相关论文: Physically Realistic Solutions to the Ernst Equati…
A new class of exact solutions to the axisymmetric and stationary vacuum Einstein equations containing n arbitrary complex parameters and one arbitrary real solution of the axisymmetric three-dimensional Laplace equation is presented. The…
This paper presents solutions to Einstein's equation -- and the numerical methods used to construct them -- that describe simple cosmological models on manifolds with compact non-orientable spatial slices. These solutions have been…
We classify solutions of the vacuum weighted Einstein field equations on smooth metric measure spacetimes $(M,g,h\, dvol_g)$ of dimension 4, where the underlying manifold $(M,g)$ is a $pr$-wave. We use this result to provide examples of…
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…
In this dissertation, we prove a number of results regarding the conformal method of finding solutions to the Einstein constraint equations. These results include necessary and sufficient conditions for the Lichnerowicz equation to have…
We show that a set of conformally invariant equations derived from the Fefferman-Graham tensor can be used to construct global solutions of the vacuum Einstein equations, in all even dimensions. This gives, in particular, a new, simple…
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)…
Supersymmetric domain-wall solutions of maximal gauged supergravity are classified in 4, 5 and 7 dimensions in the presence of non-trivial scalar fields taking values in the coset SL(N, R)/SO(N) for N=8, 6 and 5 respectively. We use an…
Within a semiclassical framework, we investigate spherically symmetric solutions of the Einstein equations that (i) develop a trapped region within a finite time as measured by distant observers, and (ii) remain sufficiently regular at the…
We present a simple technique for generating new solutions of Einstein's equations using such function transformations that leave the field equations in the Ernst form. In this context we recover all the known covariant transformations of…
The Ernst formulation of the Einstein equations is generalised to accommodate $f(R)$ theories of gravity. It is shown that, as in general relativity, the axisymmetric $f(R)$ field equations for a vacuum spacetime that is either stationary…
The derivation of the Demianski-Newman solution within the framework of the Ernst complex formalism is considered. We show that this solution naturally arises as a two-soliton specialization of the axisymmetric multi-soliton electrovacuum…
We construct a new rotating solution of Einstein's theory in vacuum by exploiting the Lie point symmetries of the field equations in the complex potential formalism of Ernst. In particular, we perform a discrete symmetry transformation,…
A new family of exact solutions of the Einstein field equations for static and axially simmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply written in…
A new class of higher-dimensional exact solutions of Einstein's vacuum equation is presented. These metrics are written in terms of the exponential of a symmetric matrix and when this matrix is diagonal the solution reduces to…
Motivated by conventional gauge theories, we consider a theory of gravity in which the Einstein-Hilbert action is replaced by a term that is quadratic in the Riemann tensor. We focus on cosmological solutions to the field equations in flat,…
We find exact static solutions of the Einstein equations in the spacetime with plane symmetry, where an infinite slab with finite thickness and homogeneous energy (mass) density is present. In the first solution the pressure is isotropic,…
Let $M^n$ be either a simply connected space form or a rank-one symmetric space of noncompact type. We consider Weingarten hypersurfaces of $M\times\mathbb R$, which are those whose principal curvatures $k_1,\dots ,k_n$ and angle function…
An infinite family of new exact solutions of the Einstein vacuum equations for static and axially symmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply…
A new class of solutions of the Einstein field equations in spherical symmetry is found. The new solutions are mathematically described as the metrics admitting separation of variables in area-radius coordinates. Physically, they describe…