Topic
Killing tensor
About: Killing tensor is a research topic. Over the lifetime, 234 publications have been published within this topic receiving 6008 citations. The topic is also known as: Killing tensor field.
Papers published on a yearly basis
Papers
TL;DR: In this article, it was shown that in all except the spherically symmetric cases there is a nontrivial causality violation, i.e., there are closed timelike lines which are not removable by taking a covering space; moreover, when the charge or angular momentum is so large that there are no Killing horizons, this causal violation is of the most flagrant possible kind in that it is possible to connect any event to any other by a future-directed time line.
Abstract: The Kerr family of solutions of the Einstein and Einstein-Maxwell equations is the most general class of solutions known at present which could represent the field of a rotating neutral or electrically charged body in asymptotically flat space. When the charge and specific angular momentum are small compared with the mass, the part of the manifold which is stationary in the strict sense is incomplete at a Killing horizon. Analytically extended manifolds are constructed in order to remove this incompleteness. Some general methods for the analysis of causal behavior are described and applied. It is shown that in all except the spherically symmetric cases there is nontrivial causality violation, i.e., there are closed timelike lines which are not removable by taking a covering space; moreover, when the charge or angular momentum is so large that there are no Killing horizons, this causality violation is of the most flagrant possible kind in that it is possible to connect any event to any other by a future-directed timelike line. Although the symmetries provide only three constants of the motion, a fourth one turns out to be obtainable from the unexpected separability of the Hamilton-Jacobi equation, with the result that the equations, not only of geodesics but also of charged-particle orbits, can be integrated completely in terms of explicit quadratures. This makes it possible to prove that in the extended manifolds all geodesics which do not reach the central ring singularities are complete, and also that those timelike or null geodesics which do reach the singularities are entirely confined to the equator, with the further restriction, in the charged case, that they be null with a certain uniquely determined direction. The physical significance of these results is briefly discussed.
2,493 citations
TL;DR: In this paper, it was shown that every type of vacuum solution of Einstein's equations admits a quadratic first integral of the null geodesic equations (conformal Killing tensor of valence 2), which is independent of the metric and of any Killing vectors arising from symmetries.
Abstract: It is shown that every type {22} vacuum solution of Einstein's equations admits a quadratic first integral of the null geodesic equations (conformal Killing tensor of valence 2), which is independent of the metric and of any Killing vectors arising from symmetries. In particular, the charged Kerr solution (with or without cosmological constant) is shown to admit a Killing tensor of valence 2. The Killing tensor, together with the metric and the two Killing vectors, provides a method of explicitly integrating the geodesics of the (charged) Kerr solution, thus shedding some light on a result due to Carter.
663 citations
TL;DR: In this article, it was shown that the existence of such an operator for scalar fields is automatically implied by the corresponding constant for particle trajectories in the classical limit, that is to say, by the presence of a Killing vector or a "Killing tensor" in the first and second order cases, respectively.
Abstract: The relationship between relativistic quantum current conservation laws in a curved-space background and the corresponding "good quantum numbers," i.e., operators that commute with the fundamental wave operator in a first-quantized field theory, is considered. It is shown that under favorable circumstances (such as vanishing Ricci curvature) the existence of such an operator for scalar fields is automatically implied by the existence of the corresponding constant for particle trajectories in the classical limit, that is to say, by the existence of a Killing vector or a "Killing tensor" in the first- and second-order cases, respectively. Thus the fourth constant of the motion for a scalar quantum field in the Kerr metric background arises automatically from the Killing tensor defining the fourth constant of the classical motion. Another application is to the Runge-Lenz constants in the nonrelativistic hydrogen atom problem. The "Schiff conjecture" concerning the relationship between classical mechanics and first-quantized field theory in connection with the equivalence principle is discussed in passing.
231 citations
TL;DR: In this article, two model-independent parametric deviations from the Kerr metric were constructed from a generalization of the quasi-Kerr and bumpy metrics and one built directly from perturbations of the Kerr spacetime in Lewis-Papapetrou form.
Abstract: We generalize the bumpy black hole framework to allow for alternative theory deformations. We construct two model-independent parametric deviations from the Kerr metric: one built from a generalization of the quasi-Kerr and bumpy metrics and one built directly from perturbations of the Kerr spacetime in Lewis-Papapetrou form. We find the conditions that these ``bumps'' must satisfy for there to exist an approximate second-order Killing tensor so that the perturbed spacetime still possesses three constants of the motion (a deformed energy, angular momentum and Carter constant) and the geodesic equations can be written in first-order form. We map these parametrized metrics to each other via a diffeomorphism and to known analytical black hole solutions in alternative theories of gravity. The parametrized metrics presented here serve as frameworks for the systematic calculation of extreme mass-ratio inspiral waveforms in parametrized non-general relativity theories and the investigation of the accuracy to which space-borne gravitational wave detectors can constrain such deviations.
211 citations
TL;DR: In this paper, the authors investigated the hidden symmetries of the Sen black hole and showed the capture regions in a two dimensional impact parameter space (or equivalently the ''shadows'' observed at infinity) to form a variety of shapes such as the disk, circle, dot, arc, and their combinations.
Abstract: Important classes of null geodesics and hidden symmetries in the Sen black hole are investigated. First, we obtain the principal null geodesics and circular photon orbits. Then, an irreducible rank-two Killing tensor and a conformal Killing tensor are derived, which represent the hidden symmetries. Analyzing the properties of Killing tensors, we clarify why the Hamilton-Jacobi and wave equations are separable in this spacetime. We also investigate the gravitational capture of photons by the Sen black hole and compare the result with those by the various charged/rotating black holes and naked singularities in the Kerr-Newman family. For these black holes and naked singularities, we show the capture regions in a two dimensional impact parameter space (or equivalently the ``shadows'' observed at infinity) to form a variety of shapes such as the disk, circle, dot, arc, and their combinations.
192 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 15 |
| 2020 | 5 |
| 2019 | 6 |
| 2018 | 7 |
| 2017 | 14 |
| 2016 | 7 |