arXiv subjects

Vojtech Pravda

Publications and source records attributed to Vojtech Pravda.

21 records · Page 2Linked to original sources

arXiv2008

Newman-Penrose formalism in higher dimensions: vacuum spacetimes with a non-twisting geodetic multiple Weyl aligned null direction

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 metric and of the Weyl tensor on the affine parameter r along null geodesics generated by the WAND for type III and N spacetimes and for a special class of type II and D spacetimes, containing e.g. Schwarzschild-Tangherlini black holes and black strings and branes. For types III and N, all metric components are at most quadratic polynomials in r while for types II and D the r-dependence of the metric as well as of the Weyl tensor is determined by an integer m corresponding to the rank of the expansion matrix S_{ij}. It is shown that for non-vanishing expansion, all these spacetimes contain a curvature singularity. As an illustrative example, a shearing expanding type N five-dimensional vacuum solution is also re-derived using higher-dimensional NP formalism. This solution can be, however, identified with a direct product of a known four-dimensional type N metric with an extra dimension.

gr-qc↗

arXiv2007

Type D Einstein spacetimes in higher dimensions

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 change when the Killing generator becomes null, such as at Killing horizons.) Next we demonstrate that the same Weyl types characterize warped product spacetimes with a one-dimensional Lorentzian (timelike) factor, whereas warped spacetimes with a two-dimensional Lorentzian factor are restricted to the types D or O. By exploring the Bianchi identities, we then analyze the simplest non-trivial case from the above classes - type D vacuum spacetimes, possibly with a cosmological constant, dropping, however, the assumptions that the spacetime is static, stationary or warped. It is shown that for ``generic'' type D vacuum spacetimes the corresponding principal null directions are geodetic in any dimension (this applies also to type II spacetimes). For n>=5, however, there may exist particular cases of type D spacetimes which admit non-geodetic multiple principal null directions and we present such examples in any n>=7. Further studies are restricted to five dimensions, where the type D Weyl tensor is described by a 3x3 matrix Φ_{ij}. In the case with ``twistfree'' (A_{ij}=0) principal null geodesics we show that in a ``generic'' case Φ_{ij} is symmetric and eigenvectors of Φ_{ij} coincide with those of the expansion matrix S_{ij}, providing us with three preferred spacelike directions of the spacetime. Similar results are also obtained when relaxing the twistfree condition and assuming instead that Φ_{ij} is symmetric. The n=5 Myers-Perry black hole and Kerr-NUT-AdS metrics in arbitrary dimension are briefly studied as specific examples of type D vacuum spacetime.

gr-qc↗

arXiv2006

Black rings with a small electric charge: gyromagnetic ratios and algebraic alignment

We study electromagnetic test fields in the background of vacuum black rings using Killing vectors as vector potentials. We consider both spacetimes with a rotating S^1 and with a rotating S^2 and we demonstrate, in particular, that the gyromagnetic ratio of slightly charged black rings takes the value g=3 (this will in fact apply to a wider class of spacetimes). We also observe that a S^2-rotating black ring immersed in an external "aligned" magnetic field completely expels the magnetic flux in the extremal limit. Finally, we discuss the mutual alignment of principal null directions of the Maxwell 2-form and of the Weyl tensor, and the algebraic type of exact charged black rings. In contrast to spherical black holes, charged rings display new distinctive features and provide us with an explicit example of algebraically general (type G) spacetimes in higher dimensions. Appendix A contains some global results on black rings with a rotating 2-sphere. Appendix C shows that g=D-2 in any D>=4 dimensions for test electromagnetic fields generated by a time translation.

gr-qc↗