Conformal Einstein spaces

We study conformal transformations in four-dimensional manifolds. In particular, we present a new set of two necessary and sufficient conditions for a space to be conformal to an Einstein space. The first condition defines the class of spaces conformal to C spaces, whereas the last one (the vanishing of the Bach tensor) gives the particular subclass ofC spaces which are conformally related to Einstein spaces.This work has been partly supported bym a grand from the National Science Foundation.     

Deformations of the embedded Einstein spaces

We discuss a method of studying the stability of solutions of Einstein's equations, which can be outlined as follows: Consider an embedding of a given Einstein spaceV ₄ into a pseudo-Euclidean spaceE _p,q ^N (N > 4,p + q =N) (p,q) describing the signature of the spaceE _p,q ^N . Then all the geometrical objects ofV ₄ can be expressed in terms of the embedding functions,Z ^A (x ⁱ ),A = 1, 2,...,N, i = 0, 1, 2, 3. Then let us deform the embedding:Z ^A Z ^A + ^A , being an infinitesimal parameter. The Einstein equations can be developed then in the powers of; we study the equations arising by requirement of the vanishing of the first- or second-order terms. Some partial results concerning the de Sitter, Einstein, and Minkowskian spaces are given.     

Conformally Steckel metrics in Einstein spaces

Anisotropic conformally Steckel metrics that satisfy Einstein vacuum equations containing a Λ term are examined in the paper. The metrics allow the integration of the isotropic geodetic Hamilton-Jacobi equations by complete variable separation. Tomsk State University. Translated from Izeestiya Vysshikn Uchebnykh Zavedenii, Fizika, No. 10, pp. 34–43, October, 1999.     

Nonlinear lagrangians and Einstein spaces

It is shown that, for a Riemannian spaceV _d of dimensiond, solutions of the equation ((–g)^1/2 R ⁿ)/g^ab = 0 forn = (1/4)(d+2) may be interpreted as (d + 1)-dimensional Einstein spaces.     

Vacuum Einstein spaces with axial symmetry

Four classes of solutions are found to the equations R=–2_{; ;} and g _;=0 in three-dimensional space with metric gdxdx and signature (+ ––), equivalent to the Einstein equations R_ij=0 in a vacuum for the metric . The metric ds² assumes axial symmetry and symmetry with respect to the reflection .Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–45, September, 1976.     

Conformal Einstein spaces in N-dimensions: Part II

This paper generalizes the main result of “Conformal Einstein spaces in N-dimensions” published in Ann. Global Anal. Geom. 20(2) (2001). We present necessary and sufficient tensorial conditions for a certain class of semi-Riemannian manifolds to be conformally related to Einstein spaces.     

Algebraically special hypersurface-homogeneous Einstein spaces in general relativity

This paper illustrates the value of the Newman—Penrose complex null tetrad formalism by using it to obtain all algebraically special Einstein spaces admitting three-parameter groups of motions acting on timelike surfaces containing the repeated principal null direction. Taken together with earlier work, this enables us to give a complete list of Einstein spaces which are both algebraically special and hypersurface-homogeneous or homogeneous.     

Einstein equations and Lagrangians on symmetry-restricted phase spaces

When Lagrangians are restricted to subspaces of the phase space satisfying certain symmetry conditions, they do not always yield the correct Einstein equations. An example was found by Hawking in the Lagrangian for spatially homogeneous universes. First we show that this problem is not limited to general relativity. Then we visualize certain terms which do not appear in Lagrangians on symmetry-restricted phase spaces but which nevertheless contribute to the Euler-Lagrange derivatives. We apply our general formula to the Schwarzschild metric, the Friedmann universes, and spatially homogeneous universes.     

Quantum theory of spin-3/2 field in Einstein spaces

A quantum theory of a free massless spin-3/2 field on Einstein spaces (R _ab=g_ab) is formulated in an algebraic framework. Attention is confined to the structure of the quantum operator algebra. In particular, the issue of positivity of the anticommutator is investigated and found to depend on whether or not the space-time admits rero-frequency neutrino solutions. Using methods developed for the purpose, a class of space-time that does not admit neutrino zero modes is characterized. An appendix introduces a useful technique for obtaining an initial value formulation of spinor field equations.Supported in part by the NSF, under contract No. PHY 78-24275. Submitted to the Department of Physics, University of Chicago in partial fulfillment of the requirements for the Ph.D. degree.     

