Test particle motion in a gravitational plane wave collision background (original) (raw)
Related papers
Geodesics on Cosmic Landscapes of Colliding Plane Waves
2015
On a Cosmic Landscape, the metric structure vested with two orthogonal space-like Killing vectors; a class of solutions of the Einstein-Maxwell's field equations, is spotlighted from the global structural viewpoints of the Khan-Penrose and Bell-Szekeres space-time continua or Cosmic Landscapes: a platform for discussing the motion of a test particle. A solution, spring-boarded by the Ferrari-Ibanez hybrid formalism, also provides a launch-pad for discussing the motion of a test particle on a Degenerate Cosmic Landscape. When a particle is placed along the path of two colliding plane waves, it will be forced to follow a geodesic, defined by the properties of the global structure, leading to either a singularity or a horizon. In the nullcoordinates,(,), the interaction region is bounded, so given the initial conditions the later developments are plotted numerically. The time of fall into the singularity or horizon is also obtained.
An Approach to Colliding Plane Waves in General Relativity
International Journal for Research in Applied Science & Engineering Technology (IJRASET), 2021
For many years after Einstein proposed his general theory of relativity, only a few exact solutions were known. Today the situation is completely different, and we now have a vast number of such solutions. However, very few are well understood in the sense that they can be clearly interpreted as the fields of real physical sources. The obvious exceptions are the Schwarzschild and Kerr solutions. These have been very thoroughly analysed, and clearly describe the gravitational fields surrounding static and rotating black holes respectively. In practice, one of the great difficulties of relating the particular features of general relativity to real physical problems, arises from the high degree of non-linearity of the field equations. Although the linearized theory has been used in some applications, its use is severely limited. Many of the most interesting properties of space-time, such as the occurrence of singularities, are consequences of the non-linearity of the equations.
Asymmetric collision of gravitational plane waves: A new class of exact solutions
General Relativity and Gravitation, 1989
A new three-parameter class of solutions to the Einstein vacuum equations is presented which represents the collision of a pair of gravitational plane waves. Depending on the choice of the parameters, one of the colliding waves has a smooth or unbounded wavefront, or it is a shock, or impulsive, or shock accompanied by an impulsive wave, while the second is any of the above types. A subfamily of the solutions develops no curvature singularity in the interaction region formed by the colliding waves.
Physical Review D, 2002
We investigate how the accuracy and stability of numerical relativity simulations of 1D colliding plane waves depends on choices of equation formulations, gauge conditions, boundary conditions, and numerical methods, all in the context of a first-order 3+1 approach to the Einstein equations, with basic variables some combination of first derivatives of the spatial metric and components of the extrinsic curvature tensor. Hyperbolic schemes, specifically variations on schemes proposed by Bona and Massó and Anderson and York, are compared with variations of the Arnowitt-Deser-Misner formulation. Modifications of the three basic schemes include raising one index in the metric derivative and extrinsic curvature variables and adding a multiple of the energy constraint to the extrinsic curvature evolution equations. Redundant variables in the Bona-Massó formulation may be reset frequently or allowed to evolve freely. Gauge conditions which simplify the dynamical structure of the system are imposed during each time step, but the lapse and shift are reset periodically to control the evolution of the spacetime slicing and the longitudinal part of the metric. We show that physically correct boundary conditions, satisfying the energy and momentum constraint equations, generically require the presence of some ingoing eigenmodes of the characteristic matrix. Numerical methods are developed for the hyperbolic systems based on decomposing flux differences into linear combinations of eigenvectors of the characteristic matrix. These methods are shown to be second-order accurate, and in practice second-order convergent, for smooth solutions, even when the eigenvectors and eigenvalues of the characteristic matrix are spatially varying.
Geodesic motion in Bogoslovsky-Finsler Plane Gravitational Waves
2020
We study the free motion of a massive particle moving in the background of a Finslerian deformation of a plane gravitional wave in Einstein's General Relativity. The deformation is a curved version of a one-parameter family of Relativistic Finsler structures introduced by Bogoslovsky, which are invariant under a deformation of Cohen and Glashow's Very Special Relativity group ISIM(2). The partially broken Carroll Symmetry we derive using Baldwin-Jeffery-Rosen coordinates allows us to integrate the geodesics equations. The transverse coordinates of timelike Finsler-geodesics are identical to those of the underlying plane gavitational wave for any value of the Bogoslovsky-Finsler parameter b. We conclude by replacing the underlying plane gravitational wave by a homogenous pp-wave solution of the Einstein-Maxwell equations. The theory is extended to the Finsler-Friedmann-Lemaitre model.
Particle trapping by a plane gravitational wave
2021
Bialynicki-Birula and Charzynski [1] argued that the gravitational wave emitted during the merger of a black hole binary may trap particles. In this Letter we amplify their statement by describing particle motion in the wave proposed by Lukash [2] to study anisotropic cosmological models. Bounded geodesics (found both analytically and numerically) arise when the wave is of Bianchi type VI. Their symmetries are identified. PACS numbers: 04.20.-q Classical general relativity; 04.30.-w Gravitational waves ∗ mailto: elbistan@itu.edu.tr † corresponding author. mailto:zhangpm5@mail.sysu.edu.cn ‡ mailto:horvathy@lmpt.univ-tours.fr 1 ar X iv :2 10 8. 00 83 8v 1 [ gr -q c] 2 A ug 2 02 1
Kinetic Description of Particle Interaction with a Gravitational Wave
General Relativity and Gravitation, 1997
T he int eract ion of ch arged part icles, m oving in a uniform m agn et ic ® eld, w ith a plane polarized grav it at ional wave is considered using t he Fokker± P lanck± Kolm ogorov (f p k) ap proach. B y using a st och ast icity criterion, we det erm ine t he ex act locat ions in phase space, where reson an ce overlapping occu rs. We invest igat e the diOE usion of orbits aroun d each prim ary reson ance of order m by deriving gen eral an aly t ical ex pressions for an eOE ect ive diOE usion coe cient. A solution of t he corresp onding diOE usion equat ion (Fokker± P lanck equ at ion) for t he st at ic case is found. Num erical integrat ion of the full equ at ions of m ot ion an d subsequent calculat ion of the diOE usion coe cient veri® es t he analyt ical resu lt s. KE Y W ORDS : Fokker± P lanck equat ion w ith m agn et ic ® eld
2010
Black objects in higher dimensional space-times have a remarkably richer structure than their four dimensional counterparts. They appear in a variety of configurations (e.g. black holes, black branes, black rings, black Saturns), and display complex stability phase diagrams. They might also play a key role in high energy physics: for energies above the fundamental Planck scale, gravity is the dominant interaction which, together with the hoop-conjecture, implies that the trans-Planckian scattering of point particles should be well described by black hole scattering. Higher dimensional scenarios with a fundamental Planck scale of the order of TeV predict, therefore, black hole production at the LHC, as well as in future colliders with yet higher energies. In this setting, accurate predictions for the production cross-section and energy loss (through gravitational radiation) in the formation of black holes in parton-parton collisions is crucial for accurate phenomenological modelling in Monte Carlo event generators.