Possible Resonator Configurations for the Spherical Gravitational Wave Antenna

We solve algebraically the equations of motion for a spherical antenna coupled to an arbitrary number of small resonators, free to move radially, and investigate the conditions under which damping forces can be neglected in the system. We show that in order that the antenna's modes be decoupled a preferred distribution of the resonators on its surface should be used. We find that either 5, 6, 10 or 16 resonators can be used as long as they are conveniently positioned on the antenna's surface. We calculate and analyse the frequency shift and the signal-to-noise ratio of the coupled system for the various distributions studied.     

Chaos Hidden Behind Time Parametrization in the Mixmaster Cosmology

We define the Maupertuis clock which counts Kasner epochs in the Mixmaster cosmology. The characteristic time scale as measured by this clock is just the length of a given Kasner epoch. We show that in every transition from one Kasner epoch to another one unit of information is lost. Relationships of the Maupertuis time with other time parametrizations used in general relativity (cosmological time, Misner time, Chitre-Misner time, curvature time and superspace time) are investigated. In the logarithmic (mechanical) time nearby trajectories diverge linearly, and the system behaves as if it were integrable and the chaos is hidden behind this parametrization. The physical meaning of the Maupertuis time, as a chaos indicator, is discussed. We also investigate the dependence of the Lyapunov exponents on time reparametrizations.     

Weak Lensing, Shear and the Cosmic Virial Theorem in a Model with a Scale-Dependent Gravitational Coupling

It is argued that, in models where the gravitational coupling is scaledependent, predictions concerning weak gravitational lensing and shear are essentially similar to the ones derived from General Relativity. This is consistent with recent negative results of observations of the MS1224, CL2218 and A1689 systems aimimg to infer from those methods the presence of dark matter. It is shown, however, that the situation is quite different when an analysis based on the Cosmic Virial Theorem is concerned.     

Superenergy of Gravitational Waves in the Exact Theory

Gravitational waves and radiation in the exact theory are studied in a unique framework. The observer's point of view is introduced. Some results by Lichnerowicz are generalized and interpreted in terms of reference frames. This allows us to recognize the role played by the gravitational force field in the exact generalization of Bel's superenergy flux theorem. It is also possible to recover the usual concept of wave as energy transmission, by means of a suitable superenergy scalar.     

Letter: Gravitational Entropy of Constrained Instanton

The seeds for quantum creations of universes areconstrained gravitational instantons. For all compactconstrained instantons with a U(1) isometry, the period of the group parameter is identifiedas the reciprocal of the temperature. If remains a free parameter under the constraints, then theEuclidean action becomes the negative of the entropy. Asexamples, we perform the calculations forthe Taub-nut and Taub-Bolt-type models andstudy the quantum creation of the Taub-nutuniverse.     

The Investigation of the Model of Gravitational Repulsion in Einstein's General Theory of Relativity

The gravitational field of a static, sphericallysymmetric source of mass M and scalar charge q isconsidered. It is shown that the metric expression forthis source is considerably simplified in two limiting cases: a) for M2 4q²/G,that is when the mass of the source is the maincontributor in the gravitational field; b) forq² M²G/4, when theenergy-momentum tensor of the static, spherically symmetric scalar field is the main contributorin the gravitational field. In the limiting caseq² M²G/4, the geodesicsof the massive and massless particles are studied. It isshown that gravitational forces of repulsion act on a particle movingnon-radially in this field. As a result, voids should becreated in the region surrounding such sources in theUniverse. Moreover, the stars with considerable scalar charge q² M²G/4 will act not as convexgravitational lenses as in the case whenq² M²G/4, but as concavegravitational lenses for the electromagnetic rays oflarge impact parameter.     

A Comment on Differential Identities for the Weyl Spinor Perturbations

It is shown that in a type-D vacuum space-time with cosmological constant, the components of the Weyl spinor perturbations along the principal spinors of the background conformal curvature satisfy differential identities, which are valid in all the normalized spin frames {o ^A , ^A } such that o ^A and ^A are double principal spinors of the background conformal curvature.     

