Time shift phenomena in Einstein Rosen solitary-like waves

Dagotto, A D; Gleiser, Reinaldo J.; Nicasio, Carlos O.

doi:10.1088/0264-9381/8/6/015

Cited by 11 publications

(4 citation statements)

References 8 publications

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“…where N 1 = (|a| 4 q 4 + 64a 2 i q 6 ) − 128a r a i qp 2 1 (q 2 + p 4 1 ) 2 + 64(|a| 2 + a 2 i )q 4 p 4 1 + 64(|a| 2 + a 2 r )q 2 p 8 1 + 64a 2 r p 12 1 , (53) D 1 = q 4 (|a| 2 + 64q 2 ) 2 + 256q 4 (|a| 2 + a 2 r + 64q 2 )p 4 1 + 1024a r a i qp 6 1 (q 2 − p 4 1 ) + 384q 2 (3|a| 2 − 4a 2 r + 64q 2 )p 8 1 +256(a 2 r + 64q 2 )p 12 1 + 4096p 16 1 , (54) N 2 = |a| 4 q 4 + 64a 2 i q 6 − 384a r a i p 2 1 q(q 4 + p 8 1 ) + 192q 2 p 4 1 (|a| 2 − 5a 2 i )(q 2 − p 4 1 ) + 1280a r a i q 3 p 6 1 + 64a 2 r p 12 1 , (55) D 2 = q 4 (|a| 2 + 64q 2 ) 2 + 256q 4 (|a| 2 + a 2 r + 64q 2 )p 4 1 + 1024a r a i qp 6 1 (q 2 − p 4 1 ) + 384q 2 (3|a| 2 − 4a 2 r + 64q 2 )p 8 1 +256(a 2 r + 64q 2 )p 12 1 + 4096p 16 1 , (56) and p 1 = 2u + 4u 2 + q 2 .…”

Section: Null Infinitymentioning

confidence: 99%

“…Basically following the analysis in Ref. [16], where how to measure a time shift for gravitation solitons was proposed, we numerically analyze the asymptotic behavior of the wave packets at future null infinity v → ∞ and past null infinity u → −∞. In principle, we can find a time shift of the wave amplitudes by comparing its arrival time at future null infinity with that of a massless test particle starting off past null infinity at the same time.…”

Section: Time Shiftmentioning

confidence: 99%

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Nonlinear effects for a cylindrical gravitational two-soliton

Tomizawa¹,

Mishima²

2015

Phys. Rev. D

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Using a cylindrical soliton solution to the four-dimensional vacuum Einstein equation, we study non-linear effects of gravitational waves such as Faraday rotation and time shift phenomenon. In the previous work, we analyzed the single-soliton solution constructed by the Pomeransky's improved inverse scattering method. In this work, we construct a new two-soliton solution with complex conjugate poles, by which we can avoid light-cone singularities unavoidable in a single soliton case. In particular, we compute amplitudes of such non-linear gravitational waves and time-dependence of the polarizations. Furthermore, we consider the time shift phenomenon for soliton waves, which means that a wave packet can propagate at slower velocity than light.

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Section: Null Infinitymentioning

confidence: 99%

Section: Time Shiftmentioning

confidence: 99%

Nonlinear effects for a cylindrical gravitational two-soliton

Tomizawa¹,

Mishima²

2015

Phys. Rev. D

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“…Most of the studies were devoted to rather restricted aspects of nonlinearity originating from the Einstein gravity, for example, the global structure of spacetimes or formation of singularities. Relatively recently, several researchers have studied the physical wave phenomena related to nonlinear interaction of gravitational waves itself: the gravitational Faraday effect [5,6], the time shift phenomena [7,8], and so on (for more details, see [9] and references therein). From the present standpoint after the direct discovery of gravitational waves, it is not too much to say that many physically interesting solutions, regardless of whether or not they are known, still remain without being thoroughly investigated in different ways than before.…”

mentioning

confidence: 99%

Construction and application of variations on the cylindrical gravitational waves of Weber, Wheeler, and Bonnor

Mishima

Tomizawa

2017

Phys. Rev. D

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To clarify certain nonlinear properties of strong gravitational field, we investigate cylindrically symmetric gravitational waves that are localized as regular wave packets in the space of radial and time coordinates. The waves are constructed by applying a certain kind of harmonic mapping method to the seed solutions with linear polarization, which are generalizations of the solution representing a cylindrical gravitational pulse wave discussed by Weber-Wheeler and Bonnor. The solutions obtained here, though their form is rather simple, show occurrence of strong mutual conversion between a linear mode and a cross mode apparently. The single localized wave shows the conversion in the vicinity of the symmetric axis where the self-interaction is strengthened, and the collision between multiple waves also causes the conversion. These phenomena can be thought to be the emergence of genuine nonlinearity that the Einstein gravity holds. Finally we discuss a simple, but interesting application of the solutions to the case of the Einstein-Maxwell system.

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“…These include the family described in [ll], and also the solutions As a general remark, we should point out rbat in the asymptotically flat case, all these solutions display the very interesting phenomenon of time shifts and non-linear interference for both the electromagnetic and gravitational solitonic waves. These have been discussed in detail in [U] (see also [16]) where, however, only some asymptotic features of the solutions were used. In fact, our interest in the properties of these bisolitonic solutions arose after similar properties were found for the single soliton metrics 1171.…”

Section: Introductionmentioning

confidence: 99%

Two-soliton solutions of the Einstein-Maxwell equations

Dagotto¹,

Gleiser²,

Nicasio³

1993

Class. Quantum Grav.

Self Cite

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The authors present a family of solutions of the Einstein-Maxwell equations obtained as a two-soliton transformation of a Minkowskian seed, using Alekseev's inverse scattering method (AISM). For general values of the arbitrary parameters that arise from the AISM, the metrics are of Petrov type I, and represent cylindrically symmetric perturbations of a conical spacetime ('thin cosmic string'), that preserve the asymptotic flatness of the background, up to an additional deficit angle. The metrics can be made regular on the symmetry axis by an adequate choice of parameters. In the limit in which the C-energy goes to infinity, the metric is singular, but can be 'renormalized', obtaining either (i) a family of metrics where the symmetry axis contains a curvature singularity, or (ii) a family of cylindrically symmetric metrics with a regular axis, that can be interpreted as simple solitonic perturbations of an unstable Melvin universe. These contain a subfamily of diagonal metrics. They include a comparison with other metrics, obtained as limiting cases and, in the case of vacuum solutions, they show, by an explicit calculation, that the results obtained are equivalent to the Belinski-Zakharov transformation for two pairs of complex-conjugate soliton poles for the same seed.

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Time shift phenomena in Einstein Rosen solitary-like waves

Cited by 11 publications

References 8 publications

Nonlinear effects for a cylindrical gravitational two-soliton

Nonlinear effects for a cylindrical gravitational two-soliton

Construction and application of variations on the cylindrical gravitational waves of Weber, Wheeler, and Bonnor

Two-soliton solutions of the Einstein-Maxwell equations

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