Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold M = M 0 × n i=1 M i (n ≥ 1) are investigated under dimensional reduction to a D 0-dimensional effective non-minimally coupled σ-model which generalizes the familiar Brans-Dicke model. It is argued that the Einstein frame should be considered as the physical one. The general prescription for the Eins...

We prove global stability of Minkowski space for the Einstein vacuum equations in harmonic (wave) coordinate gauge for the set of restricted data coinciding with the Schwarzschild solution in the neighborhood of space-like infinity. The result contradicts previous beliefs that wave coordinates are ”unstable in the large” and provides an alternative approach to the stability problem originally s...

Static axisymmetric Einstein–Maxwell–Dilaton and stationary axisymmetric Einstein–Maxwell–Dilaton–Axion theories in four space–time dimensions are shown to be integrable by means of the inverse scattering transform method. PASC number(s): 97.60.Lf, 04.60.+n, 11.17.+y

In a space-time M with a Killing vector field ξa which is either everywhere timelike or everywhere spacelike, the collection of all trajectories of ξa gives a 3-dimensional space S. Besides the symmetry-reduced action from that of Einstein-Hilbert, an alternative action of the fields on S is also proposed which gives the same fields equations as those reduced from the vacuum Einstein equation o...

The classical unified theory of Weyl is revisited. The possibility of stable extended electron model in the Einstein-Weyl space is suggested .

A Hilbert manifold structure is described for the phase space F of asymptotically flat initial data for the Einstein equations. The space of solutions of the constraint equations forms a Hilbert submanifold C ⊂ F . The ADM energy-momentum defines a function which is smooth on this submanifold, but which is not defined in general on all of F . The ADM Hamiltonian defines a smooth function on F w...