On null isotropy in spacetimes

Null isotropy in a spacetime is defined. The relation of null isotropy to the constant curvature and infinitesimal spatial isotropy is investigated. The influence of null isotropy on conjugate points along null geodesics and curvature singularities is investigated.     

Universal time delay in static spherically symmetric spacetimes for null and timelike signals

A perturbative method of computing the total travel time of both null and lightlike rays in arbitrary static spherically symmetric spacetimes in the weak field limit is proposed.The resultant total time takes a quasi-series form of the impact parameter.The coefficient of this series at a certain order n is shown to be determined by the asymptotic expansion of the metric functions to the order n+1.For the leading order(s),the time delay,as well as the difference between the time delays of two types of relativistic signals,is shown to take a universal form for all SSS spacetimes.This universal form depends on the mass M and a post-Newtonian parameter y of the spacetime.The analytical result is numerically verified using the central black hole of galaxy M87 as the gravitational lensing center.     

Some D type metric forms for spacetimes with shear,nongeodesic, and nondiverging principal null congruences

In the context of a null tetrad formalism it is assumed that the two real vectors of the tetrad have neither expansion nor rotation and that they are nongeodesic and/or have shear. This assumption is rarely used in search of algebraically special spacetimes. General relations for the connection and for the Ricci and Weyl tensors are presented. An additional assumption that these vectors are principal leads to Petrov type D spacetimes, reducible in some cases to conformally flat ones. Twenty-two explicit metric forms, probably hitherto unknown, are found.     

On geometrodynamics and null fields

The possibility of describing null electromagnetic fields by purely metric concepts has recently been subject to some doubt. Following a method devised by Hlavatý, we here investigate the relations that a Riemannian manifold must satisfy in order to correspond to a null electromagnetic field. It is shown that in most cases the fulfilment of five geometrical relations is a necessary and sufficient condition for the existence of a null electromagnetic field. The latter is unique, except for an arbitrary constant phase factor (as in the case of non-null fields). However, in some exceptional cases, there is a larger degree of arbitrariness in the null electromagnetic field that corresponds to a given metric. Such fields (which always possess wave fronts) are not reducible to metric concepts. We then turn to examine how it can occur that null electromagnetic fields require the fulfilment of five relations, rather than three, as non-null ones. In order to settle this question, we make an attempt to consider null fields as a limiting case of non-null ones, by superimposing an arbitrary infinitesimal non-null field on a finite null one. It is then shown that the Rainich vector of such a field does not have a well defined limit, when the perturbing non-null field tends to zero. It is thereby inferred that null electromagnetic fields really have a special status within the frame of geometrodynamics.     

On the motion of a three-body system on hypersurface of proper energy

Based on the fact that for hamiltonian system there exists equivalence between phase trajectories and geodesic trajectories on the Riemannian manifold, the classical three-body problem is formulated in the framework of six ordinary differential equations (ODEs) of the second order on the energy hypersurface of body system. It is shown that in the case when the total interaction potential of the body system depends on the relative distances between particles, the three of six geodesic equations describing rotations of formed by three bodies triangle are solved exactly. Using this fact, it is shown that the three-body problem can be described in the limits of three nonlinear ODEs of canonical form, which in phase space is equivalent to the autonomous sixth-order system. The equations of geodesic deviations on the manifold (the space of relative distances between particles) are derived in an explicit form. A system of algebraic equations for finding the homographic solutions of restricted three-body problem is obtained. The initial and asymptotic conditions for solution of the classical scattering problem are found.     

Tunnelling Effect and Hawking Radiation from a Vaidya Black Hole

We extend Parikh＇s study to the non-stationary black hole. As an example of the non-stationary black hole, we investigate the tunnelling effect and Hawking radiation from a Vaidya black hole whose Bondi mass is identical to its mass parameter. The Hawking radiation is considered as a tunnelling process across the event horizon and we calculate the tunnelling probability. It is found that the is the function of Bondi mass re（υ）. result is different from Parikh＇s study because dr H/dυ     

Testing noncommutative spacetimes and violations of the Pauli Exclusion Principle through underground experiments

We propose to deploy limits that arise from different tests of the Pauli Exclusion Principle: i) to provide theories of quantum gravity with experimental guidance; ii) to distinguish, among the plethora of possible models, the ones that are already ruled out by current data; iii) to direct future attempts to be in accordance with experimental constraints. We first review experimental bounds on nuclear processes forbidden by the Pauli Exclusion Principle,which have been derived by several experimental collaborations making use of various detector materials. Distinct features of the experimental devices entail sensitivities on the constraints hitherto achieved that may differ from one another by several orders of magnitude. We show that with choices of these limits, well-known examples of flat noncommutative space-time instantiations of quantum gravity can be heavily constrained, and eventually ruled out.We devote particular attention to the analysis of the κ-Minkowski and θ-Minkowski noncommutative spacetimes.These are deeply connected to some scenarios in string theory, loop quantum gravity, and noncommutative geometry.We emphasize that the severe constraints on these quantum spacetimes, although they cannot rule out theories of top-down quantum gravity to which they are connected in various ways, provide a powerful limitation for those models. Focus on this will be necessary in the future.     