Time Evolution in the Presence of Gravity

We present a suggestion on the interpretation of canonical time evolution when gravitation is present, based on the nonlinear gauge approach to gravity. Essentially, our proposal consists of an internal-time concept, with the time variable taken from the dynamical fields characteristic of the nonlinear realization of the internal time-translational symmetry. Physical time evolution requires the latter symmetry to be broken. After disregarding other breaking mechanisms, we appeal to the Jordan–Brans–Dicke action, conveniently interpreted, to achieve that goal. We show that nontrivial time evolution follows, the special relativistic limit being recovered in the absence of gravity.     

The Extensions of Gravitational Soliton Solutions with Real Poles

We analyse vacuum gravitationalsoliton solutions with real poles in thecosmological context. It is well known that thesesolutions contain singularities on certain nullhypersurfaces. Using a Kasner seed solution, we demonstrate thatthese may contain thin sheets of null matter or may besimple coordinate singularities, and we describe anumber of possible extensions through them.     

Some Properties of the Bel and Bel-Robinson Tensors

The properties of the Bel and Bel-Robinson tensors seem to indicate that they are closely related to the gravitational energy-momentum. We present some new properties of these tensors which might throw some light onto this relationship. First, for any spacetime we find a decomposition of the Bel tensor in terms of the Bel-Robinson tensor and two other tensors, which we call the pure matter super-energy tensor and the matter-gravity coupling super-energy tensor. We show that the pure matter super-energy tensor of any Einstein-Maxwell field is simply the square of the usual energy-momentum tensor. This, together with the fact that the Bel-Robinson tensor has dimensions of energy density square, leads us to the definition of square root for the Bel-Robinson tensor: a two-covariant symmetric traceless tensor with dimensions of energy density and such that its square gives the Bel-Robinson tensor. We prove that this square root exists if and only if the spacetime is of Petrov type O, N or D, and its general expression is explicitly presented. The properties of this new tensor are examined and some interesting explicit examples are analyzed. Of particular interest are an invariant function that appears in the spherically symmetric metrics and an expression for the energy carried out by pure plane gravitational waves. We also examine the decomposition of the whole Bel tensor for Vaidya's radiating metric and Kerr-Newman's solution. Finally, we generalize the definition of square root to a factorization of the Bel-Robinson tensor and get the general solution for all Petrov types.     

几周期余弦-高斯激光脉冲的时间重心

研究了几周期超短余弦-高斯脉冲的时间重心与绝对相位以及与余弦函数参量之间的关系．给出了几周期超短余弦-高斯脉冲时间重心的解析表达式和模拟图形．结果表明，余弦-高斯脉冲的时间重心随着绝对相位的变化而发生漂移，并且脉冲宽度对余弦-高斯脉冲时间重心的漂移量也有一定的影响．余弦函数的参量在一定取值范围内对余弦-高斯脉冲也有较大的影响，它可能导致几周期余弦-高斯脉冲的时间重心有较大的漂移．     

Gravitational Waves and Discontinuous Motions

The mathematical theory of gravitational wave-fronts is revisited with the help of orthogonal decomposition techniques. Thus many important well known results about gravitational waves in empty space are readily obtained in the local geometry framework and in general coordinates. Then different kinds of motion in the presence of a wave are investigated. Our study shows that a discontinuity effect, in traversing the wave-front, arises in the motion. The importance of this effect increases with the complexity of the considered particle. No essential discontinuity is present in simple motions such as that of a point particle and, differently from what usually believed, that of a dust of particles governed by the geodesic deviation equation.     

Charged Gravitational Instantons in Five-Dimensional Einstein-Gauss-Bonnet-Maxwell Theory

We study a solution of the Einstein-Gauss-Bonnet theory coupled to a Maxwell field in five dimensions, whose euclidean continuation gives rise to an instanton describing black hole pair production. We also discuss the dual theory with a 3-form field coupled to gravity.     

