Related papers: On the Goldberg-Sachs theorem in higher dimensions…
Previous work has found a higher-dimensional generalization of the "geodesic part" of the Goldberg-Sachs theorem. We investigate the generalization of the "shear-free part" of the theorem. A spacetime is defined to be algebraically special…
We prove that higher dimensional Einstein spacetimes which possess a geodesic, non-degenerate double Weyl aligned null direction (WAND) $\ell$ must additionally possess a second double WAND (thus being of type D) if either: (a) the Weyl…
The Sachs equations governing the evolution of the optical matrix of geodetic WANDs (Weyl aligned null directions) are explicitly solved in n-dimensions in several cases which are of interest in potential applications. This is then used to…
In more than four spacetime dimensions, a multiple Weyl-aligned null direction (WAND) need not be geodesic. It is proved that any higher-dimensional Einstein spacetime admitting a non-geodesic multiple WAND also admits a geodesic multiple…
General properties of Kerr-Schild spacetimes with (A)dS background in arbitrary dimension are studied. It is shown that the geodetic Kerr-Schild vector k is a multiple WAND of the spacetime. Einstein Kerr-Schild spacetimes with…
We analyze asymptotic properties of higher-dimensional vacuum spacetimes admitting a "non-degenerate" geodetic multiple WAND. After imposing a fall-off condition necessary for asymptotic flatness, we determine the behaviour of the Weyl…
Einstein spacetimes in 5d that are of genuine type II in the null alignment classification are considered. It is shown that the unique geodesic multiple Weyl aligned null direction (mWAND) cannot have an optical matrix of rank 1 or 3. This…
Vacuum spacetimes admitting a non-twisting geodetic multiple Weyl aligned null direction (WAND) are analyzed in arbitrary dimension using recently developed higher-dimensional Newman-Penrose (NP) formalism. We determine dependence of the…
The Goldberg-Sachs theorem is generalized for all four-dimensional manifolds endowed with torsion-free connection compatible with the metric, the treatment includes all signatures as well as complex manifolds. It is shown that when the Weyl…
We study the geometrical properties of null congruences generated by an aligned null direction of the Weyl tensor (WAND) in spacetimes of the Weyl and Ricci type N (possibly with a non-vanishing cosmological constant) in an arbitrary…
Algebraic classification of higher dimensional, shear-free, twist-free, expanding (or non-expanding) spacetime is studied with the limit of $D\rightarrow\infty$. Similar to classification of any arbitrary dimension $D>4$, this spacetime is…
We present an algebraic classification, based on the null alignment properties of the Weyl tensor, of the general Kundt class of spacetimes in arbitrary dimension for which the non-expanding, non-twisting, shear-free null direction \boldk…
We study a class of higher dimensional warped Einstein spacetimes with one extra dimension. These were originally identified by Brinkmann as those Einstein spacetimes that can be mapped conformally on other Einstein spacetimes, and have…
We investigate the Weyl tensor algebraic structure of a fully general family of D-dimensional geometries that admit a non-twisting and shear-free null vector field k. From the coordinate components of the curvature tensor we explicitly…
Vacuum solutions admitting a hypersurface-orthogonal repeated principal null direction are an important class of 4d algebraically special spacetimes. We investigate the 5d analogues of such solutions: vacuum spacetimes admitting a…
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…
We review recent developments and applications of the classification of the Weyl tensor in higher dimensional Lorentzian geometries. First, we discuss the general setup, i.e. main definitions and methods for the classification, some…
We investigate general properties of Kerr-Schild (KS) metrics in n>4 spacetime dimensions. First, we show that the Weyl tensor is of type II or more special if the null KS vector k is geodetic (or, equivalently, if T_{ab}k^ak^b=0). We…
We show that all static spacetimes in higher dimensions are of Weyl types G, I_i, D or O. This applies also to stationary spacetimes if additional conditions are fulfilled, as for most known black hole/ring solutions. (The conclusions…
We consider a general class of four-dimensional geometries admitting a null vector field that has no twist and no shear but has an arbitrary expansion. We explicitly present the Petrov classification of such Robinson-Trautman (and Kundt)…