Robinson-Trautman waves exhibit an explicit memory effect, with their news-free sector matching boosted rescaled Schwarzschild black holes and the vacuum sector of Euclidean Liouville theory.
Boosted Schwarzschild Metrics from a Kerr-Schild Perspective
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abstract
The Kerr-Schild version of the Schwarzschild metric contains a Minkowski background which provides a definition of a boosted black hole. There are two Kerr-Schild versions corresponding to ingoing or outgoing principle null directions. We show that the two corresponding Minkowski backgrounds and their associated boosts have an unexpected difference. We analyze this difference and discuss the implications in the nonlinear regime for the gravitational memory effect resulting from the ejection of massive particles from an isolated system. We show that the nonlinear effect agrees with the linearized result based upon the retarded Green function only if the velocity of the ejected particle corresponds to a boost symmetry of the ingoing Minkowski background. A boost with respect to the outgoing Minkowski background is inconsistent with the absence of ingoing radiation from past null infinity.
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An approximate solution for a general boosted Kerr-Newman black hole is derived from a BMS twisting metric, shown to satisfy Einstein equations up to 1/r^4, with analysis of horizons, ergosphere, and electromagnetic fields for a timelike observer.
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Memory of Robinson-Trautman waves
Robinson-Trautman waves exhibit an explicit memory effect, with their news-free sector matching boosted rescaled Schwarzschild black holes and the vacuum sector of Euclidean Liouville theory.
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General Boosted Black Holes: A First Approximation
An approximate solution for a general boosted Kerr-Newman black hole is derived from a BMS twisting metric, shown to satisfy Einstein equations up to 1/r^4, with analysis of horizons, ergosphere, and electromagnetic fields for a timelike observer.