相关论文: A variational principle for stationary, axisymmetr…

This revision includes clarified exposition and simplified analysis. Solutions of the Einstein equations which are periodic and have standing gravitational waves are valuable approximations to more physically realistic solutions with…

We prove that extreme Kerr initial data set is a unique absolute minimum of the total mass in a (physically relevant) class of vacuum, maximal, asymptotically flat, axisymmetric data for Einstein equations with fixed angular momentum. These…

We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be considered as a simple star model: a self-gravitating perfect fluid ball with constant mass density rotating in rigid motion. Using…

The existence of stationary solutions to the Einstein-Vlasov system which are axially symmetric and have non-zero total angular momentum is shown. This provides mathematical models for rotating, general relativistic and asymptotically flat…

Using the Euclidon method, a stationary solution of Einstein's vacuum equations was obtained, describing N rotating axially symmetric masses, which in the absence of rotation describes N arbitrary axially symmetric static masses, for…

A new approximate solution of vacuum and stationary Einstein field equations is obtained. This solution is constructed by means of a power series expansion of the Ernst potential in terms of two independent and dimensionless parameters…

We review explicit solutions to the stationary axisymmetric Einstein-Maxwell equations which can be interpreted as disks of charged dust. The disks of finite or infinite extension are infinitesimally thin and constitute a surface layer at…

For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measure the departure of the data set from the stationary regime, it vanishes if and only if the data is…

From a particularly simple solution of the Ernst equation, we build a solution of the vacuum stationary axisymmetric Einstein equations depending on three parameters. The parameters are associated to the total mass of the source and its…

We obtain an approximate global stationary and axisymmetric solution of Einstein's equations which can be thought as a simple star model: a self-gravitating perfect fluid ball with a differential rotation motion pattern. Using the…

Axially symmetric stationary metrics governed by the Einstein-Euler equations for slowly rotating perfect fluids have been constructed in an arbitrarily large bounded domain containing the support of the mass density. However the problem of…

The non-linear superposition of the stationary euclidon solution with an arbitrary axially symmetric stationary gravitational field on the basis of the method of variation of parameters was constructed. Stationary soliton solution of the…

We show how to reduce the general formulation of the mass-angular momentum inequality, for axisymmetric initial data of the Einstein equations, to the known maximal case whenever a geometrically motivated system of equations admits a…

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 present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the…

It is shown that the vacuum Einstein equations for an arbitrary stationary axisymmetric space-time can be completely separated by re-formulating the Ernst equation and its associated linear system in terms of a non-autonomous…

Axisymmetric and stationary solutions are constructed to the Einstein--Vlasov and Vlasov--Poisson systems. These solutions are constructed numerically, using finite element methods and a fixed-point iteration in which the total mass is…

In analogy with the standard derivation of the Schwarzschild solution, we find all static, cylindrically symmetric solutions of the Einstein field equations for vacuum. These include not only the well known cone solution, which is locally…

In this work we present an approximate solution of the Einstein equations describing a global model for the gravitational field generated by a bounded, self-gravitating stationary and axisymmetric body rotating rigidly with constant angular…

We consider vacuum metrics admitting conformal compactification which is smooth up to the scri $\mathscr{I^+}$. We write metric in the Bondi-Sachs form and expand it into power series in the inverse affine distance $1/r$. Like in the case…