相关论文: Ernst equation, Fay identities and variational for…

We find a reconstruction algorithm able to generate all the static spherically symmetric interior solutions in the framework of Ho\v{r}ava gravity and Einstein-\ae ther theory in presence of anisotropic fluids. We focus for simplicity on…

The standard method of proving analyticity of stationary vacuum metrics invokes the quotient-space version of Einstein equations. We verify that the same conclusion can be obtained using the KID equations on maximal surfaces.

We show that homogeneous Einstein metrics on Euclidean spaces are Einstein solvmanifolds, using that they admit periodic, integrally minimal foliations by homogeneous hypersurfaces. For the geometric flow induced by the orbit-Einstein…

We examine the space of solutions to the affine quasi--Einstein equation in the context of homogeneous surfaces. As these spaces can be used to create gradient Yamabe solitions, conformally Einstein metrics, and warped product Einstein…

The functional potential formalism is used to analyze stationary axisymmetric spaces in the Einstein-Maxwell-Dilaton theory. Performing a Legendre transformation, a ``Hamiltonian''is obtained, which allows to rewrite the dynamical equations…

The Einstein's field equations of FRW universes filled with a dissipative fluid described by full theory of causal transport equations are analyzed. New exact solutions are found using a non-local transformations on the nonlinear…

We consider the problem of finding complete conformal metrics with prescribed curvature functions of the Einstein tensor and of more general modified Schouten tensors. To achieve this, we reveal an algebraic structure of a wide class of…

The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations…

We derive the general solution to the coupled Einstein and Dirac field equations in static and hyperplane-symmetric spacetime of arbitrary dimension including a cosmological constant of either sign. As a result, only a massful Dirac field…

We study Yamabe metrics, and the moduli space of Yamabe metrics, on an arbitrary closed 3-manifold M. The main focus is on the boundary behavior of the moduli space, i.e. the behavior of degenerating sequences of unit volume Yamabe metrics…

In this article, we provide a discussion on a composite class of exact static spherically symmetric vacuum solutions of Einstein's equations. We construct the composite solution of Einstein field equation by match the interior vacuum metric…

This paper investigates axially symmetric space-times that admit a homothetic vector field based on Lyra's geometry. The cases when the displacement vector is a function of $t$ and when it is constant are studied. In the context of this…

According to Birkhoff's theorem the only spherically symmetric solution of the vacuum Einstein field equations is the Schwarzschild solution. Inspite of imposing asymptotically flatness and staticness as initial conditions we obtain that…

Here we give a more detailed account of the part of the conference report that was devoted to reinterpreting the Einstein `unified models of gravity and electromagnetism' (1923) as the unified theory of dark energy (cosmological constant)…

There is an intriguing analogy between the gravitational dynamics of the horizons and thermodynamics. In case of general relativity, as well as for a wider class of Lanczos-Lovelock theories of gravity, it is possible to interpret the field…

We complete the visible, hidden, sectorial, and discrete symmetries of Ernst-like potential spaces in stationary, axisymmetric Einstein-Maxwell-Scalar Field (EMSF) and Einstein-ModMax-Scalar Field (EMMSF) theories. In the real potential…

We prove that, given a stress-free, axially symmetric elastic body, there exists, for sufficiently small values of the gravitational constant and of the angular frequency, a unique stationary axisymmetric solution to the Einstein equations…

In this article we find the general, exact solution for the gravitational field equations for diagonal, vacuum, separable metrics. These are metrics each of whose terms can be separated into functions of each space-time variable separately.…

We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a…

This is the first in a series of papers on the construction of explicit solutions to the stationary axisymmetric Einstein equations which describe counter-rotating disks of dust. These disks can serve as models for certain galaxies and…