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

In this article, the boundary singularity for stationary solutions of the linearized Boltzmann equation with cut-off inverse power potential is analyzed. In particular, for cut-off hard-potential cases, we establish the asymptotic…

New axisymmetric stationary solutions of the vacuum Einstein equations in five-dimensional asymptotically flat spacetimes are obtained by using solitonic solution-generating techniques. The new solutions are shown to be equivalent to the…

It was first shown in (Catanese-LeBrun 1997) that certain high-dimensional smooth closed manifolds admit pairs of Einstein metrics with Ricci curvatures of opposite sign. After reviewing subsequent progress that has been made on this topic,…

The aim of this paper is to introduce the Inverse Scattering Method for later studies of some problems in nonlinear dynamics, and describe the kink solution of the Sine Gordon Equation using the Inverse Scattering Method as a methodological…

We show that a stationary solution of the Einstein-Maxwell equations which is close to a non-degenerate Reissner-Nordstr\"om-de Sitter solution is in fact equal to a slowly rotating Kerr-Newman-de Sitter solution. The proof uses the…

Vacuum Einstein theory in three spacetime dimensions is locally trivial, but admits many solutions that are globally different, particularly if there is a negative cosmological constant. The classical theory of such locally "anti-de Sitter"…

One way to understand more about spacetime singularities is to construct solutions of the Einstein equations containing singularities with prescribed properties. The heuristic ideas of the BKL picture suggest that oscillatory singularities…

Here I present a stationary cylindrically symmetric asymptotically Einstein static universe solution with the matter consisting of a cosmological and rotating dust term which admits predicted black hole event horizon.

The soliton technique is applied to the 5D static Einstein-Maxwell equations, and an infinite number of solutions are explicitly obtained. We study the rod structure of 2-soliton solutions and we show that the 5D Reissner-Nordstrom solution…

We analyse the issue of uniqueness of solutions of the static vacuum Einstein equations with prescribed geometric or Bartnik boundary data. Large classes of examples are constructed where uniqueness fails. We then discuss the implications…

Current spectral simulations of Einstein's equations require writing the equations in first-order form, potentially introducing instabilities and inefficiencies. We present a new penalty method for pseudo-spectral evolutions of second order…

Non stationary cylindrically symmetric exact solutions of the Einstein-Maxwell equations are derived as single soliton perturbations of a Levi-Civita metric, by an application of Alekseev inverse scattering method. We show that the metric…

In this work, we investigate the stability issue of the inverse problem of determining the locations and time-dependent amplitudes of point sources in a parabolic equation with a non-self adjoint elliptic operator from boundary…

It was shown recently that stochastic quantization can be made into a well defined quantization scheme on (pseudo-)Riemannian manifolds using second order differential geometry, which is an extension of the commonly used first order…

We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modifcation introduced in the cosmological equations leads to several new…

A classical theorem in conformal geometry states that on a manifold with non-positive Yamabe invariant, a smooth metric achieving the invariant must be Einstein. In this work, we extend it to the singular case and show that in all…

We consider the inverse scattering problem on the energy interval in three dimensions. We are focused on stability and instability questions for this problem. In particular, we prove an exponential instability estimate which shows…

In this paper, we construct models that admit the traversable wormhole geometries in the framework of Einstein's gravity with two scalar fields. As well known, the energy conditions are broken and we show that there appears a ghost. The…

In this paper we prove a local removable singularity theorem for certain minimal laminations with isolated singularities in a Riemannian three-manifold. This removable singularity theorem is the key result used in our proof that a complete,…

The standard scattering theory (SST) in non relativistic quantum mechanics (QM) is analyzed. Self-contradictions of SST are deconstructed. A direct way to calculate scattering probability without introduction of a finite volume is…