Comment on the Brans-Dicke-Bianchi type-I solution

We should like to point out that the Brans-Dicke-Bianchi type-I vacuum solution recently given by Ram and Singh is wrong. The correct solution is nothing but a special case of the general BDT-Bianchi type-I solutions given by us recently (Lorenz-Petzold, 1984). It is the aim of this comment to rediscuss the corresponding field equations and to disprove the statement that the (correct) solution has no analogy in Einstein's theory.     

General vacuum solution for Brans-Dicke-Bianchi type-II

In this paper we have obtained the general vacuum solution for Bianchi type-II in the Brans-Dicke theory for total anistropyR ₁R ₂R ₃. It is known that by use of our method, we can find the general solution for Bianchi type-II vacuum case in the general relativity theory, first given by Taub (1951). Some physical properties of this model are also discussed.     

Comment on the LRS-BDT-Bianchi type-V vacuum solution

We wish to point out that the anisotropic LRS-BDT-Bianchi type-V vacuum solution recently given by Ram and Singh is wrong. Moreover, the correct solution is nothing but an isotropic FRW (k=–1) solution given by us previously.     

Comment on the vacuum Bianchi type I solution in the Brans-Dicke theory

We wish to point out that the axialsymmetric Bianchi type I vacuum solution recently given by Ram, is wrong. Moreover, the correct solution is only a special case of the general triaxial Bianchi type I solution given by Ruban and Finkelstein.     

A bianchi type-III cosmological model in Brans-Dicke theory for vacuum field

An exact solution of Brans-Dicke (B-D) field equations for the metric tensor of a spatially homogeneous Bianchi type-III configuration has been obtained for vacuum field. It is shown that in the limiting case the solution reduces to that of Einstein field equations in vacuum.     

Comment on the general vacuum solutions in Brans-Dicke cosmology

We would like to point out that the non-flat FRW-solutions of the Brans-Dicke theory, recently obtained by Chauvet, can be presented in a much simpler form.     

Comment on the inhomogeneous Bianchi type-VI0 solution

The inhomogeneous Bianchi type-VI₀ perfect fluid solution given recently by Roy and Narain (1985) is shown to be identical with the solution first given by Tomita (1978).     

Comment on the BDT-Bianchi type-VI0 stiff matter solution

We wish to point out that the Brans-Dicke-Bianchi type-VI₀ stiff matter solution recently given by Ram and Singh is not the most general solution of the corresponding field equations. Moreover, this solution has no vacuum limit and the general relativistic limit is obtained only after making an asymptotic expansion. In this paper we rediscuss the entire problem in a different way. In the limit =const., , we obtain both the stiff matter and the vacuum relativistic limit first given by Ellis and MacCallum (1969) in analytic form.     

Comment on the Bianchi type-V solution in the scale-covariant theory

We make some critical remarks on the recent papers by Beesham (1986a-c) concerning exact solutions of the scale-covariant theory.     

The isotropization of the vacuum Bianchi type — V solution

In a recent paper, the general vacuum Bianchi type-V solution in Brans-Dicke theory was presented and the isotropization of the model was discussed. It is pointed out that this solution was derived previously. Some remarks are made about the isotropization of the model.     

Bianchi type-III model in the Lyttleton-Bondi universe

The exterior field of the Bianchi type-III metric in the Lyttleton-Bondi universe is considered and an exact cosmological model is presented. Some physical properties of the model are discussed.     

LRS Bianchi type V vacuum cosmological solution in Brans-Dicke theory

In this note a new solution of the BD field equations, for a Bianchi type V space-time, is obtained. The solution has its general relativistic analogue. Some properties of the solution are also discussed.     

Bianchi type-III cosmological model in the presence of zero-mass scalar fields

An exact Bianchi type-III cosmological model in the presence of zero-mass scalar fields is obtained when the source of the gravitational field is a perfect fluid with pressure equal to energy density. Some properties of the model are also discussed.     

