Effects Of Finite Distance Research Articles

Finite distance effects on the Hellings–Downs curve in modified gravity

There is growing interest in the overlap reduction function in pulsar timing array observations as a probe of modified gravity. However, current approximations to the Hellings–Downs curve for subluminal gravitational wave propagation, say v<1, diverge at small angular pulsar separation. In this paper, we find that the overlap reduction function for the v<1 case is sensitive to finite distance effects. First, we show that finite distance effects introduce an effective cut-off in the spherical harmonics decomposition at ℓ∼1-v2kL, where ℓ is the multipole number, k the wavenumber of the gravitational wave and L the distance to the pulsars. Then, we find that the overlap reduction function in the small angle limit approaches a value given by πkLv2(1-v2)2 times a normalization factor, exactly matching the value for the autocorrelation recently derived. Although we focus on the v<1 case, our formulation is valid for any value of v.

Deflection of charged massive particles by a four-dimensional charged Einstein–Gauss–Bonnet black hole

Based on the Jacobi metric method, this paper studies the deflection of a charged massive particle by a novel four-dimensional charged Einstein–Gauss–Bonnet black hole. We focus on the weak field approximation and consider the deflection angle with finite distance effects. To this end, we use a geometric and topological method, which is to apply the Gauss–Bonnet theorem to the Jacobi space to calculate the deflection angle. We find that the deflection angle contains a pure gravitational contribution δ g, a pure electrostatic δ c and a gravitational–electrostatic coupling term δ gc. We find that the deflection angle increases (decreases) if the Gauss–Bonnet coupling constant α is negative (positive). Furthermore, the effects of the BH charge, the particle charge-to-mass ratio and the particle velocity on the deflection angle are analyzed.

Weighing the spacetime along the line of sight using times of arrival of electromagnetic signals

We present a new method of measuring the mass density along the line of sight, based on precise measurements of the variations of the times of arrival (TOA's) of electromagnetic signals propagating between two distant regions of spacetime. The TOA variations are measured between a number of slightly displaced pairs of points from the two regions. These variations are due to the nonrelativistic geometric effects (Roemer delays and finite distance effects) as well as the gravitational effects in the light propagation (gravitational ray bending and Shapiro delays). We show that from a sufficiently broad sample of TOA measurements we can determine two scalars quantifying the impact of the spacetime curvature on the light propagation, directly related to the first two moments of the mass density distribution along the line of sight. The values of the scalars are independent of the angular positions or the states of motion of the two clock ensembles we use for the measurement and free from any influence of masses off the line of sight. These properties can make the mass density measurements very robust. The downside of the method is the need for extremely precise signal timing.

Gravitational deflection angle of light: Definition by an observer and its application to an asymptotically nonflat spacetime

The gravitational deflection angle of light for an observer and source at finite distance from a lens object has been studied by Ishihara et al. [Phys. Rev. D, 94, 084015 (2016)], based on the Gauss-Bonnet theorem with using the optical metric. Their approach to finite-distance cases is limited within an asymptotically flat spacetime. By making several assumptions, we give an interpretation of their definition from the observer's viewpoint: The observer assumes the direction of a hypothetical light emission at the observer position and makes a comparison between the fiducial emission direction and the direction along the real light ray. The angle between the two directions at the observer location can be interpreted as the deflection angle by Ishihara et al. The present interpretation does not require the asymptotic flatness. Motivated by this, we avoid such asymptotic regions to discuss another integral form of the deflection angle of light. This form makes it clear that the proposed deflection angle can be used not only for asymptotically flat spacetimes but also for asymptotically nonflat ones. We examine the proposed deflection angle in two models for the latter case; Kottler (Schwarzschild-de Sitter) solution in general relativity and a spherical solution in Weyl conformal gravity. Effects of finite distance on the light deflection in Weyl conformal gravity result in an extra term in the deflection angle, which may be marginally observable in a certain parameter region. On the other hand, those in Kottler spacetime are beyond reach of the current technology.

Effects of finite distance between a pair of opposite transversal dimensions in microchannel configurations: DSMC analysis in transitional regime

The influence of transversal walls on a stationary near-isothermal gas flow in three dimensional microchannel configurations is studied using the Direct Simulation Monte Carlo (DSMC) method in the late slip regime and the transitional regime of the gas flow, for some selected values of the rarefaction parameter. The study was performed considering a straight, a 90 degree bend and a T-junction microchannels, with a rectangular cross-section. Implicit boundary conditions were utilized for applying a given pressure at the inlet and outlet boundaries. Some of the obtained results concern two dimensional configurations by confining the third dimension between two specularly reflecting walls, so that the flow in the third direction is homogeneous. A comparison of the DSMC produced results with those given by the finite volume based SIMPLE-TS was performed. The hard sphere model was used. The No Time Counter (NTC) scheme was used for computing the particle collisions. A DSMC based software was developed to study the gas flow in microchannel configurations, and a part of the results were obtained using an OpenMP parallel version of the software.

SDCS quantum mechanical flux formula revisited for electron-hydrogen ionization

Through a simple, classical, energy conservation analysis, we propose a finite distance reinterpretation of the standard energy fraction definition used for the single differential cross section (SDCS) for the electron-hydrogen S wave ionization process. The energy modification is due to the fact that, at finite distances from the nucleus, the continuum electrons have to overcome the remaining potential energy to be completely free. As a consequence, the flux formula for extracting at finite distances SDCS is also modified. Differently from the usual observations, the proposed corrections yield finite and well behaved SDCS values also at the asymmetrical situation where one of the continuum electrons carries all the energy while the other has zero energy. Results of calculations performed at various impact energies, for both singlet and triplet symmetry, are presented and compared favorably with benchmark theoretical data. Although we do not know how, we believe that finite distance effects should strongly affect the evaluation of the flux and consequently the SDCS, also in the full electron-hydrogen case. PACS: 34.8.Dp, 03.65.Nk, 34.10.+x