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We study the properties of the ergosurface of the Pomeransky–Senkov black rings, and show that it splits into an “inner” and an “outer” region. As for the singular set, the topology of the “outer ergosurface” depends upon the value of parameters.  相似文献   
2.
We answer a question raised by Brass on the number of maximally repeated sub-patterns in a set of n points in Rd. We show that this number, which was conjectured to be polynomial, is in fact Θ(2n/2) in the worst case, regardless of the dimension d.  相似文献   
3.
We define the (total) center of mass for suitably asymptotically hyperbolic time-slices of asymptotically anti-de Sitter spacetimes in general relativity. We do so in analogy to the picture that has been consolidated for the (total) center of mass of suitably asymptotically Euclidean time-slices of asymptotically Minkowskian spacetimes (isolated systems). In particular, we unite—an altered version of—the approach based on Hamiltonian charges with an approach based on CMC-foliations near infinity. The newly defined center of mass transforms appropriately under changes of the asymptotic coordinates and evolves in the direction of an appropriately defined linear momentum under the Einstein evolution equations.  相似文献   
4.
We construct initial data sets which satisfy the vacuum constraint equations of General Relativity with positive cosmological constant. More precisely, we deform initial data with ends asymptotic to Schwarzschild–de Sitter to obtain non-trivial initial data with exactly Kerr–de Sitter ends. The method is inspired from Corvino’s gluing method. We obtain here a extension of a previous result for the time-symmetric case by Chru?ciel and Pollack (Ann H Poincaré 9(4):639–654, 2008). We also deal with the case of asymptotically Kerr–de Sitter initial data.  相似文献   
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