On the geometry of generalized Robertson-Walker spacetimes: curvature and Killing fields

The curvature and Killing vector fields of a class of spacetimes generalizing Robertson-Walker ones (without any assumption on the fiber) is widely studied. Such spacetimes admitting non-trivial Killing vector fields are characterized, and in the globally hyperbolic case, explicitly listed.     

Twistfree and Papapetrou vacuum spacetimes with a spacelike killing vector

We show that, for the case of vacuum solutions of the Einstein equations with a spacelike hypersurface orthogonal Killing vector /³ and associated metricds ² =e ^2U (dx ³)² +e ^–2U _ab dx ^a dx ^b whereU is not a constant, there exists at every point of the quotient 3-space a plane of vectorsK ^a such that £_KR_ab=0 andK ^a R_ab=0 whereR{inab} is the Ricci tensor formed from _ab . Then in the case whereU{in,a} is a timelike or spacelike vector in the quotient 3-space, Petrov type I solutions of the vacuum field equations are obtained. In the simpler case whereU{in,a} is a null vector in the quotient 3-space, the complete solution of the vacuum field equations is obtained. It is shown that this solution is Petrov type III of Kundt's class. For the case of Papapetrou solutions where there is a twist potential which is a function ofU, solutions corresponding to the twistfree solutions are given.     

On potentials for several classes of spinor and tensor fields in curved spacetimes

Already known results with respect to the existence of a vector potential for the Maxwell field tensor and a tensor potential for Weyl's conformal curvature tensor in four-dimensional spacetimes are generalized. It is shown that there exists a spinor potential of type (n–1,1) for any totally symmetric spinor field of rankn. From this theorem we deduce a series of corollaries, for example, that every antisymmetric tensor of second rank admits a linear representation in terms of the first derivatives of two vector fields. Further, some investigations are made on the existence of potentials for arbitrary symmetric spinors of type (n, m).     

On the nature of cosmological redshift and spectral shift in Schwarzschild-like and other spacetimes

The kinematical nature of the spectral shift in different types of spacetime, cosmological redshift and frequency shift in Schwarzschild spacetime being the most prominent representatives, has been a subject of recent interest. We demonstrate that the kinematical nature of the spectral shift is an inherent feature of the particular type of spacetimes. The general solution is found: necessary and sufficient conditions for the spectral shift arising from a kinematical origin are formulated. The status of the relative speed is discussed.     

On the Robinson theorem and shearfree geodesic null congruences

Null electromagnetic fields and shearfree geodesic null congruences in curved and flat spacetimes are studied. We point out some mathematical problems connected with the validity of the Robinson theorem. The problem of finding nonanalytic twisting congruences in the Minkowski space is reduced to the construction of holomorphic functions with specific boundary conditions.Institute of Theoretical Physics, University of Warsaw Poland     

On generalized torsion two-forms in general relativity: a result of null tetrad formalism

The method of reduction of a connection form from a principal fibre-bundle to a sub-bundle is studied by considering the null tetrad formalism in space-time and discussing in detail the resulting Generalized Maurer-Cartan Structural Equations. Vacuum space-times satisfying Einstein field equations and admitting the vanishing of the induced curvature form in the reduced bundle are investigated. It is shown that these hypotheses imply the existence of a field surface orthogonal to a real null geodesic vector of the tetrad field. This work was carried out under the auspices of the National Group of Mathematical Physics of CNR.     

Modal analysis of rib waveguide through finite element and mode matching methods

Two mode solvers based on the finite element and the mode matching methods are compared by way of analyzing rib waveguides. Differences between the normalized propagation constants provided by the two methods are always less than 10^–4 which is at least about one order of magnitude smaller than previously reported values. Results for lossy waveguides and field comparison are also presented.     

On the current through a virtual cathode

Two existing opinions about the current passing through a virtual cathode in a closed equipotential cavity are considered: (i) the current is always smaller than half the limiting current (as follows from the steady-state consideration) and (ii) the current oscillates in time about the mean value that is exactly equal to the limiting current (as follows from the non-steady-state self-consistent simulation by the coarse particle method). The history of this issue is described. The invalidity of the former opinion is shown.     

Relative periods and open-string integer invariants for a compact Calabi–Yau hypersurface

In this work we compute relative periods for B-branes, realized in terms of divisors in a compact Calabi–Yau hypersurface, by means of direct integration. Although we exemplify the method of direct integration with a particular Calabi–Yau geometry, the recipe automatically generalizes for divisors in other Calabi–Yau geometries as well. From the calculated relative periods we extract double-logarithmic periods. These periods qualify to describe disk instanton generated N=1 superpotentials of the corresponding compact mirror Calabi–Yau geometry in the large volume regime. Finally we extract the integer invariants encoded in these brane superpotentials.     

On the tunneling through a time dependent barrier

Tunneling of a nucleon through a monotonically shrinking rectangular barrier is solved exactly. Some consequences for the nucleon-transfer in the approach phase of two colliding heavy nuclei are discussed.