Operational significance of the deviation equation in relativistic geodesy

Deviation equation: Second order differential equation for the 4-vector which measures the distance between reference points on neighboring world lines in spacetime manifolds. Relativistic geodesy: Science representing the Earth (or any planet), including the measurement of its gravitational field, in a four-dimensional curved spacetime using differential-geometric methods in the framework of Einstein's theory of gravitation (General Relativity).Comment: 9 pages, 4 figures, contribution to the "Encyclopedia of Geodesy". arXiv admin note: text overlap with arXiv:1811.1047

Markov Chain Monte Carlo Method without Detailed Balance

We present a specific algorithm that generally satisfies the balance condition without imposing the detailed balance in the Markov chain Monte Carlo. In our algorithm, the average rejection rate is minimized, and even reduced to zero in many relevant cases. The absence of the detailed balance also introduces a net stochastic flow in a configuration space, which further boosts up the convergence. We demonstrate that the autocorrelation time of the Potts model becomes more than 6 times shorter than that by the conventional Metropolis algorithm. Based on the same concept, a bounce-free worm algorithm for generic quantum spin models is formulated as well.Comment: 5 pages, 5 figure

On the differential geometry of curves in Minkowski space

We discuss some aspects of the differential geometry of curves in Minkowski space. We establish the Serret-Frenet equations in Minkowski space and use them to give a very simple proof of the fundamental theorem of curves in Minkowski space. We also state and prove two other theorems which represent Minkowskian versions of a very known theorem of the differential geometry of curves in tridimensional Euclidean space. We discuss the general solution for torsionless paths in Minkowki space. We then apply the four-dimensional Serret-Frenet equations to describe the motion of a charged test particle in a constant and uniform electromagnetic field and show how the curvature and the torsions of the four-dimensional path of the particle contain information on the electromagnetic field acting on the particle.Comment: 10 pages. Typeset using REVTE

Wave and Particle Scattering Properties of High Speed Black Holes

The light-like limit of the Kerr gravitational field relative to a distant observer moving rectilinearly in an arbitrary direction is an impulsive plane gravitational wave with a singular point on its wave front. By colliding particles with this wave we show that they have the same focussing properties as high speed particles scattered by the original black hole. By colliding photons with the gravitational wave we show that there is a circular disk, centered on the singular point on the wave front, having the property that photons colliding with the wave within this disk are reflected back and travel with the wave. This result is approximate in the sense that there are observers who can see a dim (as opposed to opaque) circular disk on their sky. By colliding plane electromagnetic waves with the gravitational wave we show that the reflected electromagnetic waves are the high frequency waves.Comment: Latex file, 22 pages, 1 figure, accepted for publication in Classical and Quantum Gravit

On the Clock Paradox in the case of circular motion of the moving clock

In this paper we deal analytically with a version of the so called clock paradox in which the moving clock performs a circular motion of constant radius. The rest clock is denoted as (1), the rotating clock is (2), the inertial frame in which (1) is at rest and (2) moves is I and, finally, the accelerated frame in which (2) is at rest and (1) rotates is A. By using the General Theory of Relativity in order to describe the motion of (1) as seen in A we will show the following features. I) A differential aging between (1) and (2) occurs at their reunion and it has an absolute character, i.e. the proper time interval measured by a given clock is the same both in I and in A. II) From a quantitative point of view, the magnitude of the differential aging between (1) and (2) does depend on the kind of rotational motion performed by A. Indeed, if it is uniform there is no any tangential force in the direction of motion of (2) but only normal to it. In this case, the proper time interval reckoned by (2) does depend only on its constant velocity v=romega. On the contrary, if the rotational motion is uniformly accelerated, i.e. a constant force acts tangentially along the direction of motion, the proper time intervals $do depend$ on the angular acceleration alpha. III) Finally, in regard to the sign of the aging, the moving clock (2) measures always a $shorter$ interval of proper time with respect to (1).Comment: LaTex2e, 9 pages, no figures, no tables. It is the follow-on of the paper physics/040503

