In the general Euclidean formulation of the AdS/CFT correspondence put forth in [25], one considers Riemannian manifolds of the form M × Y , where M is conformally compactifiable with conformal boundaryat-infinity N. It is then a problem of fundamental interest to determine, for a given compact manifold N with a given conformal structure, the complete Einstein manifolds of negative Ricci curvat...

We define an elliptic equation for Hermitian metrics which is related to the Einstein condition. Solutions to this equation are closely related to Kähler-Einstein metrics, and are automatically Kähler-Einstein when a certain non-positive condition is satisfied by c1(M). Given this, a natural flow equation arises taking Hermitian metrics to Kähler metrics. We prove short time existence and regul...

We calculate the structure of individual vortices in rotating Bose-Einstein condensates in a transverse harmonic trap. Making a Wigner-Seitz approximation for the unit cell of the vortex lattice, we derive the Gross-Pitaevskii equation for the condensate wave function in each cell of the lattice, including effects of varying coarse grained density. We calculate the Abrikosov parameter, the frac...

s of Publications I–VIII 58

It is shown how a metric structure can be induced in a simple way starting with a gauge structure and a preferred volume, by spontaneous symmetry breaking. A polynomial action, including coupling to matter, is constructed for the symmetric phase. It is argued that assuming a preferred volume, in the context of a metric theory, induces only a limited modification of the theory. §1 Attempts to Us...

N(k)-quasi Einstein manifolds are introduced and studied.

We define an elliptic equation for Hermitian metrics which is related to the Einstein condition. Solutions to this equation are closely related to Kähler-Einstein metrics, and are automatically Kähler-Einstein when a certain non-positive condition is satisfied by c1(M). Given this, a natural flow equation arises taking Hermitian metrics to Kähler metrics. We prove short time existence and regul...

The logarithmic correction to Bekenshtein–Hawking entropy in the framework of 4D Einstein–Gauss–Bonnet gravity coupled with nonlinear electrodynamics is obtained. We explore black hole solution spherically symmetric metric. term has a structure similar semi-classical Einstein equations. energy emission rate holes and conditions are studied. quasinormal modes test scalar field investigated. grav...

The main result of this paper is that the space of conformally compact Einstein metrics on any given manifold is a smooth, infinite dimensional Banach manifold, provided it is non-empty, generalizing earlier work of Graham-Lee and Biquard. We also prove full boundary regularity for such metrics in dimension 4 and a local existence and uniqueness theorem for such metrics with prescribed metric a...