Relativistic Hydrodynamic Cosmological Perturbations

Relativistic cosmological perturbation analysescan be made based on several different fundamental gaugeconditions. In the pressureless limit the variables incertain gauge conditions show the correct Newtonian behaviors. Considering the generalcurvature (K) and the cosmological constant ()in the background medium, the perturbed density in thecomoving gauge, and the perturbed velocity and the perturbed potential in the zero-shear gaugeshow the same behavior as the Newtonian ones in generalscales. In the first part, we elaborate these Newtoniancorrespondences. In the second part, using the identified gauge-in variant variables withcorrect Newtonian correspondences, we present therelativistic results with general pressures in thebackground and perturbation. We present the generalsuper-sound-horizon scale solutions of the above mentionedvariables valid for general K, Lambda, and generallyevolving equation of state. We show that, for vanishingK, the super-sound-horizon scale evolution ischaracterised by a conserved variable which is the perturbedthree-space curvature in the comoving gauge. We alsopresent equations for the multi-component hydrodynamicsituation and for the rotation and gravitational wave.     

Creation of Closed or Open Universe from Constrained Instanton

In the no-boundary universe the universe is created from an instanton. However, no instanton exists for the realistic FRW universe with a scalar field. The instanton leading to its quantum creation may be modified and reinterpreted as a constrained gravitational instanton.     

Naked Singularity of the Vaidya-de Sitter Spacetime and Cosmic Censorship Conjecture

We investigate the formation of a locally nakedsingularity in the collapse of radiation shells in anexpanding Vaidya-de Sitter background. This is achievedby considering the behaviour of non-spacelikeand radial geodesics originating at thesingularity. A specific condition is determined for theexistence of radially outgoing, null geodesicsoriginating at the singularity which, when thiscondition is satisfied, becomes locally naked. Thiscondition turns out to be the same as that in thecollapse of radiation shells in an asymptotically flatbackground. Therefore we have established, at least forthe case considered here, that the asymptoticflatness of the spacetime is not essential for thedevelopment of a locally naked singularity. Our resultthen unequivocally supports the view that no specialrole be given to asymptotic observers (or, for thatmatter, any set of observers) in the formulation of theCosmic Censorship Hypothesis.     

Newtonian Cosmology in Lagrangian Formulation: Foundations and Perturbation Theory

The Newtonian theory of spatially unbounded, self-gravitating, pressureless continua in Lagrangian form is reconsidered. Following a review of the pertinent kinematics, we present alternative formulations of the Lagrangian evolution equations and establish conditions for the equivalence of the Lagrangian and Eulerian representations. We then distinguish open models based on Euclidean space R³ from closed models based (without loss of generality) on a flat torus T³. Using a simple averaging method we show that the spatially averaged variables of an inhomogeneous toroidal model form a spatially homogeneous background model and that the averages of open models, if they exist at all, in general do not obey the dynamical laws of homogeneous models. We then specialize to those inhomogeneous toroidal models whose (unique) backgrounds have a Hubble flow, and derive Lagrangian evolution equations which govern the (conformally rescaled) displacement of the inhomogeneous flow with respect to its homogeneous background. Finally, we set up an iteration scheme and prove that the resulting equations have unique solutions at any order for given initial data, while for open models there exist infinitely many different solutions for given data.     

Spinor Factorizations of the Bel-Robinson Tensor

Recently Bonilla and Senovilla studied factorizations of the symmetric and tracefree rank four Bel-Robinson tensor T_abcd into two symmetric tracefree rank two tensors. While the Bel-Robinson tensor has the dimension of energy density squared, each of these factors has the dimension of energy density. When the two factors can be chosen to be equal they are called the square root of T_abcd. The approach used was purely tensorial. In this paper we use spinors and show that the factors can be found in a very simple way using the principal null directions of the Weyl tensor. We obtain a factorization of the Weyl spinor into two symmetric rank two spinors, which when multiplied by their complex conjugates give the tracefree and symmetric factors of T_abcd. The factorization is immediately seen to be non-unique in most cases and the number of essentially non-equivalent factorizations becomes clear. It also becomes obvious that the square root only can exist in spacetimes of Petrov types N, D and O, in which cases one can equally well speak about the square root of the Weyl spinor. Explicit formulas for the factors of the Weyl spinor are given for all Petrov types.     

Invariant Foliation of Dynamical Spacetimes

We present a gauge-theoretical derivation of the Frobenius foliation condition. It is based on a nonlinear coset realization of the Poincaré group, implying the time component ⁰ of the coframe to be invariant. By means of the unitary gauge fixing of the boosts, three Goldstone-like degrees of freedom of ⁰ are eliminated. The remaining Higgs-like boson, satisfying the foliation condition, plays the role of time.