Time machine and geodesic motion in Kerr metric

The existence of nontrivial causality violation is a peculiar property of the space-time around a naked singularity. In the case of Kerr metric witha > m we have found that for a particular class of geodesies that could in principle violate causality, the conditions for causality violation are never satisfied.On leave of absence from Institute of Astronomy, Polish Academy of Sciences, Warsaw, Poland.     

de Sitter spacetime: effects of metric perturbations on geodesic motion

Gravitational perturbations of the de Sitter spacetime are investigated using the Regge–Wheeler formalism. The set of perturbation equations is reduced to a single second order differential equation of the Heun-type for both electric and magnetic multipoles. The solution so obtained is used to study the deviation from an initially radial geodesic due to the perturbation. The spectral properties of the perturbed metric are also analyzed. Finally, gauge- and tetrad-invariant first-order massless perturbations of any spin are explored following the approach of Teukolsky. The existence of closed-form, i.e. Liouvillian, solutions to the radial part of the Teukolsky master equation is discussed.     

Conformal changes and geodesic completeness

Let (M, g) be a causal spacetime. ConditionN will be satisfied if for each compact subsetK ofM there is no future inextendible nonspacelike curve which is totally future imprisoned inK. IfM satisfies conditionN, then wheneverE is an open and relatively compact subset ofM the spacetimeE with the metricg restricted toE is stably causal. Furthermore, there is a conformal factor such that (M, ² g) is both null and timelike geodesically complete. IfM is an open subset of two dimensional Minkowskian space, thenM is conformal to a geodesically complete spacetime.     

On the latitudinal and radial motion of timelike vortical trajectories in the Kerr metric

The timelike vortical geodesies of the Kerr metric are integrated numerically in ther- subspace of the Boyer-Lindquist coordinates. We find that the trajectories, under physically reasonable conditions, are essentially conical (in the sense of constant). This behavior is not that which one would infer from previous qualitative discussions.     

Kerr metric in eight dimensions

A Kerr-type metric is constructed in eight dimensions using the octonionic structure constants.     

Equations of motion and orbit perturbations of a neutral particle in a quasi-isotropic Kerr metric

In this paper, using a quasi-isotropic from the Kerr metric, we have deduced the equations of motion of a neutral test particle in the gravitational field of a spherical homogeneous rotating body. The perturbation equations of the particle's orbit have also been derived.On leave from Shanghai Observatory, China     

Conformal Anomaly and Large-ScaleGravitational Coupling

We present a model in which the breakdown of conformal symmetry of a quantumstress-tensor due to the trace anomaly is related to a cosmological effect in agravitational model. This is done by characterizing the traceless part of thequantum stress-tensor in terms of the stress-tensor of a conformal invariantclassical scalar field. We introduce a conformal frame in which the anomaloustrace is identified with a cosmological constant. In this conformal frame weestablish the Einstein field equations by connecting the quantum stress-tensorwith the large-scale distribution of matter in the universe.     

The Kerr metric in cosmological background

A metric satisfying Einstein’s equations is given which in the vicinity of the source reduces to the well-known Kerr metric and which at large distances reduces to the Robertson-Walker metric of a homogeneous cosmological model. The radius of the event horizon of the Kerr black hole in the cosmological background is found out.     

Causality violation in the Kerr metric

The conjecture that geodesics in the Kerr matric witha > m cannot violate causality in the sense of meeting a turning point before making up for lost time, is found to be untrue for null geodesics.     

Kerr metric in the deSitter background

In addition to the Kerr metric with cosmological constant Λ several other metrics are presented giving a Kerr-like solution of Einstein’s equations in the background of deSitter universe. A new metric of what may be termed as rotating deSitter space-time—a space-time devoid of matter but containing null fluid with twisting null rays, has been presented. This metric reduces to the standard deSitter metric when the twist in the rays vanishes. Kerr metric in this background is the immediate generalization of Schwarzschild’s exterior metric with cosmological constant.     

