Using the technique of Rindler and Perlick we calculate the total precession per revolution of a gyroscope circumventing the source of Weyl metrics. We establish thereby a link between the multipole moments of the source and an “observable” quantity. Special attention deserves the case of the γ-metric. As an extension of this result we also present the corresponding expressions for some station...

The inverse problem for Schrödinger operators on metric graphs is investigated in the presence of magnetic field. Graphs without loops and with Euler characteristic zero are considered. It is shown that the knowledge of the Titchmarsh-Weyl matrix function (Dirichlet-to-Neumann map) for just two values of the magnetic field allows one to reconstruct the graph and potential on it provided a certa...

The fundamental quasinormal modes of black holes in higher-derivative gravity given by the Einstein-Weyl action are known to be moderately corrected Weyl term. Here we will show that first several overtones highly sensitive even a relatively small correction, which might important when representing earlier stage hole ringdown. In addition, have solved problem related analytical parametrized app...

This work is concerned with perfect-fluid solutions of Einstein's equations for a metric in generalized Kerr-Schild form. Since the original Kerr-Schild paper, ] a lot of generalizations of the Kerr-Schild ansatz have appeared. Bilge and Giirses have shown how the Newman-Penrose spin coefficients, trace-free Ricci, Ricci scalar, and Weyl spinors transform under the most general Kerr-Schild tran...

The goal of this paper is to express the Bach tensor of a four dimensional conformal geometry of an arbitrary signature by the Cartan normal conformal (CNC) connection. We show that the Bach tensor can be identified with the Yang–Mills current of the connection. It follows from that result that a conformal geometry whose CNC connection is reducible in an appropriate way has a degenerate Bach te...

We construct consistent interacting gauge theories for M conformal massless spin-2 fields (“Weyl gravitons”) with the following properties: (i) in the free limit, each field fulfills the equation Bμν = 0, where Bμν is the linearized Bach tensor, (ii) the interactions contain no more than four derivatives, just as the free action and (iii) the internal metric for the Weyl gravitons is not positi...

Scalar curvature invariants are studied in type N solutions of vacuum Einstein's equations with in general non-vanishing cosmological constant Λ. Zero-order invariants which include only the metric and Weyl (Riemann) tensor either vanish, or are constants depending on Λ. Even all higher-order invariants containing covariant derivatives of the Weyl (Riemann) tensor are shown to be trivial if a t...

The electric and the magnetic part of the Weyl tensor, as well as the invariants obtained from them, are calculated for the Bondi vacuum metric. One of the invariants vanishes identically and the other only exhibits contributions from terms of the Weyl tensor containing the static part of the field. It is shown that the necessary and sufficient condition for the spacetime to be purely electric ...