On the spectra of type-III solar radio bursts observed at low frequencies

The spectra of strong bursts observed at low frequencies by OGO-5 during 1968–1970 are presented. They usually exhibit an intense main peak between 100 kHz and 1 MHz, and sometimes a less intense secondary peak between 1 and 3.5 MHz. Main peaks of 10^–12 Wm^–2 Hz^–1 or more were obtained in very strong events, but because of antenna calibration problems those could be one or two orders of magnitude too high. Recently published work supports the finding that type III bursts at low frequencies can be at least four orders of magnitude more intense than at ground-based frequencies of observation. It is found that the energy received at the Earth increases with decreasing frequency approximately as f ^–n, where 3 n 4.     

Seyfert星系的环境

本文对CfA样本中的属群星系进行了最近邻间距分析,发现在最近邻距离小于20kpc的星系中存在明显的Seyfert核超(即其中Seyfert星系所占比率高出平均值约3倍)。这表明近距星系的存在可能是产生Seyfert核活动的有利环境。     

A solution of linearized Einstein field equations in vacuum used for the detection of the stochastic background of gravitational waves

A solution of linearized Einstein field equations in vacuum is given and discussed. First it is shown that, computing from our particular metric the linearized connections, the linearized Riemann tensor and the linearized Ricci tensor, the linearized Ricci tensor results equal to zero. Then the effect on test masses of our solution, which is a gravitational wave, is discussed. In our solution test masses have an apparent motion in the direction of propagation of the wave, while in the transverse direction they appear at rest. In this way it is possible to think that gravitational waves would be longitudinal waves, but, from careful investigation of this solution, it is shown that the tidal forces associated with gravitational waves act along the directions orthogonal to the direction of propagation of waves. The computation is first made in the long wavelengths approximation (wavelength much larger than the linear distances between test masses), then the analysis is generalized to all gravitational waves.

In the last sections of this paper it is shown that the frequency dependent angular pattern of interferometers can be obtained from our solution and the total signal seen from an interferometer for the stochastic background of gravitational waves is computed.     

Thermodynamics of the vacuum

The fact that the energy-momentum tensor has nonzero vacuum expectation value in some space-times (the so-called back reaction) indicates a nontrivial thermodynamics of such vacua. A consequent thermodynamic analysis of the problem in Robertson-Walker space-times shows that, in the generic case, the number of the independent extensives is 2, in spite of the fact that the energy density is completely determined by the time-evolution of the geometry since the preparation of the vacuum state. The appearance of a second independent extensive seems to be in direct connection with the extra entropy term in theGeneralized Second Law of Bekenstein and Hawking.     

Comment on the GRT-LRS Bianchi type-V solutions

We wish to point out that the locally rotationally symmetric (LRS) Bianchi type-V electromagnetic solutions recently given by Roy and Singh (1983) on the basis of the general theory of relativity (GRT) are wrong. The correct electromagnetic solutions are nothing but the vacuum and stiff matter solutions first given by Ftaclas (1978), which have been generalized by Jantzen (1980) and independently by Lorenz (1981).     

Fast solar electrons,interplanetary plasma and km-wave type-III radio bursts observed from the IMP-6 spacecraft

IMP-6 spacecraft observations of low frequency radio emission, fast electrons, and solar wind plasma are used to examine the dynamics of the fast electron streams which generate solar type-III radio bursts. Of twenty solar electron events observed between April, 1971 and August, 1972, four were found to be amenable to detailed analysis. Observations of the direction of arrival of the radio emission at different frequencies were combined with the solar wind density and velocity measurements at 1 AU to define an Archimedean spiral trajectory for the radio burst exciter. The propagation characteristics of the exciter and of the fast electrons observed at 1 AU were then conpared. We find that: (1) the fast electrons excite the radio emission at the second harmonic; (2) the total distance travelled by the electrons was between 30 and 70% longer than the length of the smooth spiral defined by the radio observations; (3) this additional distance travelled is the result of scattering of the electrons in the interplanetary medium; (4) the observations are consistent with negligible true energy loss by the fast electrons.     

Comment on the GRT-LRS Bianchi type V solutions

The points raised by Lorenz-Petzold (1985) on our paper (1983) are discussed. It is shown that the conclusions drawn by him are not substantiated.