scholarly journals Chirality in gravitational and electromagnetic interactions with matter

2018 ◽  
Vol 15 (supp01) ◽  
pp. 1840004
Author(s):  
Robin W. Tucker ◽  
Timothy J. Walton
Keyword(s):  
Finite Energy ◽  
Geodesic Equation ◽  
Einstein Equations ◽  
Analytic Structure ◽  
Astrophysical Jet ◽  
Aspect Ratios ◽  
Test Particles ◽  
Astrophysical Objects ◽  
Minkowski Metrics ◽  
Energy Pulse

It has been suggested that single and double jets observed emanating from certain astrophysical objects may have a purely gravitational origin. We discuss new classes of pulsed gravitational wave solutions to the equation for perturbations of Ricci-flat spacetimes around Minkowski metrics, as models for the genesis of such phenomena. We discuss how these solutions are motivated by the analytic structure of spatially compact finite energy pulse solutions of the source-free Maxwell equations generated from complex chiral eigen-modes of a chirality operator. Complex gravitational pulse solutions to the linearized source-free Einstein equations are classified in terms of their chirality and generate a family of non-stationary real spacetime metrics. Particular members of these families are used as backgrounds in analyzing time-like solutions to the geodesic equation for test particles. They are found numerically to exhibit both single and double jet-like features with dimensionless aspect ratios suggesting that it may be profitable to include such backgrounds in simulations of astrophysical jet dynamics from rotating accretion discs involving electromagnetic fields.

The Kerr solution

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Kerr Black Hole ◽  
Geodesic Equation ◽  
Einstein Equations ◽  
Kerr Metric ◽  
Kerr Solution ◽  
Axially Symmetric ◽  
Observable Universe ◽  
Einstein Vacuum Equations ◽  
Einstein Vacuum ◽  
The Many

This chapter covers the Kerr metric, which is an exact solution of the Einstein vacuum equations. The Kerr metric provides a good approximation of the spacetime near each of the many rotating black holes in the observable universe. This chapter shows that the Einstein equations are nonlinear. However, there exists a class of metrics which linearize them. It demonstrates the Kerr–Schild metrics, before arriving at the Kerr solution in the Kerr–Schild metrics. Since the Kerr solution is stationary and axially symmetric, this chapter shows that the geodesic equation possesses two first integrals. Finally, the chapter turns to the Kerr black hole, as well as its curvature singularity, horizons, static limit, and maximal extension.

scholarly journals Shapovalov Wave-Like Spacetimes

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1372 ◽  
Author(s):  
Konstantin Osetrin ◽  
Evgeny Osetrin
Keyword(s):  
Jacobi Equation ◽  
Eikonal Equation ◽  
Separation Of Variables ◽  
Complete Classification ◽  
Complete Separation ◽  
Einstein Equations ◽  
Coordinate Systems ◽  
Test Particles ◽  
Hamilton Jacobi Equation

A complete classification of space-time models is presented, which admit the privileged coordinate systems, where the Hamilton–Jacobi equation for a test particle is integrated by the method of complete separation of variables with separation of the isotropic (wave) variable, on which the metric depends (wave-like Shapovalov spaces). For all types of Shapovalov spaces, exact solutions of the Einstein equations with a cosmological constant in vacuum are found. Complete integrals are presented for the eikonal equation and the Hamilton–Jacobi equation of motion of test particles.

scholarly journals “Twisted” black holes are unphysical

2017 ◽  
Vol 32 (18) ◽  
pp. 1771001 ◽  
Author(s):  
Finnian Gray ◽  
Jessica Santiago ◽  
Sebastian Schuster ◽  
Matt Visser
Keyword(s):  
Black Holes ◽  
Event Horizon ◽  
Rotation Axis ◽  
Einstein Equations ◽  
Entire Region ◽  
Asymptotically Flat ◽  
Ricci Flat ◽  
Vacuum Einstein Equations ◽  
Astrophysical Objects

So-called “twisted” black holes were recently proposed by [H. Zhang, arXiv:1609.09721 ], and were further considered by [S. Chen and J. Jing, arXiv:1610.00886 ]. More recently, they were severely criticized by [Y. C. Ong, J. Cosmol. Astropart. Phys. 1701, 001 (2017)]. While these spacetimes are certainly Ricci-flat, and so mathematically satisfy the vacuum Einstein equations, they are also merely minor variants on Taub–NUT spacetimes. Consequently, they exhibit several unphysical features that make them quite unreasonable as realistic astrophysical objects. Specifically, these “twisted” black holes are not (globally) asymptotically flat. Furthermore, they contain closed time-like curves that are not hidden behind any event horizon — the most obvious of these closed time-like curves are small azimuthal circles around the rotation axis, but the effect is more general. The entire region outside the horizon is infested with closed time-like curves.

