Non-existence of stationary two-black-hole configurations

We resume former discussions of the question, whether the spin–spin repulsion and the gravitational attraction of two aligned black holes can balance each other. To answer the question we formulate a boundary value problem for two separate (Killing-) horizons and apply the inverse (scattering) method to solve it. Making use of results of Manko, Ruiz and Sanabria-Gómez and a novel black hole criterion, we prove the non-existence of the equilibrium situation in question.     

The curvature problem in general relativity

This essay investigates the relationships among the metric, the connection, the curvature, and the covariant curvature derivatives in general relativity. The extent to which the connection or the curvature together, possibly with certain curvature derivatives, determines the metric is considered, as well as other related problems. Some topological aspects of the problem are included and some applications to holonomy and symmetry groups are given.This article received honorable mention from the Gravity Research Foundation for 1987.     

Non-existence of stationary two-black-hole configurations: the degenerate case

In a preceding paper we examined the question whether the spin–spin repulsion and the gravitational attraction of two aligned sub-extremal black holes can balance each other. Based on the solution of a boundary value problem for two separate (Killing-) horizons and a novel black hole criterion we were able to prove the non-existence of the equilibrium configuration in question. In this paper we extend the non-existence proof to extremal black holes.     

Dark matter problem and effective curvature Lagrangians

A ‘radical’ conservative unifying model of scalar dark matter and modified gravity is proposed here. After a conformal mapping, the dependence of the effective Lagrangian on the curvature is not only singular but also bifurcates into several almost Einsteinian spaces, distinguished only by a different gravitational strength and cosmological constant. A swallow tail or butterfly catastrophe in the bifurcation set indicates the possibility for the coexistence of different Einsteinian domains in our Universe. This finding may shed new light on the nature and large scale distribution not only of dark matter but also on ‘dark energy’, regarded as an effective cosmological constant.     

Stationary two-black-hole configurations: A non-existence proof

Based on the solution of a boundary problem for disconnected (Killing) horizons and the resulting violation of characteristic black hole properties, we present a non-existence proof for equilibrium configurations consisting of two aligned rotating black holes. Our discussion is principally aimed at developing the ideas of the proof and summarizing the results of two preceding papers (Neugebauer and Hennig, 2009 [2], Hennig and Neugebauer, 2011 [3]). From a mathematical point of view, this paper is a further example (Meinel et al., (2008) [29]) for the application of the inverse (“scattering”) method to a non-linear elliptic differential equation.     

The role of Gauss curvature in a membrane phase separation problem

Consider a two-phase lipid vesicle. Below the transition temperature, the phases separate into non-connecting domains that coarsen into larger areas. The free energy of phase properties determines the length of the boundaries separating the regions. The two phases correspond to different lipid compositions, and in cells, this fluctuation in composition is a dynamic process vital to its function. We prove that a small patch of the minority lipids forms at a point of the membrane where the Gauss curvature attains a maximum. This patch has a round shape approximately and its boundary has a constant geodesic curvature. The proof consists of three steps. The construction of a family of good approximate solutions, an improvement of the approximate solutions so that their geodesic curvature is a constant modulo translation, and the identification of an exact solution from the family of the improved approximate solutions. Our theoretical results are supported by vesicle experiments.     

测量光纤外腔Fabry-Perot干涉仪的白光干涉术

提出了一种基于白光干涉术测量低锐度光纤外腔Fabry Perot干涉仪（EFPI）的方法用宽带光源注入F P腔,在接收端用一高锐度的可调谐光纤F P滤波器对EFPI的反射光谱进行扫描,获得了周期性变化的光谱输出为了测量出EFPI的腔长,对光谱信号进行傅里叶变换,得到光谱的周期,由此求出EFPI的绝对腔长证明了用低锐度EFPI的测量准确度由腔长决定F P腔越长,测量准确度越高在腔长分别是200 μm,400 μm和600 μm时,测量的腔长与实际腔长相同.     

An Extended Extrinsic Mechanism for Anomalous Hall Effect

The extrinsic mechanism for anomalous Hall effect in ferromagnets is extended to include the contributions both from spin-orbit-dependent impurity scattering and from the spin-orbit coupling induced by external electric fields. The results obtained suggest that, within the framework of the extrinsic mechanisms, the anomalous Hall current in a ferromagnet may also contain a substantial amount of dissipationless contribution independent of impurity scattering. After the contribution from the spin-orbit coupling induced by external electric fields is included, the total anomalous Hall conductivity is about two times larger than that due to soin-orbit dependent impurity scatterings.     

An Extended Extrinsic Mechanism for Anomalous Hall Effect

The extrinsic mechanism for anomalous Hall effect in ferromagnets is extended to include the contributions both from spin-orbit-dependent impurity scattering and from the spin-orbit coupling induced by external electric fields. The results obtained suggest that, within the framework of the extrinsic mechanisms, the anomalous Hall current in a ferromagnet may also contain asubstantial amount of dissipationless contribution independent of impurity scattering. After the contribution from the spin-orbit coupling induced by external electric fields is included, the total anomalous Hall conductivity is about two times larger than that due to spin-orbit dependent impurity scatterings.     

Extrinsic Curvature Embedding Diagrams

Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the extrinsic curvature (instead of the intrinsic curvature). Such an extrinsic curvature embedding diagram, when used together with the usual kind of intrinsic curvature embedding diagram, carries the information of how a surface is embedded in the higher dimensional curved space. Simple examples are given to illustrate the idea.     

Extrinsic symplectic symmetric spaces

We define the notion of extrinsic symplectic symmetric spaces and exhibit some of their properties. We construct large families of examples and show how they fit in the perspective of a complete classification of these manifolds. We also build a natural ?$?$-quantization on a class of examples.     

Conditions for the occurence of strong curvature singularities

Necessary and sufficient conditions for the occurrence of strong curvature singularities as defined by Tipler and Królak are derived. It is shown that both necessary and sufficient conditions involve not only the divergence of tetrad components of the Riemann, Ricci or Weyl tensor but also the divergence of their integrals along nonspacelike geodesics running into the singularity.     

Extrinsic fibre-optic sensors for remote measurement: Part one

The impact of incorporating fibre-optic components into well established optical techniques such as laser Doppler velocimetry, non-contact vibration measurement, holography and light scattering, is discussed in the two sections of this paper. The possibilities range from simply including a fibre ‘optic link’ in a conventional system to facilitate measurements in difficult or remote areas to the realization of entirely new optical configurations in which virtually all of the conventional optical components have been replaced by their fibre-optic equivalents. In part one, fibre properties, optical sources, directional couplers and modulators are discussed.     

Extrinsic fibre-optic sensors for remote measurement: Part two

The impact of incorporating fibre optic components into well established optical techniques such as laser Doppler velocimetry, non-contact vibration measurement, holography and light scattering, is discussed in the two sections of this paper. The possibilities range from simply including a fibre ‘optic link’ in a conventional system to facilitate measurements in difficult or remote areas, to the realization of entirely new optical configurations in which virtually all of the conventional optical components have been replaced by their fibre-optic equivalents. In part two laser velocimetry, vibration measurement, holography and scattering are discussed.     

A simple model for the nuclear curvature energy

Using the well-known analytically soluble model of semi-infinite nuclear matter of Wilets, we deduce a closed expression for the nuclear curvature energy as a function of the surface profile asymmetry; the values obtained for the curvature coefficient are in good agreement with those extracted from realistic calculations. A generalization of this procedure could be a way out of the difficulties arising in Hartree-Fock calculations of the curvature coefficient.