Bianchi and Weyl equations as sufficient equations for Einstein spaces

When the Bianchi equation and the wave equation for the Weyl spinor are written in the form which they take for Einstein spaces, but with the symmetric 4-spinor _ABCD considered arbitrary and with the background space unspecified, ^EA _EBCD=0; (+12) _ABCD –6(AB ^EF ( _CD )EF =0 it is shown that — in general — for this pair of equations to be consistent, the background space has to be an Einstein space, and the symmetric 4-spinor _ABCD has to be the Weyl spinor of this space.     

Separation of variables in Einstein spaces. II. No ignorable coordinates

We prove that the only Einstein spaces which admit a coordinate system with no ignorable coordinates which separates the Hamilton-Jacobi equation are certain symmetric spaces of Petrov typeD due to Kasner and the constant-curvature de Sitter spaces. We also show that a space admitting a coordinate system with no ignorable coordinates which separates the Helmholtz (Schrödinger) equation must be of Petrov type     

Level density in large spectroscopic spaces

Statistical spectroscopy methods are used to calculate level densities for one-body Hamiltonians in the space of 440 single particle states. Comparisons are made with combinatorial counting and Fermi gas model. Possibilities to arrive at a more realistic level density formula including two-body effects are discussed.     

Acoustic comfort in large dining spaces

This study carried out a questionnaire field investigation in two typical large dining spaces. The results suggest that the acoustic comfort of diners has an influence on the comfort evaluation of the overall dining environment, and background noise is an important factor affecting the acoustic comfort evaluation of diners. The role of various individual sound sources in background noise has been investigated, considering general background music, speech sound, activity sound, and mechanical noise, and it has been revealed that background music, other diners’ speech sound and tableware’s impact sound has a dominant impact on the acoustic comfort evaluation of diners. Compared with the existence of background music in background noise, diners’ acoustic comfort evaluation is higher than that without background music. The loudness, articulation, noise level and preference degree of various individual sound sources are factors which affect diners’ acoustic comfort evaluation on sound sources. In terms of demographic and social factors, gender and the frequency of dining out have a significant impact on diners’ acoustic comfort evaluation.     

大空间人群声学模型

经典扩散声场理论难以适用于大空间建筑。为了探究大空间建筑中人群分布对声场的影响,本文用模拟与实测相结合的方法,提出了一种适用于大空间的人群声学模型,得到了确定等效声源和人群声源的简化方法,以及人群密度与声压级之间、人群总数与发声人数之间的关系。用实测数据对该人群声学模型进行了验证。     

FixedJ spectral distributions in large shell model spaces

A method is developed to exactly calculate the fixedJ quasiparticle centroid energies and partial widths. Some results obtained in the even-mass lead isotopes with various interactions are analysed. FixedJ quasiparticle distributions are used to predict an upper limit for the deviations between the quasiparticle approximation and the shell model results for the low-energy levels. The influence of the states with a high quasiparticle number in the low-energy region is seen to strongly depend upon the interaction. The importance of the dimensionalities and the internal widths in explaining the admixtures is stressed.     

FixedJ spectral distribution in large shell model spaces

A method is develloped to exactly calculate the fixedJ configuration centroid energies and widths. The resulting approximate level densities for²⁰⁴Pb and⁰²⁰Pb show large departures with respect to the gaussian approximate level densities. The goodness of the polynomial expansion of fixedJ configuration moments is studied and a simple improvement to this approximation is proposed which gives very good results.     

FixedJ spectral distributions in large shell model spaces

The centroids and widths defining Gaussian approximate spectroscopic strength distributions ofnJT spaces are calculated exactly via a direct method. The results in the (sd) shell nuclei and even mass Pb isotopes with 198≦A≦204 exhibit a smooth behaviour versusJ of both fixedJT centroids and widths if the spectroscopic space dimensionality is large enough.