Related papers: IDEAL characterization of vacuum pp-waves
In general relativity, an IDEAL (Intrinsic, Deductive, Explicit, ALgorithmic) characterization of a reference spacetime metric $g_0$ consists of a set of tensorial equations $T[g]=0$, constructed covariantly out of the metric $g$, its…
In general relativity, an IDEAL (Intrinsic, Deductive, Explicit, ALgorithmic) characterization of a reference spacetime metric $g_0$ consists of a set of tensorial equations $T[g]=0$, constructed covariantly out of the metric $g$, its…
The necessary and sufficient conditions for a type N vacuum solution (with cosmological constant) to admit a group of isometries of dimension $r$ are given in terms of the invariant concomitants of the Weyl tensor. This study requires…
The necessary and sufficient conditions for a spacetime with an invariant frame to admit a group of isometries of dimension $r$ are given in terms of the connection tensor $H$ associated with this frame. In Petrov-Bel types I, II and III,…
The scalar invariant, I, constructed from the "square" of the first covariant derivative of the curvature tensor is used to probe the local geometry of static spacetimes which are also Einstein spaces. We obtain an explicit form of this…
We solve the equivalence problem for vacuum PP-wave spacetimes by employing the Karlhede algorithm. Our main result is a suite of Cartan invariants that allows for the complete invariant classification of the vacuum pp-waves. In particular,…
An exhaustive list of four-dimensional $\Lambda$-vacuum spacetimes admitting a Killing vector whose self-dual Killing two-form ${\cal F}$ is null is obtained assuming that the self-dual Weyl tensor is proportional to the tensor product of…
Symmetry properties of r-times covariant tensors T can be described by certain linear subspaces W of the group ring K[S_r] of a symmetric group S_r. If for a class of tensors T such a W is known, the elements of the orthogonal subspace…
We give a classification of the type D spacetimes based on the invariant differential properties of the Weyl principal structure. Our classification is established using tensorial invariants of the Weyl tensor and, consequently, besides its…
For gravitational-wave spacetimes of Shapovalov type III, exact general solutions of geodesic deviation equations and equations of motion of test particles are obtained. Solutions are found in a privileged coordinate system, where the…
A classical pp-wave is a 4-dimensional Lorentzian spacetime which admits a nonvanishing parallel spinor field; here the connection is assumed to be Levi-Civita. We generalise this definition to metric compatible spacetimes with torsion and…
Starting with a subclass of the four-dimensional spaces possessing two commuting Killing vectors and a non-trivial Killing tensor, we fully integrate Einstein's vacuum equation with a cosmological constant. Although most of the solutions…
Scalar curvature invariants are studied in type N solutions of vacuum Einstein's equations with in general non-vanishing cosmological constant Lambda. Zero-order invariants which include only the metric and Weyl (Riemann) tensor either…
Taking wedge products of the $p$ distinct principal null directions associated with the eigen-bivectors of the Weyl tensor associated with the Petrov classification, when linearly independent, one is able to express them in terms of the…
Einstein spacetimes (that is vacuum spacetimes possibly with a non-zero cosmological constant {\Lambda}) with constant non-zero Weyl eigenvalus are considered. For type Petrov II & D this assumption allows one to prove that the non-repeated…
Universal spacetimes are spacetimes for which all conserved symmetric rank-2 tensors, constructed as contractions of polynomials from the metric, the Riemann tensor and its covariant derivatives of arbitrary order, are multiples of the…
In this paper, we initiate the rigorous mathematical study of the problem of impulsive gravitational spacetime waves. We construct such spacetimes as solutions to the characteristic initial value problem of the Einstein vacuum equations…
All classes of spatially homogeneous space-time models in the generalized scalar-tensor theory of gravity are found that allow the integration of the equations of motion of test particles and the eikonal equation by the method of %complete…
In this paper we deal with quadratic metric-affine gravity, which we briefly introduce, explain and give historical and physical reasons for using this particular theory of gravity. Further, we introduce a generalisation of well known…
We investigate the existence and the global causal structure of plane symmetric spacetimes with weak regularity when the matter consists of an irrotational perfect fluid with pressure equal to its mass-energy density. Our theory encompasses…