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arXiv · 1908.03456

On the absence of conformally flat slicings of the Kerr spacetime

Antonio de Felice·François Larrouturou·Shinji Mukohyama·Michele Oliosi
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Abstract

This work investigates the possibility of achieving a conformally flat slicing of the Kerr spacetime. We consider a hypersurface of the form $t = F(r,\theta,a)$, where $(t,r,\theta,\phi)$ are the Boyer-Lindquist coordinates, solve for a vanishing Cotton-York tensor of the induced metric order by order in the spin parameter $a$, and show that the procedure fails at the fifth order. We also prove that no coordinate change can induce a spatially flat recasting of the Kerr(-de Sitter) metric, beyond linear order in $a$, adopting a more general ansatz depending on $\phi$.

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Antonio de Felice, François Larrouturou, Shinji Mukohyama, Michele Oliosi. 2019-08-09. On the absence of conformally flat slicings of the Kerr spacetime. https://doi.org/10.1103/physrevd.100.124044

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