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.     

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.     

Comment on the Guzmán-Bianchi type-VII h solutions

It is shown that the recently presented Brans-Dicke-Bianchi type-VII _h perfect fluid solutions by Guzmán (1989) are nothing but the solutions given already by us in our previous paper (Lorenz-Petzold, 1984).     

The revised form of characteristic actions ℏ (s) in the structure of the Universe

It is shown that the recently obtained Jordan-Brans-Dicke solutions by Chauvet and Guzmán (1986) are either inconsistent, or only special power-law solutions derived previously by Lorenz-Petzold in various papers.     

The vacuum Friedmann-type solutions in Barber's theory of gravitation

Vacuumk=0 Friedmann-type solutions in the continuous creation theory of gravitation proposed by Barber have recently been found by Reddy (1987). Here we obtain thek=±1 Friedmann solutions in Barber's theory. Also, we show that these models are, in fact, vacuum Brans-Dicke solutions that have been studied earlier by Lorenz-Petzold (1984).     

Comment on the Brans-Dicke-Bianchi type-III vacuum solution

We wish to point out that the Brans-Dicke-Bianchi type-III vacuum solution recently given by Tiwari and Singh (1984) is not new. Moreover, the solution given has no correct Einstein limit, contrary to what is claimed by these authors. The Ellis-MacCallum vacuum solution in the Einstein case can be obtained from the Brans-Dicke solution first given by Lorenz-Petzold (1984a).     

Comments on the comment on the Guzman-Bianchi type-VII h solutions

In this paper, we again discuss the new Brans-Dicke-Bianchi type-VII _h perfect fluid solutions, first given by us (Guzman, 1989). It is shown that the objections presented by Lorenz-Petzold (1989) are misleading. The dust case =0 is discussed.     

Exact five-dimensional cosmological solutions

We derive some new perfect solutions in five dimensions. The solutions given are the generalizations of theL(4, 7) vacuum solution given recently by Demaret and Hanquin (1985) in an incorrect form only.     

Information content in astronomical images

We should like to point out that the special non-singular Bianchi type-I solution of no-scale supergravity, recently obtained by Barrow and Deruelle (1988), does not exist. The most general consistent non-singular Bianchi type-I solution has been derived recently by us (Lorenz-Petzold, 1988).     

A note on the magnetic perfect fluid Bianchi type-VIo solutions

We make some comments concerning the magnetic perfect fluid Bianchi type-VI_o solutions given recently by Royet al. (1985a).     

Comments on the BDT-FRW solutions with a cosmological constant

Some critical comments are made on the power-law solutions recently given by Pimentel (1985) on the basis of the Brans-Dicke field equations for Friedmann-Robertson-Walker space-times.     

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).     

大陵五型食双星CI Aur的测光解和它的光变频谱分析

本文发表了1984年11月至1985年1月期间在美国McDonald天文台对大陵五型食双星CI Aur进行的UBV测光结果,以及采用Wilson-Devinney方法求解出它的轨道要素。结果表明CI Aur是一个半分离的双星系统,它的次星充满了Roche瓣,而主星离它的Roche等位面相离很远。两颗子星温度相差很大,质量比为0.687,轨道倾角i为74.42°。 CI Aur的光变曲线呈现随机的亮度“抖动”和明显的光变起伏。作者采用了自迴归功率谱方法和调和分析方法对它的光变起伏进行了频谱分析,求出了振荡的准周期和振幅。文章最后讨论了它的两种模型。     

Robertson-Walker-type universes with conformally-invariant scalar field

Recently, Innaiah and Reddy (1985) obtained a flat Robertson-Walker-type solution for the Einstein field equations with the trace-free energy-momentum tensor of a conformally invariant scalar field as source. Here we show that the field equations force the scalar field to be independent of time. Furthermore, we obtain open and closed Robertson-Walker-type solutions and observe that, once again, the scalar field has to be independent of time.     

‘Quantized’ dimensions of sunspots and penumbra phenomenon

Several authors have studied solutions of Einstein's field equations for a conformally invariant scalar field with trace-free energy-momentum tensor for the Robertson-Walker models forK = 0, ± 1. The relationship of these solutions to a previously existing one by Som (1985) is discussed. TheK = 0 model derived by Innaiah and Reddy (1985) is shown to be a special case of the Bianchi type-I models due to Accioly, Vaidya and Som (1983a).     

Families of periodic orbits in the three-body problem

We show by a general argument that periodic solutions of the planar problem of three bodies (with given masses) form one-parameter families. This result is confirmed by numerical investigations: two orbits found earlier by Standish and Szebehely are shown to belong to continuous one-parameter families of periodic orbits. In general these orbits have a non-zero angular momentum, and the configuration after one period is rotated with respect to the initial configuration. Similar general arguments whow that in the three-dimensional problem, periodic orbits form also one-parameter families; in the one-dimensional problem, periodic orbits are isolated.     

On magnetostatic equilibrium in a stratified atmosphere

This is a study of the relationship between a magnetic field and its embedding plasma in static equilibrium in a uniform gravity. The ideal gas law is assumed. A system invariant in a given direction is treated first. We show that an exact integral of the equation for force balance across field lines can be derived in a closed form. Using this integral, exact solutions can be generated freely by integrating directly for the distributions of pressure, density and temperature necessary to keep a given magnetic field in equilibrium. Particular solutions are presented for illustration with the solar atmosphere in mind. Extending the treatment to the general system depending on all three spatial coordinates, we arrive at the general form of a theorem of Parker that a magnetic field in static equilibrium must possess certain symmetries. We derive an equation involving the Euler potentials of the magnetic field stipulating these necessary symmetries. Only those magnetic fields satisfying this equation can be in static equilibrium and for these fields, the endowed symmetries make the construction of exact solutions an essentially two dimensional problem as exemplified by the special case of invariance in a given direction.     

Exact Brans-Dicke-Bianchi type-VIIh solutions

We discuss the Brans-Dicke-Bianchi type-VII_h field equations. Exact solutions are given for the vacuum case as well as for the stiff matter case. The derived solutions are the generalizations of the GRT-solutions first given by Doroshkevichet al. (1973) and Lukash (1974a). In addition we present a new BDT-stiff matter solution which has no analogy in the GRT.     

Bianchi type-VI0 cosmological models in certain theories of gravitation

Exact Bianchi type-VI₀ cosmological solutions to Einstein's equations are presented in vacuum and for stiff-matter in the normal gauge for Lyra's geometry and in scalar-tensor theories developed by Saez and Ballester (1985) and Lau and Prokhovnik (1986). Also cosmological solutions are obtained for pure massive strings (p-strings) and for pure geometric strings. The dynamical behaviour of the models have been discussed.     

The evolution of two types of pulsars

We have discussed the evolution of two pulsar types suggested by Huanget al. (1985). Starting from the formulae given by them, we find that these two types of pulsars follow different evolutionary tracks, different structures, different average ages; and they are going to different graveyards. From these differences we may infer that the two pulsar types may have different progenitors.