformal properties of flat space-time can be described in terms of the projective geometry of a four-dimensional quadric hypersurface, Ω, embedded in projective 5-space, P 5 . In this paper it is shown how an arbitrary conformally flat metric can be defined by the selection of a single scalar field on Ω. The curvature tensor associated with this metric can then be calculated. The procedure is illustrated with a self-contained treatment of the geometry of Friedmann-Robertson-Walker models within the P 5 framework. The essential properties of these space-times, such as the location of conformal infinity, curvature singularities and matter flow lines, etc., are all incorporated in geometric diagrams that arise naturally from the projective geometric construction.

Helicoidal surfaces with prescribed curvatures in a conformally flat 3-space

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Chul Woo Lee ◽  
Jae Won Lee ◽  
Dae Won Yoon
Keyword(s):  
Mean Curvature ◽  
Extrinsic Curvature ◽  
Conformal Factor ◽  
Second Order ◽  
Conformally Flat ◽  
Non Linear ◽  
Linear Ode ◽  
Helicoidal Surfaces ◽  
Conformally Flat Metric

Abstract In this paper, we study a conformally flat 3-space 𝔽 3 {\mathbb{F}_{3}} which is an Euclidean 3-space with a conformally flat metric with the conformal factor 1 F 2 {\frac{1}{F^{2}}} , where F ⁢ ( x ) = e - x 1 2 - x 2 2 {F(x)=e^{-x_{1}^{2}-x_{2}^{2}}} for x = ( x 1 , x 2 , x 3 ) ∈ ℝ 3 {x=(x_{1},x_{2},x_{3})\in\mathbb{R}^{3}} . In particular, we construct all helicoidal surfaces in 𝔽 3 {\mathbb{F}_{3}} by solving the second-order non-linear ODE with extrinsic curvature and mean curvature functions. As a result, we give classification of minimal helicoidal surfaces as well as examples for helicoidal surfaces with some extrinsic curvature and mean curvature functions in 𝔽 3 {\mathbb{F}_{3}} .

Study of charged anisotropic spherical collapse in f(𝒢) gravity

2018 ◽  
Vol 33 (19) ◽  
pp. 1850109 ◽  
Author(s):  
M. Sharif ◽  
Saba Naz
Keyword(s):  
Conformally Flat ◽  
Matter Distribution ◽  
Dynamical Equations ◽  
Stellar Objects ◽  
Conformal Flatness ◽  
Anisotropic Factor ◽  
Spherical Collapse ◽  
Physical Impact ◽  
Conformally Flat Metric ◽  
The Relationship

This paper studies the gravitational collapse of charged anisotropic spherical stellar objects in [Formula: see text] gravity. For this purpose, we derive dynamical equations by considering Misner–Sharp mechanism and explore physical impact of charge, anisotropy and effective pressure on the rate of collapse. We establish the relationship between matter variables, Weyl tensor and the Gauss–Bonnet (GB) terms. For constant value of [Formula: see text], it turns out that conformal flatness condition is no longer valid due to the effect of anisotropic factor in the present scenario. To obtain conformally flat metric, we impose the condition of isotropic matter distribution which provides energy density homogeneity and conformal flatness of the metric. We conclude that GB terms lead to decrease in the collapse rate due to their anti-gravitational effects.

On the dynamics of spinning particle in nonlinear relativity

2021 ◽  
Vol 36 (06) ◽  
pp. 2150048
Author(s):  
H. Guergouri ◽  
T. Foughali
Keyword(s):  
Minkowski Space ◽  
Equations Of Motion ◽  
Space Time ◽  
Conformally Flat ◽  
De Sitter ◽  
Spinning Particle ◽  
Spinning Particles ◽  
Minkowski Space Time ◽  
Conformally Flat Metric ◽  
Uniform Electromagnetic Field

In order to study the dynamics of spinning particles in R-Minkowski space–time, first we have used the Bhabha–Corben model to describe how a spinning particle behave in a uniform electromagnetic field. Then, to extend the Mathisson–Papapetrou equations to R-Minkowski space–time, that correspond to de Sitter space–time given by a conformally flat metric, it was necessary to determine the Killing vectors, which allowed us to find the equations of motion that describe the dynamics of spinning particles.

Conformally flat kähler spaces

2020 ◽  
Author(s):  
O. Lesechko ◽  
O. Latysh ◽  
T. Spychak
Keyword(s):  
Conformally Flat
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