Quantum phase shift and neutrino oscillations in a stationary, weak gravitational field

A new method based on Synge's world function is developed for determining within the WKB approximation the gravitationally induced quantum phase shift of a particle propagating in a stationary spacetime. This method avoids any calculation of geodesics. A detailed treatment is given for relativistic particles within the weak field, linear approximation of any metric theory. The method is applied to the calculation of the oscillation terms governing the interference of neutrinos considered as a superposition of two eigenstates having different masses. It is shown that the neutrino oscillations are not sensitive to the gravitomagnetic components of the metric as long as the spin contributions can be ignored. Explicit calculations are performed when the source of the field is a spherical, homogeneous body. A comparison is made with previous results obtained in Schwarzschild spacetime.Comment: 14 pages, no figure. Enlarged version; added references. In the Schwarzschild case, our results on the non-radial propagation are compared with the previous work

All order covariant tubular expansion

We consider tubular neighborhood of an arbitrary submanifold embedded in a (pseudo-)Riemannian manifold. This can be described by Fermi normal coordinates (FNC) satisfying certain conditions as described by Florides and Synge in \cite{FS}. By generalizing the work of Muller {\it et al} in \cite{muller} on Riemann normal coordinate expansion, we derive all order FNC expansion of vielbein in this neighborhood with closed form expressions for the curvature expansion coefficients. Our result is shown to be consistent with certain integral theorem for the metric proved in \cite{FS}.Comment: 27 pages. Corrected an error in a class of coefficients resulting from a typo. Integral theorem and all other results remain unchange

Galilean Limit of Equilibrium Relativistic Mass Distribution

The low-temperature form of the equilibrium relativistic mass distribution is subject to the Galilean limit by taking $c\rightarrow \infty .$ In this limit the relativistic Maxwell-Boltzmann distribution passes to the usual nonrelativistic form and the Dulong-Petit law is recovered.Comment: TAUP-2081-9

Linear waves in sheared flows. Lower bound of the vorticity growth and propagation discontinuities in the parameters space

This study provides sufficient conditions for the temporal monotonic decay of enstrophy for two-dimensional perturbations traveling in the incompressible, viscous, plane Poiseuille and Couette flows. Extension of J. L. Synge's procedure (1938) to the initial-value problem allowed us to find the region of the wavenumber-Reynolds number map where the enstrophy of any initial disturbance cannot grow. This region is wider than the kinetic energy's one. We also show that the parameters space is split in two regions with clearly distinct propagation and dispersion properties

A modal impedance-angle formalism: Rigorous proofs for optical fiber mode counting and bracketing

In a companion paper, a complex-power-flow variational scheme is applied to analyze mode propagation along open circularly cylindrical graded-index waveguides. It leads to a characteristic equation in terms of impedances rather than fields. The resulting impedance-angle formalism provides the basis for the full-wave generalization for optical fibers of the mode-counting scheme previously developed for a scalar wave propagation problem. The complex-power-flow variational scheme for bent waveguides is based on energy considerations. Hence, in its derivation, it is natural to consider a waveguide section (a volume) rather than a cross section (a surface). In the proof of the mode-counting and mode-bracketing theorems, the key issue is to show that the characteristic roots and the roots of the so-called separation function alternate. For general circularly cylindrical open waveguides, the required proofs are intricate. However, the special limiting cases in which the optical fiber is surrounded by electrically or magnetically perfectly conducting walls are tractable. To account for the general case, it appears to be necessary to regard a class of optical waveguide problems with a continuous transition from perfect electric conductor to perfect magnetic conductor boundary conditions via the situation pertaining to the actual exterior medium. Thus, a half-strip is constructed on which the so-called characteristic and separation graphs are seen to alternate. As spin-off, such a "sweep" might prove useful in the design of a fiber cladding