We construct infinitely many new 1-parameter families of simply connected complete non-compact G$\_2$-manifolds with controlled geometry at infinity. The generic member each family has so-called asymptotically locally conical (ALC) geometry. However, the nature asymptotic changes two special parameter values: one value we obtain a unique (AC) geometry; on approach to other metrics collapses an ...

A bstract We study rotating global AdS solutions in five-dimensional Einstein gravity coupled to a multiplet complex scalar within cohomogeneity-1 ansatz. The onset of the gravitational and field superradiant instabilities Myers-Perry-AdS black hole mark bifurcation points resonators hairy holes, respectively. These are subject other (gravitational or scalar) instability, result which contain b...

We continue the investigation of Spin(7) holonomy metric of cohomogeneity one with the principal orbit SU(3)/U(1). A special choice of U(1) embedding in SU(3) allows more general metric ansatz with five metric functions. There are two possible singular orbits in the first order system of Spin(7) instanton equation. One is the flag manifold SU(3)/T 2 also known as the twister space of CP(2) and ...

We prove that any supersymmetric solution to five-dimensional minimal gauged supergravity with $SU(2)$ symmetry, is timelike outside an analytic horizon, a Gutowski-Reall black hole or its near-horizon geometry. The proof combines delicate analysis the general form for K\"ahler metric cohomogeneity-1 symmetry. also soliton this theory, symmetry and nut complex bolt, has base enhanced $U(1)\time...

It is fair to say that our current mathematical understanding of the dynamics of gravitational collapse to a black hole is limited to the spherically symmetric situation and, in fact, even in this case much remains to be learned. The reason is that Einstein’s equations become tractable only if they are reduced to a 1 + 1 dimensional system of partial differential equations. Due to this technica...

A general class of four dimensional, stationary solutions of the Einstein-Maxwell system with a conformally coupled scalar field is constructed in this paper. The stationary case is presented and shown to belong to the Plebanski-Demianski family which implies that the static metric has the form of the C-metric. It is shown that in the static, AdS case, a new family of Black Holes arises. They t...

We study the Ricci flow starting at an SU(2) cohomogeneity-1 metric $g_{0}$ on $\mathbb{R}^{4}$ with monotone warping coefficients and whose restriction to any hypersphere is a Berger metric. If has bounded Hopf-fiber, curvature controlled by size of orbits opens faster than paraboloid in directions orthogonal then converges Taub-NUT $g_{\mathsf{TNUT}}$ Cheeger-Gromov sense infinite time. also ...