We generalize the classical junction conditions for constructing impulsive gravitational waves by the

Penrose “cut and paste” method. Specifically, we study nonexpanding impulses which propagate in spaces

of constant curvature with any value of the cosmological constant (that is, Minkowski, de Sitter, or anti–de

Sitter universes) when additional off-diagonal metric components are present. Such components encode a

possible angular momentum of the ultrarelativistic source of the impulsive wave—the so-called gyraton.

We explicitly derive and analyze a specific transformation that relates the distributional form of the metric

to a new form which is (Lipschitz) continuous. Such a transformation automatically implies an extended

version of the Penrose junction conditions. It turns out that the conditions for identifying points of the

background spacetime across the impulse are the same as in the original Penrose cut and paste construction,

but their derivatives now directly represent the influence of the gyraton on the axial motion of test particles.

Our results apply both for vacuum and nonvacuum solutions of Einstein’s field equations and can also be

extended to other theories of gravity.

Penrose “cut and paste” method. Specifically, we study nonexpanding impulses which propagate in spaces

of constant curvature with any value of the cosmological constant (that is, Minkowski, de Sitter, or anti–de

Sitter universes) when additional off-diagonal metric components are present. Such components encode a

possible angular momentum of the ultrarelativistic source of the impulsive wave—the so-called gyraton.

We explicitly derive and analyze a specific transformation that relates the distributional form of the metric

to a new form which is (Lipschitz) continuous. Such a transformation automatically implies an extended

version of the Penrose junction conditions. It turns out that the conditions for identifying points of the

background spacetime across the impulse are the same as in the original Penrose cut and paste construction,

but their derivatives now directly represent the influence of the gyraton on the axial motion of test particles.

Our results apply both for vacuum and nonvacuum solutions of Einstein’s field equations and can also be

extended to other theories of gravity.

typ: | article |
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journal: | Phys. Rev. D |

volume: | 96 |

pages: | 064043 |

year: | 2017 |

grant: | Spacetimes and Fields in Einstein's Theory of Gravity and its Generalizations, GAČR 17-01625S, 2017-2019 |

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physrevd.96.064043.pdf (200.98 kB) |