Cut-and-paste for impulsive gravitational waves with 
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: The geometric picture

Podolský, Jiř̌í; Sämann, Clemens; Steinbauer, Roland; Švarc, Robert

doi:10.1103/physrevd.100.024040

Cited by 14 publications

(29 citation statements)

References 33 publications

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“…To date, an exact solution for a single propagating plane gravitational wave with λ > 0 has not been found. One cannot use Penrose's cut-and-paste method to find such a solution because this leads to wavefronts that are spherical or hyperboloidal when λ > 0 or λ < 0, respectively [14]. Thus, to try shed some light toward an analytic solution, we numerically evolve our system with λ > 0 and with one ingoing wave, whose wave profile approximates the Dirac delta function.…”

Section: An Impulsive Wavementioning

confidence: 99%

“…Penrose's cut-and-paste method [6,8], which cuts Minkowski space-time along a null hyperplane, shunts one half along the same surface and then pastes the two halves back together gives rise to a space-time with one impulsive gravitational wave (i.e., with a Dirac delta function wave profile). This has been generalized to non-zero, constant curvature backgrounds [9][10][11][12][13][14] where the wave fronts are topologically spherical for λ > 0 and hyperboloidal for λ < 0. There do not exist, however, closed form solutions to the full non-linear Einstein equations with λ = 0 that contain gravitational waves with plane symmetric wave fronts.…”

Section: Introductionmentioning

confidence: 99%

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Can Gravitational Waves Halt the Expansion of the Universe?

2021

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We numerically investigate the propagation of plane gravitational waves in the form of an initial boundary value problem with de Sitter initial data. The full non-linear Einstein equations with positive cosmological constant λ are written in the Friedrich–Nagy gauge which yields a wellposed system. The propagation of a single wave and the collision of two with colinear polarization are studied and contrasted with their Minkowskian analogues. Unlike with λ=0, critical behaviours are found with λ>0 and are based on the relationship between the wave profile and λ. We find that choosing boundary data close to one of these bifurcations results in a “false” steady state which violates the constraints. Simulations containing (approximate) impulsive wave profiles are run and general features are discussed. Analytic results of Tsamis and Woodard, which describe how gravitational waves could affect an expansion rate at an initial instance of time, are explored and generalized to the entire space–time. Finally we put forward boundary conditions that, at least locally, slow down the expansion considerably for a time.

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Section: An Impulsive Wavementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Can Gravitational Waves Halt the Expansion of the Universe?

2021

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show abstract

“…To date, an exact solution for a single propagating plane gravitational wave with λ > 0 has not been found. One cannot use Penrose's cut-and-paste method to find such a solution because this leads to wavefronts that are spherical or hyperboloidal when λ > 0 or λ < 0 respectively [16]. Thus, to try shed some light toward an analytic solution, we numerically evolve our system with λ > 0 and with one ingoing wave, whose wave profile approximates the Dirac delta function.…”

Section: An Impulsive Wavementioning

confidence: 99%

“…with a Dirac delta function wave profile.) This has been generalized to non-zero, constant curvature backgrounds [11,12,13,14,15,16] where the wave fronts are topologically spherical for λ > 0 and hyperboloidal for λ < 0. There do not exist however, closed form solutions to the full non-linear Einstein equations with λ = 0 that contain gravitational waves with plane symmetric wave fronts.…”

Section: Introductionmentioning

confidence: 99%

Can gravitational waves halt the expansion of the universe?

Frauendiener¹,

Hakata²,

Stevens³

2021

Preprint

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We numerically investigate the propagation of plane gravitational waves in the form of an initial boundary value problem with de Sitter initial data. The full non-linear Einstein equations with positive cosmological constant λ are written in the Friedrich-Nagy gauge which yields a wellposed system. The propagation of a single wave and the collision of two with colinear polarization are studied and contrasted with their Minkowskian analogues. Unlike with λ = 0, critical behaviours are found with λ > 0 and are based on the relationship between the wave profile and λ. We find that choosing boundary data close to one of these bifurcations results in a "false" steady state which violates the constraints. Simulations containing (approximate) impulsive wave profiles are run and general features are discussed. Analytic results of Woodard and Tsamis [1, 2], which describe how gravitational waves could affect an expansion rate at an initial instance of time, are explored and generalized to the entire spacetime. Finally we put forward boundary conditions that, at least locally, slow down the expansion considerably for a time.

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“…By means of this useful geometrical approach, Penrose was able to study certain classes of impulsive plane-fronted and sphericallyfronted waves in Minkowski's backgrounds. Later works of works of Podolskỳ et al [27], [30], [28] apply this method to generate spacetimes whose metric again contains a Dirac delta function with support on the null hypersurface. The most general construction so far describes pp-waves with additional gyratonic terms [30].…”

Section: Introductionmentioning

confidence: 99%

Null shells: general matching across null boundaries and connection with cut-and-paste formalism

Manzano,

Mars

2021

Preprint

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Null shells are a useful geometric construction to study the propagation of infinitesimally thin concentrations of massless particles or impulsive waves. In this paper, we determine and study the necessary and sufficient conditions for the matching of two spacetimes with respective null embedded hypersurfaces as boundaries. Whenever the matching is possible, it is shown to depend on a diffeomorphism between the set of null generators in each boundary and a scalar function, called step function, that determines a shift of points along the null generators. Generically there exists at most one possible matching but in some circumstances this is not so. When the null boundaries are totally geodesic, the point-to-point identification between them introduces a freedom whose nature and consequences are analyzed in detail. The expression for the energy-momentum tensor of a general null shell is also derived. Finally, we find the most general shell (with non-zero energy, energy flux and pressure) that can be generated by matching two Minkowski regions across a null hyperplane. This allows us to show how the original Penrose's cut-and-paste construction fits and connects with the standard matching formalism.

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Cut-and-paste for impulsive gravitational waves with Λ : The geometric picture

Cited by 14 publications

References 33 publications

Can Gravitational Waves Halt the Expansion of the Universe?

Can Gravitational Waves Halt the Expansion of the Universe?

Can gravitational waves halt the expansion of the universe?

Null shells: general matching across null boundaries and connection with cut-and-paste formalism

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