相关论文: Ghost points in inverse scattering constructions o…

We prove in this note that local geometric uniqueness holds true without loss of regularity for Einstein equations coupled with a large class of matter models. We thus extend the Planchon-Rodnianski uniqueness theorem for vacuum spacetimes.…

In this article we deduce two new exact solutions of Einstein's equations for eternal black holes, now related to stiff matter, one `static' and another rotating (stationary like the Kerr one), thus the number of these eternal solutions…

Solutions of the stationary axisymmetric Einstein equations describing the interior of circularly rotating dust are investigated in order to study their potential applicability as galaxy models. It is shown that such interior solutions…

We prove that static, spherically symmetric, asymptotically flat soliton and black hole solutions of the Einstein-Yang-Mills equations are unstable for arbitrary gauge groups, at least for the ``generic" case. This conclusion is derived…

It is proved that if the scattering amplitudes at a fixed wavenumber for two obstacles from a certain large class of obstacles differ a little, than the obstacles differ a little. Error estimate is given. It is proved that there is an…

We study the structure of stationary and axisymmetric metrics solving the vacuum Einstein equations of General Relativity in four and higher dimensions, building on recent work in hep-th/0408141. We write the Einstein equations in a new…

A review of the author's results is given. Inversion formulas and stability estimates for the solutions to 3D inverse scattering problems with fixed-energy data are obtained. Inversions of exact and noisy data are stidied. The inverse…

We prove a uniqueness theorem for traversable wormhole solutions in the Einstein-Maxwell-dilaton gravity with a phantom scalar field and a possible phantom electromagnetic field. In a certain region of the parameter space, determined by the…

We study the Riemann geometric approach to be aimed at unifying soliton systems. The general two-dimensional Einstein equation with constant scalar curvature becomes an integrable differential equation. We show that such Einstein equation…

Einstein's equations for stationary axisymmetric fields are reformulated as the equations for affine geodesics in a two--dimensional space. The affine collineations of this space are investigated and used to relate explicit solutions of…

We study the perturbations of two classes of static black ellipsoid solutions of four dimensional vacuum Einstein equations. Such solutions are described by generic off--diagonal metrics which are generated by anholonomic transforms of…

We compute a lower bound for the scalar curvature of a gradient Einstein soliton under a certain assumption on its potential function. We establish an asymptotic behavior of the potential function on a noncompact gradient shrinking Einstein…

An explicit one-parameter Lie point symmetry of the four-dimensional vacuum Einstein equations with two commuting hypersurface-orthogonal Killing vector fields is presented. The parameter takes values over all of the real line and the…

We consider the equations for the coefficients of stationary rotating axisymmetric metrics governed by the Einstein-Euler equations, that is, the Einstein equations together with the energy-momentum tensor of a barotropic perfect fluid.…

We consider a fixed angle inverse scattering problem in the presence of a known Riemannian metric. First, assuming a no caustics condition, we study the direct problem by utilizing the progressing wave expansion. Under a symmetry assumption…

We provide a geometric framework for the construction of non-vacuum black holes whose metrics are stationary and axisymmetric. Under suitable assumptions we show that the Einstein equations reduce to an Einstein-harmonic map type system and…

The uniqueness theorem for static, spherically symmetric, asymptotically flat, higher dimensional phantom black holes, with non-degenerate event horizon , being the solutions of Einstein phantom/dilaton Maxwell/anti-Maxwell gravity systems…

After a brief summary of the foundations of general relativity, we will concentrate on the stationary exact solutions of the Einstein and Einstein-Maxwell equations. A number of these solutions can be interpreted as black holes,…

Einstein's equations are known to lead to the formation of black holes and spacetime singularities. This appears to be a manifestation of the mathematical phenomenon of finite-time blowup: a formation of singularities from regular initial…

We study gravitational collapse of a spherically symmetric scalar field in Einstein-aether theory (general relativity coupled to a dynamical unit timelike vector field). The initial value formulation is developed, and numerical simulations…