Exact solution for Schwarzschild black hole in radiation gauge

Recently Chen and Zhu propose a true radiation gauge for gravity [Phys. Rev. D 83, 061501(R) (2011)]. This work presents a general solution for the metric of Schwarzschild black hole in this radiation gauge

The collapse distance of femtosecond pulses in air

The conventional semi-empirical formula for collapse distance [Phys. Rev. 179, 862 (1969), Prog. Quant. Electr. 4, 35 (1975)] has been widely used in many applications. However, it is not applicable when the dispersion length is smaller than or has similar order-of-magnitude as the collapse distance. For the "enough short" pulses, there exists a threshold for the initial peak power, with which the collapse distance has a maximum value due to the competition between the Kerr self-focusing and the group velocity dispersion. New semi-empirical formulas are obtained for the collapse distance of the pulse with the initial power being less or larger than the threshold, and they can match the numerical simulations gracefully

Parallel simulation for the ultra-short laser pulses' propagation in air

A parallel 2D+1 split-step Fourier method with Crank-Nicholson scheme running on multi-core shared memory architectures is developed to study the propagation of ultra-short high-intensity laser pulses in air. The parallel method achieves a near linear speed-up with results for the efficiency of more than 95% on a 24-core machine. This method is of great potential application in studying the long-distance propagation of the ultra-short high intensity laser pulses

Post-Newtonian dynamics basing on Mathisson-Papapetrou equations with Corinaldesi-Papapetrou condition in Kerr spacetime

We derive the post-Newtonian dynamics for a spinning body with Corinaldesi-Papapetrou spin supplementary condition in Kerr spacetime. Both the equations of motion for the center-of-mass of body and the spin evolution are obtained. For the non-relativistic case, our calculations show that the magnitude of spin measured in the rest frame of the body's center-of-mass does not change with time, though the center-of-mass does not move along the geodesic. Moreover, we find that the effects of the spin-orbit and spin-spin couplings will be suppressed by the Lorentz factor when the body has a relativistic velocity.Comment: 11 pages, 0 figur

The weak-field-limit solution for Kerr black hole in radiation gauge

In this work we present the solution for a rotating Kerr black hole in the weak-field limit under the radiation gauge proposed by Chen and Zhu [Phys. Rev. D83, 061501(R) (2011)], with which the two physical components of the gravitational wave can be picked out exactly.Comment: Submitted to Eur. phys. J. Plus; Minor revisio

Post-Minkowskian solution for the small-deflection motion of test particles in Kerr-Newman spacetime

We derive the second-order post-Minkowskian solution for the small-deflection motion of test particles in the external field of the Kerr-Newman black hole via an iterative method. The analytical results are exhibited in the coordinate system constituted by the particles' initial velocity unit vector, impact vector, and their cross-product. The achieved formulas explicitly give the dependences of the particles' trajectory and velocity on the time once their initial position and velocity are specified, and can be applied not only to a massive particle, but also to a photon as well.Comment: Submitted to Class. Quantum Gra

An Automatic Machine Translation Evaluation Metric Based on Dependency Parsing Model

Most of the syntax-based metrics obtain the similarity by comparing the sub-structures extracted from the trees of hypothesis and reference. These sub-structures are defined by human and can't express all the information in the trees because of the limited length of sub-structures. In addition, the overlapped parts between these sub-structures are computed repeatedly. To avoid these problems, we propose a novel automatic evaluation metric based on dependency parsing model, with no need to define sub-structures by human. First, we train a dependency parsing model by the reference dependency tree. Then we generate the hypothesis dependency tree and the corresponding probability by the dependency parsing model. The quality of the hypothesis can be judged by this probability. In order to obtain the lexicon similarity, we also introduce the unigram F-score to the new metric. Experiment results show that the new metric gets the state-of-the-art performance on system level, and is comparable with METEOR on sentence level.Comment: 9 page

Second-order time delay by a radially moving Kerr-Newman black hole

We derive the analytical time delay of light propagating in the equatorial plane and parallel to the velocity of a moving Kerr-Newman black hole up to the second post-Minkowskian order via integrating the null geodesic equations. The velocity effects are expressed by a very compact form. We then concentrate on analyzing the magnitudes of the correctional effects on the second-order contributions to the delay and discuss their possible detection. Our result in the first post-Minkowskian approximation is in agreement with Kopeikin and Sch\"{a}fer's formulation which is based on the retarded Li\'{e}nard-Wiechert potential

Roto-translational Effects on Deflection of Light and Particle by Moving Kerr Black Hole

Velocity effects in first-order Schwarzschild deflection of light and particles have been explored in the previous literature. In this paper, we investigate the roto-translational-motion induced deflection by one moving Kerr black hole with an arbitrary but constant speed. It is shown that the coupling between the effects of the rotation and the translational motion always exists for both light and particles. The contribution of the roto-translational deflection to the total bending angle is discussed in detail. This ratio takes upper limit for light and it decreases monotonically with increasing translational velocity for a massive particle. For a given translational velocity of black hole, this ratio increases with the particle' velocity. In addition, the Post-Newtonian dynamics of the photon and particle is also presented

Gravitational Deflection of Light and Massive Particle by a Moving Kerr-Newman Black Hole

The gravitational deflection of test particles including light, due to a radially moving Kerr-Newman black hole with an arbitrary constant velocity being perpendicular to its angular momentum, is investigated. In harmonic coordinates, we derive the second post-Minkowskian equations of motion for test particles, and solve them by high-accuracy numerical calculations. We then concentrate on discussing the kinematical corrections caused by the motion of the gravitational source to the second-order deflection. The analytical formula of light deflection angle up to second order by the moving lens is obtained. For a massive particle moving with a relativistic velocity, there are two different analytical results for Schwarzschild deflection angle up to second order reported in the previous works, i.e., $\alpha(w)=2\left(1+\frac{1}{w^2}\right)\frac{M}{b}+3\pi\left(\frac{1}{4}+\frac{1}{w^2}\right)\frac{M^2}{b^2}$ and $\alpha(w)=2\left(1+\frac{1}{w^2}\right)\frac{M}{b}+\left[3\pi\left(\frac{1}{4}+\frac{1}{w^2}\right)+2\left(1-\frac{1}{w^4}\right)\right]\frac{M^2}{b^2}$, where $M,$ $b,$ and $w$ are the mass of the lens, impact parameter, and the particle's initial velocity, respectively. Our numerical result is in perfect agreement with the former. Furthermore, the analytical formula for massive particle deflection up to second order in the Kerr geometry is achieved. Finally, the possibilities of detecting the motion effects on the second-order deflection are also analyzed