Related papers: Space-times admitting a three-dimensional conforma…
A global extension theorem is established for isotropic singularities in polytropic perfect fluid Bianchi space-times. When an extension is possible, the limiting behaviour of the physical space-time near the singularity is analysed.
Perfect fluid equations are formulated which are invariant under the $\ell$-conformal Newton-Hooke group for an arbitrary integer or half-integer value of the parameter $\ell$. For $\ell=\frac32$ the corresponding conserved charges are…
Circularly rotating axisymmetric perfect fluid space-times are investigated to second order in the small angular velocity. The conditions of various special Petrov types are solved in a comoving tetrad formalism. A number of theorems are…
We construct conformastat spherically symmetric spacetimes representing anisotropic fluid matter distributions from given solutions of the Poisson's equation of Newtonian gravity and its corresponding circular speed profile. As simple…
We determine the conformal algebra of Bianchi III and Bianchi V spacetimes or, equivalently, we determine all Bianchi III and Bianchi V spacetimes which admit a proper conformal Killing vector. The algorithm that we use has been developed…
We introduce a formulation of Eulerian general relativistic hydrodynamics which is applicable for (perfect) fluid data prescribed on either spacelike or null hypersurfaces. Simple explicit expressions for the characteristic speeds and…
A non-relativistic (Galilei-invariant) model of a perfect fluid coupled to a solenoidal field in arbitrary spatial dimension is considered. It contains an arbitrary parameter $\kappa$ and in the particular case of $\kappa=1$ it describes a…
The gravitational collapse of cylindrically distributed perfect fluid is studied. We assume the collapsing speed of fluid is very large and investigate such a situation by recently proposed high-speed approximation scheme. We show that if…
In a recent series of papers new exact analytical interior spacetimes sourced by stationary rigidly rotating cylinders of fluids have been displayed. A fluid with an axially directed pressure has been first considered, then a perfect fluid,…
The acceleration transformations form a 4-parameter Abelian subgroup of the conformal group of Minkowski spacetime. The passive interpretation of acceleration transformations leads to a congruence of uniformly accelerated observers in…
We consider the conformal Einstein equations for polytropic perfect fluid cosmologies which admit an isotropic singularity. For the polytropic index gamma strictly greater than 1 and less than or equal to 2 it is shown that the Cauchy…
Simply-connected homogeneous spacetimes for kinematical and aristotelian Lie algebras (with space isotropy) have recently been classified in all dimensions. In this paper, we continue the study of these "maximally symmetric" spacetimes by…
The cycle-preserving symmetries for the nine two-dimensional real spaces of constant curvature are collectively obtained within a Cayley-Klein framework. This approach affords a unified and global study of the conformal structure of the…
The diagonal metric tensor whose components are functions of one spatial coordinate is considered. Einstein's field equations for a perfect-fluid source are reduced to quadratures once a generating function, equal to the product of two of…
Finite-dimensional nonrelativistic conformal Lie algebras spanned by polynomial vector fields of Galilei spacetime arise if the dynamical exponent is z=2/N with N=1,2,.... Their underlying group structure and matrix representation are…
Self-similarity in general relativity is briefly reviewed and the differences between self-similarity of the first kind and generalized self-similarity are discussed. The covariant notion of a kinematic self-similarity in the context of…
We prove the existence of a large class of dynamical solutions to the Einstein-Euler equations for which the fluid density and spatial three-velocity converge to a solution of the Poisson-Euler equations of Newtonian gravity. The results…
In a recent paper, a new conformally flat metric was introduced, describing an expanding scalar field in a spherically symmetric geometry. The spacetime can be interpreted as a Schwarzschild-like model with an apparent horizon surrounding…
We consider four-dimensional vacuum spacetimes which admit a nonvanishing spacelike Killing field. The quotient with respect to the Killing action is a three-dimensional quotient spacetime $(M,g)$. We establish several results regarding…
In this second part of the `essay on the completion of quantum theory' we define the {\em unitary setting of completed quantum mechanics}, by adding as intrinsic data to those from Part I (arXiv:1711.08643) the choice of a north pole N and…