Chaos and dynamics of spinning particles in Kerr spacetime

We study chaos dynamics of spinning particles in Kerr spacetime of rotating black holes use the Papapetrou equations by numerical integration. Because of spin, this system exists many chaos solutions, and exhibits some exceptional dynamic character. We investigate the relations between the orbits chaos and the spin magnitude S, pericenter, polar angle and Kerr rotation parameter a by means of a kind of brand new Fast Lyapulov Indicator (FLI) which is defined in general relativity. The classical definition of Lyapulov exponent (LE) perhaps fails in curve spacetime. And we emphasize that the Poincaré sections cannot be used to detect chaos for this case. Via calculations, some new interesting conclusions are found: though chaos is easier to emerge with bigger S, but not always depends on S monotonically; the Kerr parameter a has a contrary action on the chaos occurrence. Furthermore, the spin of particles can destroy the symmetry of the orbits about the equatorial plane. And for some special initial conditions, the orbits have equilibrium points.     

Kerr 时空黑洞熵和测不准关系

通过应用在量子引力中、由广义测不准关系得出的新的态密度方程,直接求解轴对称Kerr黑洞背景下Bose场和Fermi场的配分函数.然后,在黑洞视界附近计算黑洞背景下Bose场和Fermi场的熵.在所得结论中不存在用brick wall模型计算黑洞熵时出现的发散项,也不存在紫外因子.得到黑洞熵与视界面积成正比的结论.     

The geodetic effect along polar orbits in the Kerr spacetime

A gyroscope following a closed polar orbit in the Kerr spacetime is considered. An exact expression is derived giving the shift of the gyroscope's orientation per revolution in terms of the mass and angular momentum parameters of the Kerr metric and the orbit's coordinate radius.     

The matter‐antimatter interpretation of Kerr spacetime

Repulsive gravity is not very popular in physics. However, one comes across it in at least two main occurrences in general relativity: in the negative‐r region of Kerr spacetime, and as the result of the gravitational interaction between matter and antimatter, when the latter is assumed to be CPT‐transformed matter. Here we show how these two independent developments of general relativity are perfectly consistent in predicting gravitational repulsion and how the above Kerr negative‐r region can be interpreted as the habitat of antimatter. As a consequence, matter particles traveling along vortical geodesics can pass through the throat of a rotating black hole and emerge as antimatter particles (and vice versa). An experimental definitive answer on the gravitational behavior of antimatter is awaited in the next few years.

     

Violation of the Strong Equivalence Principle due to the self-force in a Kerr spacetime

As is known, a charge in a gravitational field experiences a (gravitationally-induced) self-interaction force (self-force) only in curved space-times (in any reference frame), but not in the accelerated frames in flat spacetimes. Therefore, the presence of any self-force indicates, from a formal point of view, a violation of the Strong Equivalence Principle (SEP); as a result, observability of the self-force in the validity domain of classical electrodynamics (CE) means observability of the related violation of SEP. In this paper we investigate the observability of the self-force on a charge at rest on the symmetry axis in a Kerr spacetime, as recently calculated in a paper by the same authors, in the validity domain of CE. Analysis shows that, in the validity domain of CE, no effect of the self-force is observable outside the Schwarzschild radius. In contrast, some effect is observable for very large values of the angular momentum, in a small neighbourhood of the turning point (where a reversal of the tidal forces direction takes place), between the outer horizon and the Schwarzschild radius. This is the only case we have found where SEP fails because of the self-force.     

Point charge in the vicinty of a Kerr black hole

We derive the expression for the electromagnetic field of a point charge at rest on the symmetry axis near a rotating Kerr black hole. This is a generalization of the previously obtained solution for the field of a point charge near a nonrotating Schwarzschild black hole. Unlike the Schwarzschild case the charge is found to give rise to magnetic fields as seen by a stationary or locally nonrotating observer.     

