In this paper, we consider very rough solutions to Cauchy problem for the Einstein vacuum equations in CMC spacial harmonic gauge, and obtain the local well-posedness result in Hs, s > 2. The novelty of our approach lies in that, without resorting to the standard paradifferential regularization over the rough, Einstein metric g, we manage to implement the commuting vector field approach to prov...

The energy distributions of four 2+1 dimensional black hole solutions were obtained by using the Einstein and Møller energy-momentum complexes. While r → ∞, the energy distributions of Virbhadra’s solution for the Einstein-massless scalar equation becames EEin ∼ π κ (1 − q)R and EMøl ∼ − 2π κ q(1− q)R, and the energy distributions of these three solutions become EEin ∼ πΛr κ and EMøl ∼ − 4πΛr κ...

In Newtonian theory, there are static equilibrium configurations of charged particles in which the gravitational attractions and the electric repulsions among the particles exactly balance. In general relativity, it is well known that the Einstein equation has such a static solution corresponding to these Newtonian situations, namely there is the Majumdar-Papapetrou solution [2,3] describing an...

The aim of this paper is to evaluate the energy distribution of some 2 + 1 black hole solutions applying the Landau-Lifshitz and Weinberg definitions. The metrics under consideration describe the charged black hole, the solution coupling to a static scalar field and the static and circularly symmetric exact solution of the Einstein-massless scalar equation. Further, we compare the expressions f...

In this paper, we evaluate energy and momentum density distributions for the Weyl metric by using the well-known prescriptions of Einstein, Landau-Lifshitz, Papaterou and Möller. The metric under consideration is the static axisymmetric vacuum solution to the Einstein field equations and one of the field equations represents the Laplace equation. Curzon metric is the special case of this spacet...

We consider the general asymptotic expression of stationary space-time. Using Killing equation, we reduce the dynamical freedom of Einstein equation to the ingoing gravitational wave Ψ0. The general form of this function can be got. With the help of asymptotically algebraic special condition, we prove that all Newman-Penrose constants vanish. PACS number : 04.20.-q, 04.20.Ha

The effect of multi-particle Coulomb final state interactions on higher-order intensity correlations is determined in general, based on a scattering wave function which is solution of the n-body Coulomb Schrödinger equation in (a large part of) the asymptotic region of n-body configuration space. In particular, we study Coulomb effects on the n-particle Bose-Einstein correlation functions of si...

We show, using purely classical considerations and logical extrapolation of results belonging to point particle theories, that the metric background field in which a string propagates must satisfy an Einstein or an Einstein–like equation. Additionally, there emerge restrictions on the worldsheet curvature, which seems to act as a source for spacetime gravity, even in the absence of other matter...

We study the time-dependent Gross–Pitaevskii equation describing Bose–Einstein condensation of trapped dipolar quantum gases. Existence and uniqueness as well as the possible blow-up of solutions are studied. Moreover, we discuss the problem of dimension-reduction for this nonlinear and nonlocal Schrödinger equation.

A hodograph transformation for a wide family of multidimensional nonlinear partial differential equations is presented. It is used to derive solutions of the heavenly equation (dispersionless Toda equation) as well as a family of explicit ultra-hyperbolic selfdual vacuum spaces admiting only one Killing vector which is not selfdual, we also give the corresponding explicit Einstein–Weyl structures.