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...

The volumes, spectra and geodesics of a recently constructed infinite family of fivedimensional inhomogeneous Einstein metrics on the two S bundles over S are examined. The metrics are in general of cohomogeneity one but they contain the infinite family of homogeneous metrics T . The geodesic flow is shown to be completely integrable, in fact both the Hamilton-Jacobi and the Laplace equation se...

The equations of 10 or 11 dimensional supergravity admit supersymmetric compactifications on 7-manifolds of G2 holonomy, but these supergravity vacua are deformed away from special holonomy by the higher-order corrections of string or M-theory. We find simple expressions for the first-order corrections to the Einstein and Killing spinor equations in terms of the calibrating 3-form of the leadin...

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 ...