The emission positions of kHz QPOs and Kerr spacetime influence

Based the Alfven wave oscillation model (AWOM) and relativistic precession model (RPM) for twin kHz QPOs, we estimate the emission positions of most detected kHz QPOs to be at r=18+/−3 km (R/15 km), except Cir X-1 at r∼30+/−5 km (R/15 km). For the proposed Keplerian frequency as an upper limit to kHz QPO, the spin effects in Kerr Spacetime are discussed, which have about a 5% (2%) modification for that of the Schwarzchild case for the spin frequency of 1000 (400) Hz. The application to the four typical QPO sources, Cir X-1, Sco X-1, SAX J1808.4-3658 and XTE 1807-294, is mentioned.

     

Beam collimation light deflection and time delay in the Kerr spacetime

By using an alternative method valid in weak and strong gravitational fields, we study beam collimation, light bending and time delays in the equatorial Kerr spacetime. Three applications are carried out. First, it is shown that the interaction spin-orbit could collimate a beam only if the particle or photon moves in a opposite direction to the compact object's spin. Secondly, the deflection angles of light rays grazing a quasar, a pulsar (PSR 1937+214), and a rotating black hole are computed and compared with approximate solutions. Finally, we calculate the photon's time delay traveling from SN1987A to Earth. The result of this undertaking is compared with a similar calculation using the PPN formalism.     

Dynamics of extended bodies with spin-induced quadrupole in Kerr spacetime: generic orbits

We discuss motions of extended bodies in Kerr spacetime by using Mathisson–Papapetrou–Dixon equations. We firstly solve the conditions for circular orbits, and calculate the orbital frequency shift due to the mass quadrupoles. The results show that we need not consider the spin-induced quadrupoles in extreme-mass-ratio inspirals for space-based gravitational wave detectors. We quantitatively investigate the temporal variation of rotational velocity of the extended body due to the coupling of quadrupole and background gravitational field. For generic orbits, we numerically integrate the Mathisson–Papapetrou–Dixon equations for evolving the motion of an extended body orbiting a Kerr black hole. By comparing with the monopole–dipole approximation, we reveal the influences of quadrupole moments of extended bodies on the orbital motion and chaotic dynamics of extreme-mass-ratio systems. We do not find any chaotic orbits for the extended bodies with physical spins and spin-induced quadrupoles. Possible implications for gravitational wave detection and pulsar timing observation are outlined.     

Self-interaction correction in a simple model

We discuss various ways to handle self-interaction corrections (SIC) to Density Functional Theory (DFT) calculations. To that end, we use a simple model of few particles in a finite number of states together with a simple zero-range interaction for which full Hartree-Fock can easily be computed as a benchmark. The model allows to shed some light on the balance between orthonormality of the involved states and energy variance.     

The global monopole spacetime and its topological charge

We show that the global monopole spacetime is one of the exact solutions of the Einstein equations by treating the matter field as a non-linear sigma model, without the weak field approximation applied in the original derivation by Barriola and Vilenkin. Furthermore, we find the physical origin of the topological charge in the global monopole spacetime. Finally,we generalize the proposal which generates spacetime from thermodynamical laws to the case of spacetime with global monopole charge.     

Separability of Dirac equation in higher dimensional Kerr–NUT–de Sitter spacetime

It is shown that the Dirac equations in general higher dimensional Kerr–NUT–de Sitter spacetimes are separated into ordinary differential equations.     

Effective dynamics of a classical point charge

The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an UV cutoff. The Abraham–Lorentz force is recovered and its similarity to quantum anomalies is underlined. The full cutoff-dependent linearized equation of motion is obtained, no runaway trajectories are found but the effective dynamics shows acausality if the cutoff is beyond the classical charge radius. The strength of the radiation reaction force displays a pole in its cutoff-dependence in a manner reminiscent of the Landau-pole of perturbative QED. Similarity between the dynamical breakdown of the time reversal invariance and dynamical symmetry breaking is pointed out.     

Inertial frames and tidal forces along the symmetry axis of the Kerr spacetime

The gravitational field along the symmetry axis of the Kerr spacetime is examined. The equations of parallel transport along this axis are solved for the timelike geodesics case, and the corresponding tidal tensor is constructed.     

Injection of charge carriers from a point contact

Electron injection has been carried out in KCl, KBr, mixed KCl and KBr crystals under constant electric field and at different temperatures. The activation energy connected to ionic zone has been obtained and found to be characteristic for alkalihalides.