MOTION AROUND A GLOBAL MONOPOLE

2000 ◽  
Vol 15 (06) ◽  
pp. 869-873
Author(s):  
A. BANERJEE ◽  
T. GHOSH
Keyword(s):  
Gravitational Field ◽  
Einstein Equations ◽  
Global Monopole ◽  
Test Particles ◽  
Light Rays ◽  
Bending Of Light

The motion of test particles and light rays in the perturbed gravitational field around a global monopole is studied. The metric of the monopole was previously obtained by solving the linearized semiclassical Einstein equations (Hiscock). The bending of light ray passing by such a monopole has contributions from the conical object as well as from the perturbed terms. The possibility of trapping particles in the perturbed gravitational field is also discussed.

scholarly journals THE PRINCIPLE OF LEAST ACTION FOR TEST PARTICLES IN A FOUR-DIMENSIONAL SPACE–TIME EMBEDDED IN 5D

2008 ◽  
Vol 23 (04) ◽  
pp. 249-259 ◽  
Author(s):  
J. PONCE DE LEON
Keyword(s):  
Dimensional Space ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Geodesic Equation ◽  
Space Time ◽  
Geodesic Motion ◽  
Least Action ◽  
Test Particles ◽  
Principle Of Least Action ◽  
Dimensional Space Time

It is well known that, in the five-dimensional scenario of braneworld and space–time-mass theories, geodesic motion in 5D is observed to be non-geodesic in 4D. Usually, the discussion is purely geometric and based on the dimensional reduction of the geodesic equation in 5D, without any reference to the test particle whatsoever. In this work we obtain the equation of motion in 4D directly from the principle of least action. So our main thrust is not the geometry but the particle observed in 4D. A clear physical picture emerges from our work. Specifically, that the deviation from the geodesic motion in 4D is due to the variation of the rest mass of a particle, which is induced by the scalar field in the 5D metric and the explicit dependence of the space–time metric on the extra coordinate. Thus, the principle of least action not only leads to the correct equations of motion, but also provides a concrete physical meaning for a number of algebraic quantities appearing in the geometrical reduction of the geodesic equation.

scholarly journals INVARIANT DEFINITION OF REST MASS AND DYNAMICS OF PARTICLES IN 4D FROM BULK GEODESICS IN BRANE-WORLD AND NON-COMPACT KALUZA–KLEIN THEORIES

2003 ◽  
Vol 12 (05) ◽  
pp. 757-780 ◽  
Author(s):  
J. PONCE DE LEON
Keyword(s):  
Rest Mass ◽  
Geodesic Equation ◽  
Brane World ◽  
Test Particles ◽  
Higher Dimensional ◽  
Jacobi Formalism ◽  
Comprehensive Picture ◽  
Definition Of ◽  
Invariant Definition ◽  
Kaluza Klein

In the Randall–Sundrum brane-world scenario and other non-compact Kaluza–Klein theories, the motion of test particles is higher-dimensional in nature. In other words, all test particles travel on five-dimensional geodesics but observers, who are bounded to spacetime, have access only to the 4D part of the trajectory. Conventionally, the dynamics of test particles as observed in 4D is discussed on the basis of the splitting of the geodesic equation in 5D. However, this procedure is not unique and therefore leads to some problems. The most serious one is the ambiguity in the definition of rest mass in 4D, which is crucial for the discussion of the dynamics. We propose the Hamilton–Jacobi formalism, instead of the geodesic one, to study the dynamics in 4D. On the basis of this formalism we provide an unambiguous expression for the rest mass and its variation along the motion as observed in 4D. It is independent of the coordinates and any parameterization used along the motion. Moreover, we are able to show a comprehensive picture of the various physical scenarios allowed in 4D, without having to deal with the subtle details of the splitting formalism. Moreover we study the extra non-gravitational forces perceived by an observer in 4D who describes the geodesic motion of a bulk test particle in 5D. Firstly, we show that the so-called fifth force fails to account for the variation of rest mass along the particle's worldline. Secondly, we offer here a new definition that correctly takes into account the change of mass observed in 4D.

scholarly journals An Alternative Approach to the Static Spherically Symmetric, Vacuum Global Solution to the Einstein Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
Luis Herrera ◽  
Louis Witten
Keyword(s):  
Phase Transition ◽  
Einstein Equations ◽  
Spherically Symmetric ◽  
Angle Variable ◽  
Schwarzschild Black Hole ◽  
Alternative Description ◽  
Complex Transformation ◽  
Test Particles ◽  
Alternative Approach ◽  
Symmetric Vacuum

We propose an alternative description of the Schwarzschild black hole based on the requirement that the solution is static not only outside the horizon but also inside it. As a consequence of this assumption, we are led to a change of signature implying a complex transformation of an angle variable. There is a “phase transition” on the surface R=2m, producing a change in the symmetry as we cross this surface. Some consequences of this situation on the motion of test particles are investigated.

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