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Penrose junction conditions extended: Impulsive waves with gyratons

Podolský, J.; Švarc, R.; Steinbauer, R.; Sämann, C.

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.
journal:Phys. Rev. D
grants:Spacetimes and Fields in Einstein's Theory of Gravity and its Generalizations, GAČR 17-01625S; 2017-2019; hlavní řešitel: Jiří Podolský
physrevd.96.064043.pdf (200.98 kB)

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