A local analytic characterization of Schwarzschild metrics

A local characterization of Schwarzschild metrics is made by showing the space-time is locally a 2 by 2 warped product and admitting a static reference frame on its certain open subsets under some assumptions on the global analytic structure and stress-energy tensor of the space-time, such as, assuming the existence of solutions to certain partial differential equations and the existence of a radiation stress-energy tensor consistent with these solutions on the space-time.     

A local characterization of Schwarzschild and Reissner metrics

A local characterization of Schwarzschild and Reissner metrics is made by using the concepts of infinitesimal null anisotropy (or equivalently, infinitesimal isotropy) and weak affinity.     

A note on the lattice dynamics of thin films local modes and the Mössbauer effect

In a thin film interacting with the substrate local modes in the neighbourhood of the defect in the region of low or high frequencies can occur. The importance of these local modes for the Mössbauer effect is briefly discussed.     

A note on state decomposition independent local invariants

We present a method to change the fluorescence contrast between two dyes with high fluorescence anisotropy in the same solution under different polarization directions by using polarization-shaped pulses. First a theoretical relationship between contrast, anisotropy and polarization is derived for this case. Then the wavelength dependent polarization anisotropy and the change of contrast by phase-shaping for a solution of Rhodamine B and Stilbene 3 in glycerol is shown. Finally, the application of the polarization-shaped pulses is demonstrated.     

A short note on the Aharonov-Bohm effect

We point out that the Aharonov-Bohm effect is a 4-dimensional nonlocal geometric phenomenon. We give two examples which in 3 dimensions appear rather mysterious, but which are easily understood in 4 dimensions. We also discuss why it is integrated effects over fields (potentials) rather than the fields themselves that are important.     

A note on the modular conjugations for local algebras of observables

It is shown that the modular conjugations of local algebras of observables in quantum field theory satisfy an asymptotic expression. This expression is similar to a corresponding one for modular operators given by Fredenhagen.     

A note on local unitary equivalence of isotropic-like states

We consider the local unitary equivalence of a class of quantum states in a bipartite case and a multipartite case. The necessary and sufficient condition is presented. As special cases, the local unitary equivalent classes of isotropic state and Werner state are provided. Then we study the local unitary similar equivalence of this class of quantum states and analyze the necessary and sufficient condition.     

A note on the spheroidal modes vibration of an elastic sphere in linear viscoelastic fluid

Vibration characteristics of elastic nanostructures embedded in fluid medium have been used for biological and mechanical sensing, and also to investigate materials mechanical properties. An analytical approach based on the exact theory has been developed in this paper, to establish a new accurate and simple generalized frequency equation to predict spheroidal vibration of an elastic nanosphere, in a compressible viscoelastic fluid using linear Maxwell fluid model. To demonstrate the accuracy of the present approach, a comparison is made with the published theoretical results in the literature in some particular cases, which shows a very good agreement. Thus, the obtained frequency equation can be very useful to interpret the experimental measurements of vibrational dynamics of nanospheres and can serve as benchmark solution in design of liquid sensors.     

The effect of negative-energy shells on the Schwarzschild black hole

We construct Penrose diagrams for Schwarzschild spacetimes joined by massless shells of matter, in the process correcting minor flaws in the similar diagrams drawn by Dray and ’t Hooft (Commun Math Phys 99:613–625, 1985), and confirming their result that such shells generate a horizon shift. We then consider shells with negative energy density, showing that the horizon shift in this case allows for travel between the heretofore causally separated exterior regions of the Schwarzschild geometry. These drawing techniques are then used to investigate the properties of successive shells, joining multiple Schwarzschild regions. Again, the presence of negative-energy shells leads to a causal connection between the exterior regions, even in (some) cases with two successive shells of equal but opposite total energy.     

A note on a Casimir effect in a uniformly accelerated reference frame

Maxwell's equations are established for the free electromagnetic field in two-dimensional space-times. In Minkowski space they are solved under the boundary conditions set by a pair of uniformly accelerated plates. With the help of these solutions we determine the regularized energy-momentum tensor of the canonically quantized electromagnetic field at the position of one of the plates. Thereby (as a new result) we arrive at a Casimir effect in an accelerated reference frame.University of New Mexico Albuquerque New Mexico 87131This paper is dedicated to Professor Peter Mittelstaedt, University of Cologne, in honour of his sixtieth birthday.On leave of absence from the NBC Defense Research and Development Institute, D-3042 Munster, P.O.B. 1320, Federal Republic of Germany.     

POD analysis on the sphere wake at a subcritical Reynolds number

Abstract  

Flow characteristics of turbulent wake behind a sphere at a subcritical flow regime were experimentally investigated. The particle image velocimetry measurements and proper orthogonal decomposition (POD) modal analysis were employed to get detailed flow information such as the wavy structure, swirling motion and coherent structures of the sphere wake. The variation of turbulent intensities of the radial and circumferential velocity components showed the swirling motion of sphere wake in the cross-sectional planes. The relative contribution of the POD mode 1, 2 and 3 in eigenvalues was 26, 11, and 8%, respectively. The general pattern of velocity fields for the POD mode 1 in the near-wake region of x/d = 0.7–1.4 is similar with that of time-averaged mean velocity fields. In addition, the sweeping flow in the region from x/d = 1.5 to x/d = 2.0 possesses wavy structure of the sphere wake. The experimental results of the present study would contribute to the fundamental understanding of the turbulent near-wake behind a sphere.     

A note on micromagnetics at high temperature

Phenomenological field equations are proposed for studying rigid ferromagnets at temperatures close to the Curie temperature. These are discussed and compared with the equations of standard micromagnetics. Only a Gilbert's type of relaxation can be introduced.     

The effect of spherical shells of matter on the Schwarzschild black hole

Based on previous work we show how to join two Schwarzschild solutions, possibly with different masses, along null cylinders each representing a spherical shell of infalling or outgoing massless matter. One of the Schwarzschild masses can be zero, i.e. one region can be flat. The above procedure can be repeated to produce space-times with aC ⁰ metric describing several different (possibly flat) Schwarzschild regions separated by shells of matter. An exhaustive treatment of the ways of combining four such regions is given; the extension to many regions is then straightforward. Cases of special interest are: (1) the scattering of two spherical gravitational shock waves at the horizon of a Schwarzschild black hole, and (2) a configuration involving onlyone external universe, which may be relevant to quantization problems in general relativity. In the latter example, only an infinitesimal amount of matter is sufficient to remove the Wheeler wormhole to another universe.Supported in part by the Stichting voor Fundamenteel Onderzoek der Materie     

A New Variational Principle for a Nonlinear Dirac Equation on the Schwarzschild Metric

In this paper, we prove the existence of infinitely many solutions of a stationary nonlinear Dirac equation on the Schwarzschild metric, outside a massive ball. These solutions are the critical points of a strongly indefinite functional. Thanks to a concavity property, we are able to construct a reduced functional, which is no longer strongly indefinite. We find critical points of this new functional using the Symmetric Mountain Pass Lemma. Note that, as A. Bachelot-Motet conjectured, these solutions vanish as the radius of the massive ball tends to the horizon radius of the metric. Received: 2 August 1999 / Accepted: 14 February 2000