Completeness of general
                    <i>pp</i>
                    -wave spacetimes and their impulsive limit

Sämann, Clemens; Steinbauer, Roland; Švarc, Robert

doi:10.1088/0264-9381/33/21/215006

Cited by 12 publications

(28 citation statements)

References 45 publications

(74 reference statements)

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“…(whenever remaining in D[ρ 0 , θ + ]). By usingρ(s) > 0 (see (32)) and the second equation in (15), the inequalities As δ 0 nρ(s) n−2 > c 0 , inequalities (44) and (45) yield directlÿ Proof of Proposition 3.7. Define θ * and choose θ − so that…”

Section: 3mentioning

confidence: 94%

The Ehlers-Kundt conjecture about gravitational waves and dynamical systems

Flores

Sánchez

2020

Journal of Differential Equations

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Ehlers-Kundt conjecture is a physical assertion about the fundamental role of plane waves for the description of gravitational waves. Mathematically, it becomes equivalent to a problem on the Euclidean plane R 2 with a very simple formulation in Classical Mechanics: given a non-necessarily autonomous potential V (z, u), (z, u) ∈ R 2 × R, harmonic in z (i.e. source-free), the trajectories of its associated dynamical systemz(s) = −∇zV (z(s), s) are complete (they live eternally) if and only if V (z, u) is a polynomial in z of degree at most 2 (so that V is a standard mathematical idealization of vacuum). Here, the conjecture is solved in the significative case that V is bounded polynomially in z for finite values of u ∈ R. The mathematical and physical implications of this polynomial EK conjecture, as well as the non-polynomial one, are discussed beyond their original scope.

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Section: 3mentioning

confidence: 94%

The Ehlers-Kundt conjecture about gravitational waves and dynamical systems

Flores

Sánchez

2020

Journal of Differential Equations

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“…The analysis of the action of impulsive gravitational waves on free particles will be carried out elsewhere, and compared to the results of Refs. [19,20,21]. The feature discussed in the present article does not take place in the context of linearised gravitational waves, in which case the wave is supposed to be unaffected by the medium, although it becomes linearised somehow.…”

Section: Final Commentsmentioning

confidence: 96%

“…In Figure [5] we see the behaviour of the Kinetic energy of the particle, after the passage of the wave, when the initial conditions are given by Eq. (20).…”

Section: Figurementioning

confidence: 99%

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Kinetic energy and angular momentum of free particles in the gyratonic pp-waves space-times

Maluf

Rocha-Neto

Ulhoa

et al. 2018

Class. Quantum Grav.

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Gyratonic pp-waves are exact solutions of Einstein's equations that represent non-linear gravitational waves endowed with angular momentum. We consider gyratonic pp-waves that travel in the z direction and whose time dependence on the variable u = 1 √ 2 (z − t) is given by gaussians, so that the waves represent short bursts of gravitational radiation propagating in the z direction. We evaluate numerically the geodesics and velocities of free particles in the space-time of these waves, and find that after the passage of the waves both the kinetic energy and the angular momentum per unit mass of the particles are changed. Therefore there is a transfer of energy and angular momentum between the gravitational field and the free particles, so that the final values of the energy and angular momentum of the free particles may be smaller or larger in magnitude than the initial values.

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“…We mention that the completeness of general pp-wave space-times has recently been considered in Ref. [16], and pp-waves with gyratons were investigated in Ref. [17].…”

Section: Introductionmentioning

confidence: 99%

Variations of the Energy of Free Particles in the pp-Wave Spacetimes

et al. 2018

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We consider the action of exact plane gravitational waves, or ppwaves, on free particles. The analysis is carried out by investigating the variations of the geodesic trajectories of the particles, before and after the passage of the wave. The initial velocities of the particles are non-vanishing. We evaluate numerically the kinetic energy per unit mass of the free particles, and obtain interesting, quasi-periodic behaviour of the variations of the kinetic energy with respect to the width λ of the gaussian that represents the wave. The variation of the energy of the free particle is expected to be exactly minus the variation of the energy of the gravitational field, and therefore provides an estimation of the local variation of the gravitational energy. The investigation is carried out in the context of short bursts of gravitational waves, and of waves described by normalised gaussians, that yield impulsive waves in a certain limit.

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Completeness of general pp -wave spacetimes and their impulsive limit

Cited by 12 publications

References 45 publications

The Ehlers-Kundt conjecture about gravitational waves and dynamical systems

The Ehlers-Kundt conjecture about gravitational waves and dynamical systems

Kinetic energy and angular momentum of free particles in the gyratonic pp-waves space-times

Variations of the Energy of Free Particles in the pp-Wave Spacetimes

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