Ellipsoidal space-times,sources for the Kerr metric

The paper develops a systematic derivation of the Kerr metric and its possible sources in a clear geometric manner. It starts with a concise account of previous attempts at constructing an interior Kerr solution. Then a treatment of stationary-axisymmetric spacetimes, specially fitted to the needs of the following analysis, is presented. A new notion of an ellipsoidal space-time is introduced: it is a space-time in which local rest 3-spaces of some observers split naturally into congruences of concentric and coaxial ellipsoids. It is shown that these 3-spaces are natural spaces to consider the ellipsoidal figures of equilibrium. The investigation is carried out in detail for axially symmetric oblate confocal ellipsoids, but possible generalizations are indicated. The Kerr metric is found to be an ellipsoidal space-time of this special kind. Some remarks concerning an (unfound) explicit interior Kerr solution conclude the paper.     

Conformal Couplings in Induced Gravity

It is found that the induced gravity with conformal couplings requires the conformal invariance in both classical and quantum levels for consistency. This is also true for the induced gravity with an extended conformal coupling interacting with torsion.     

Dynamical mass and geodesic motion

We show that even though particles with dynamically generated masses do not have the standard point test particle energy-momentum tensor associated with them, their motion in an external gravitational field is nonetheless geodesic. We discuss dynamically massive conformal perfect fluids and construct conformal invariant particle trajectories for them, and show that such fluids behave just like standard kinematically massive perfect fluids in the particular conformal gauge in which the symmetry breaking field is taken to have a constant, spacetime independent vacuum expectation value.     

Conformal anomalies in a general background metric

By using the dimensional regularization procedure, we explicitly calculate the coefficients of conformal anomalies in a general background metric due to scalar, spin $\text{1}\text{2}$ fermion, gauge and gravitation fields.     

Christoffel formula and geodesic motion in hyperspin manifolds

A hyperspin manifoldS _N constructed fromN-component hyperspinors is an alternative to Riemannian manifoldsR _n for Kaluza-Klein-type theories of higher dimensions. Hyperspin manifolds possess a fundamental Chronometric tensor withN n-valued indices, where alwaysn=N ². Some concepts of Riemannian geometry therefore have to be extended. A hyper-Christoffel formula is presented that expresses the connection in terms of the chronometric, assuming the Chronometric is covariantly constant and the connection is torsion-free. Thus, the chronometric can be used as sole dynamical variable. Extremals and selfparallel curves, which coincide in Riemannian manifolds, in general differ in hyperspin manifolds, but coincide again for nonnull curves.     

重力场,运动积分与可积性

讨论了重力场中质点系统的运动积分及其中的Runge-Lenz型运动积分与分离变量方法中分离系数之间的关系,也讨论了系统的可积性以及它与运动积分之间的关系等问题.     

Numerical calculation of bound geodesics in the Kerr metric

Timelike geodesics, especially bound orbits in the equatorial plane (?=π/2) and spherical orbits (r=const), are calculated numerically. We plot the orbits using the Kerr-Schild coordinate system. The periastron advance and the dragging of nodes have the same values in any coordinate system and can be directly measured by an observer at infinity.     

Comparison of particle properties in Kerr metric and in rotating coordinates

Properties of particles in Kerr metric are compared with properties of particles in rotating coordinates in Minkowski space-time. It is shown that particles with negative and zero energies existing in the ergosphere of the rotating black hole also exist in the region out of the static limit in rotating coordinates in Minkowski space-time. Some similarities like the Penrose process and differences in both cases are analyzed.     

LETTER: Gauge Choice and Geodetic Deflection in Conformal Gravity

Conformal gravity has been proposed as an alternative theory of gravity which can account for flat galactic rotation curves without recourse to copious quantities of dark matter. However it was shown that for the usual choice of the metric, the result is catastrophic for null or highly relativistic geodesics, the effect is exactly the opposite yielding an effective repulsion and less deflection in this case. It is the point of this paper, that any result for massive geodesics depends on the choice of conformal gauge, in contradistinction to the case of null geodesics. We show how it is possible to choose the gauge so that the theory is attractive for all geodesics.