On the dynamics of spinning particle in nonlinear relativity

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.

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

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

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 For constant value of [Formula: see text], it turns out that conformal flatness condition is no longer valid due to the effect of anisotropic factor in the present scenario.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.

A Relativistic Algorithm with Isotropic Coordinates

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

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.

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

Field 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.