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.     

Equilibrium States in the Quadruple–Kerr Solution

The extended quadruple–Kerr metric is used to consider equilibrium states of four collinear Kerr particles. We explain our previous failure to solve numerically the full set of the balance equations, and we derive a self–consistent system of the axis conditions leading to the equilibrium of all four constituents which can be black holes or hyperextreme objects. The equilibrium configurations obtained in this paper exhibit similar features with those occurring in the systems of two Kerr particles, for instance, the balance of four Kerr black holes with positive masses does not seem possible. Equilibrium states of two identical compound Kerr objects are also discussed.     

Spontaneous creation of massive spin half particles by a rotating block hole

The techniques of second quantization in Kerr metric for the scalar and neutrino (massless) fields are extended to the massive spin half case. The normal modes of Dirac field in Kerr metric are obtained in Chandrasekhar’s representation and the field is quantized as usual by imposing equal-time anti-commutation relations. The vacuum expectation value of energy-momentum tensor is evaluated asymptotically, leading to the result that a Kerr black hole spontaneously creates, in addition to scalar and neutrino quanta, massive Dirac particles in the classical superradiant modes.     

On quadratic first integrals of the geodesic equations for type {22} spacetimes

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.     

Black holes: a physical route to the Kerr metric

As a consequence of Birkhoff's theorem, the exterior gravitational field of a spherically symmetric star or black hole is always given by the Schwarzschild metric. In contrast, the exterior gravitational field of a rotating (axisymmetric) star differs, in general, from the Kerr metric, which describes a stationary, rotating black hole. In this paper I discuss the possibility of a quasi–stationary transition from rotating equilibrium configurations of normal matter to rotating bla ck holes.     

Hamiltonian approach to frame dragging

A Hamiltonian approach makes the phenomenon of frame dragging apparent “up front” from the appearance of the drag velocity in the Hamiltonian of a test particle in an arbitrary metric. Hamiltonian (1) uses the inhomogeneous force equation (4), which applies to non-geodesic motion as well as to geodesics. The Hamiltonian is not in manifestly covariant form, but is covariant because it is derived from Hamilton’s manifestly covariant scalar action principle. A distinction is made between manifest frame dragging such as that in the Kerr metric, and hidden frame dragging that can be made manifest by a coordinate transformation such as that applied to the Robertson–Walker metric in Sect. 2. In Sect. 3 a zone of repulsive gravity is found in the extreme Kerr metric. Section 4 treats frame dragging in special relativity as a manifestation of the equivalence principle in accelerated frames. It answers a question posed by Bell about how the Lorentz contraction can break a thread connecting two uniformly accelerated rocket ships. In Sect. 5 the form of the Hamiltonian facilitates the definition of gravitomagnetic and gravitoelectric potentials.     

Slowly rotating white holes

A model of gravitationally anticollapsing objects, white holes, is constructed on the basis of the Kerr metric in the limit of small rotation with a corresponding interior metric. The extended space-time manifold is considered and the spectral shift of radiation from the point of view of a remote observer is calculated for different parameters of such white holes.     

Hidden conformal symmetry and pair production near the cosmological horizon in Kerr-Newman-Taub-NUT-de Sitter spacetime

We show that the study of the hidden conformal symmetry that is associated with the Kerr/CFT correspondence can also apply to the cosmological horizon in the Kerr-Newman-Taub-NUT-de Sitter spacetime. This symmetry allows employing some two dimensional conformal field theory methods to understand the properties of the cosmological horizon. The entropy can be understood by using the Cardy formula, and the equation for the scattering process in the near region is in agreement with that obtained from a two point function in the two-dimensional conformal field theory. We also show that pair production can occur near the cosmological horizon in Kerr-Newman-Taub-NUT-de Sitter for near extremal conditions.     

Holography at an extremal De Sitter horizon

Rotating maximal black holes in four-dimensional de Sitter space, for which the outer event horizon coincides with the cosmological horizon, have an infinite near-horizon region described by the rotating Nariai metric. We show that the asymptotic symmetry group at the spacelike future boundary of the near-horizon region contains a Virasoro algebra with a real, positive central charge. This is evidence that quantum gravity in a rotating Nariai background is dual to a two-dimensional Euclidean conformal field theory. These results are related to the Kerr/CFT correspondence for extremal black holes, but have two key differences: one of the black hole event horizons has been traded for the cosmological horizon, and the near-horizon geometry is a fiber over dS₂ rather than AdS₂.     

Kerr metric,geodesic motion,and Flyby Anomaly in fourth-order Conformal Gravity

In this paper we analyze the Kerr geometry in the context of Conformal Gravity, an alternative theory of gravitation, which is a direct extension of General Relativity (GR). Following previous studies in the literature, we introduce an explicit expression of the Kerr metric in Conformal Gravity, which naturally reduces to the standard GR Kerr geometry in the absence of Conformal Gravity effects. As in the standard case, we show that the Hamilton–Jacobi equation governing geodesic motion in a space-time based on this geometry is indeed separable and that a fourth constant of motion—similar to Carter’s constant—can also be introduced in Conformal Gravity. Consequently, we derive the fundamental equations of geodesic motion and show that the problem of solving these equations can be reduced to one of quadratures. In particular, we study the resulting time-like geodesics in Conformal Gravity Kerr geometry by numerically integrating the equations of motion for Earth flyby trajectories of spacecraft. We then compare our results with the existing data of the Flyby Anomaly in order to ascertain whether Conformal Gravity corrections are possibly the origin of this gravitational anomaly. Although Conformal Gravity slightly affects the trajectories of geodesic motion around a rotating spherical object, we show that these corrections are minimal and are not expected to be the origin of the Flyby Anomaly, unless conformal parameters are drastically different from current estimates. Therefore, our results confirm previous analyses, showing that modifications due to Conformal Gravity are not likely to be detected at the Solar System level, but might affect gravity at the galactic or cosmological scale.     

