Generalizations ofpp-wave spacetimes in higher dimensions

Vanishing Scalar Invariant Spacetimes in Higher Dimensions

We study manifolds with Lorentzian signature and prove that all scalar curvature invariants of all orders vanish in a higher-dimensional Lorentzian spacetime if and only if there exists an aligned non-expanding, non-twisting, geodesic null direction along which the Riemann tensor has negative boost order.

Type D Einstein spacetimes in higher dimensions

We show that all static spacetimes in higher dimensions n > 4 are necessarily of Weyl types G, Ii, D or O. This applies also to stationary spacetimes provided additional conditions are fulfilled, as for most known black hole/ring solutions. (The conclusions change when the Killing generator becomes null, such as at Killing horizons, on which we briefly comment.) Next we demonstrate that the sam...

Type II Einstein spacetimes in higher dimensions

This short note shows that many of the results derived by Pravda et al (Class. Quant. Grav. 24 4407-4428 ) for higher-dimensional Type D Einstein spacetimes can be generalized to all Einstein spacetimes admitting a multiple WAND; the main new result being the extension to include the Type II case. Examples of Type D Einstein spacetimes admitting non-geodesic multiple WANDs are given in all dime...

Wavepacket Ab Initio Dynamics: Generalizations to Higher Dimensions

Threshold for blowup for equivariant wave maps in higher dimensions

We consider equivariant wave maps from R + d 1 to Sd in supercritical dimensions ⩽ ⩽ d 3 6. Using mixed numerical and analytic methods, we show that the threshold of blowup is given by the codimension-one stable manifold of a self-similar solution with one instability. To probe self-similar blowup, we develop a novel numerical method, based on an adaptive rescaling of coordinates, which may be ...