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Register a new userComment on Global Structure of the Kerr Family of Gravitational Fields
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We comment on the role of the Cartesian-type Kerr-Schild coordinates in developing a faulty maximal extension of the Kerr-Newman solution in the well-known paper of Carter.
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I generalize the Dray-t Hooft gravitational shockwave to the Kerr-AdS background.
Conformal gravity theory can explain observed flat rotation curves of galaxies without invoking hypothetical dark matter. Within this theory, we obtain a generic formula for the sizes of galaxies exploiting the stability criterion of circular orbits. It is found that different galaxies have different finite sizes uniquely caused by the assumed quadratic potential of cosmological origin. Observations on where circular orbits might actually terminate could thus be very instructive in relation to the galactic sizes predicted here.
In their Letter, Kentosh and Mohageg [Phys. Rev. Lett. 108, 110801 (2012)] seek to use data from clocks aboard global positioning system (GPS) satellites to place limits on local position invariance (LPI) violations of Plancks constant, h. It is the purpose of this comment to show that discussing limits on variation of dimensional constants (such as h) is not meaningful; that even within a correct framework it is not possible to extract limits on variation of fundamental constants from a single type of clock aboard GPS satellites; and to correct an important misconception in the authors interpretation of previous Earth-based LPI experiments.
We present an exhaustive numerical investigation of the optical caustics in gravitational lensing by a spinning black hole for an observer at infinity. Besides the primary caustic, we examine higher order caustics, formed by photons performing one or several loops around the black hole. Our investigation covers the whole parameter space, including the black hole spin, its inclination with respect to the line of sight, the source distance, and the caustic order. By comparing our results with the available analytical approximations, we find perfect agreement in their respective domains of validity. We then prove that all caustics maintain their shape (a tube with astroidal cross-section) in the entire parameter space without suffering any transitions to different caustic shapes. For nearly extremal spin, however, higher order caustics grow so large that their cross-sections at fixed radii wind several times around the black hole. As a consequence, for each caustic order, the number of images ranges from 2 to 2(n+1), where n is the number of loops spanned by the caustic. As for the critical curves, we note that for high values of the spin they develop a small dip on the side corresponding to prograde orbits.
Local conformal symmetry introduces the conformal curvature (Weyl tensor) that gets split into its (gravito-) electric and magnetic (tensor) parts. Newtonian tidal forces are expected from the gravitoelectric field, whereas general-relativistic frame-dragging effects emerge from the gravitomagnetic field. The symmetric, traceless gravitoelectric and gravitomagnetic tensor fields can be visualized by their eigenvectors and eigenvalues. In this essay, we depict the gravitoelectric and gravitomagnetic fields around a slowly rotating black hole. This suggests that the phenomenon of ultra-fast outflows observed at the centers of active galaxies may give evidence for the gravitomagnetic fields of spinning supermassive black holes. We also question whether the current issues in our contemporary observations might be resolved by the inclusion of gravitomagnetism on large scales in a perturbed FLRW model.
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