Letter: Slowly Rotating, Compact Fluid Sources Embedded in Kerr Empty Space-Time

Spherically symmetric static fluid sources are endowed with rotation and embedded in Kerr empty space-time up to and including quadratic terms in an angular velocity parameter using Darmois junction conditions. The boundary behaviour of the metric tensor and partial derivatives is used to develop a series solution of Einstein's equation's for the rotating fluid. The boundary of the rotating source is expressed explicitly in terms of sinusoidal functions of the polar angle. As an example of the analysis the Schwarzschild interior solution is endowed with rotation and the equation of the fluid boundary is generated together with surface behaviour of the fluid density and angular velocity.     

Radiating Kerr particle in Einstein universe

A generalized Kerr-NUT type metric is considered in connection with Einstein field equations corresponding to perfect fluid plus a pure radiation field. A general scheme for obtaining the exact solutions of these field equations is developed. Two physically meaningful particular cases are investigated in detail. One gives the field of a radiating Kerr particle embedded in the Einstein universe. The other solution may probably represent a deSitter-like universe pervaded by a pure radiation field.     

Exact solutions inU 4 gravity. I. The ansatz for self double dual curvature

We investigate the energy-momentum and spin field equations of gravity theory on a Riemann-Cartan space-time (including metric and torsion,U ₄-manifold). The structure of the rather complicated nonlinear differential equations of second order is made considerably easier to survey by decomposing curvature into its self and anti-self double dual parts. This leads to an obvious ansatz for the self double dual curvature, whereby the field equations are reduced to Einstein's equations with cosmological term. To solve the double dual ansatz, we choose proper variables adopted to its double duality, and perform a (3+1)-decomposition of exterior calculus. We examine these equations further on a Kerr background with cosmological constant for the Riemannian geometry.     

高功率脉冲光隔离器非线性及热效应分析

从理论上分析了脉冲情况下,磁光晶体横向温度梯度引起的光弹效应、消光比以及克尔效应对光隔离器隔离度的影响,并与连续入射情况进行了对比。结果表明:在平均功率相同的情况下,脉冲光束入射比连续光束入射情况隔离度更低;当平均功率较小时,消光比对隔离度的影响较大;当平均功率较大时,消光比对隔离度的影响有限,主要表现出光弹效应对隔离度的影响;当峰值功率密度较大时,克尔效应将显著降低隔离度,并且峰值功率密度越大,对隔离度的降低程度越大。     

Longitude magneto optical Kerr effect of Fe/GaAs (0 0 1) with Al overlayers

The longitude magneto optical Kerr effect (LMOKE) is investigated on ultrathin Fe film grown on GaAs (0 0 1) substrate with Al overlayer. The formula of the longitude magneto optical Kerr effect is derived to find out the influence of the Al overlayer on the magneto optical properties of Fe/GaAs (0 0 1) sample. Results obtained from this formula fit very well with the experimental data. The change of the Kerr rotation as a function of the incident angle is also given, which can be used to find a proper angle in sample measurement. A numerical simulation was carried out to find out the relation between Kerr rotation and optical properties of the overlayer. Results from this simulation can be used to select the best overlayer material to protect the Fe/GaAs (0 0 1) sample.     

克尔磁光效应的经典理论分析

本文引入与自旋-轨道相互作用等有关的有效场概念,运用经典电磁场理论,推导了磁光克尔旋转的明确表达式.证明了各种磁光介质的极向克尔旋转θ_k的实部θ′_k和虚部θ″_k均与有效场H_i成正比,在铁磁性介质中近似与vM成正比,M为磁化强度,在亚铁磁性等介质中近似与(?)v_iM_i成正比,M_i为i次点阵的磁化强度.同时还证明了近似的横向克尔旋转θ_k~t与H_i~2正比;θ_k和θ_k~t的温度特性取决于H_i的温度特性.     

Accelerated Levi-Civita-Bertotti-Robinson metric in D dimensions

A conformally flat accelerated charge metric is found in an arbitrary dimension D. It is a solution of the Einstein-Maxwell-null fluid equations with a cosmological constant in D ≥ 4 dimensions. When the acceleration is zero, our solution reduces to the Levi-Civita-Bertotti-Robinson metric. We show that the charge loses its energy, for all dimensions, due to the acceleration.     

Initial data for two Kerr-like black holes

We prove the existence of a family of initial data for the Einstein vacuum equation which can be interpreted as the data for two Kerr-like black holes in an arbitrary location and with spins pointing in arbitrary directions. We also provide a method to compute them. If the mass parameter of one of the black holes is zero, then this family reduces exactly to the Kerr initial data. The existence proof is based on a general property of the Kerr metric which can be used in other constructions as well. Further generalizations are also discussed.