Conformally flat static space-time in the general scalar-tensor theory of gravitation

Explicit vacuum field equations in the general scalar-tensor theory of gravitation proposed by Nordtvedt are obtained with the aid of the most general conformally flat spherically-symmetric static space-time. It is shown that the most general conformally flat spherically-symmetric static solution of Nordtvedt-Barker vacuum field equations is simply the empty flat space-time of general relativity.     

Solution of a generalized equation of transfer in a two-region slab

The general equation of transfer in a two-region slab of unequal thickness with general boundary conditions has been solved by an analytical method developed by Menninget al. (1980). The scattering is regarded as isotropic and the source function is taken as a general one to accomodate different types of problems.     

Three classical tests of Hořava-Lifshitz gravity theory

Recently, a renormalizable gravity theory has been proposed by Hořava, and it might be an ultraviolet completion of general relativity or its infrared modification. Particular limit of the theory allows for the Minkowski vacuum. A spherical asymptotically flat black hole solution that represents the analogy of Schwarzschild solution of general relativity has been obtained. It will be very interesting to find the difference between traditional general relativity and Hořava-Lifshitz gravity theory. The three classical tests of general relativity including gravitational red-shift, perihelion precession of the planet Mercury, and light deflection in gravitational field in the spherical asymptotically flat black hole solution of infrared modified Hořava-Lifshitz gravity are investigated. The first order corrections from the standard general relativity is obtained. The result can be used to limit the parameters in Hořava-Lifshitz gravity and to show the viability of the theory.     

Light on dark matter: Proceedings of the First IRAS Conference

The interpretation of Einstein's general theory of relativity is discussed. The concept of gravitational forces are shown to be redundant in general relativity.     

The Confrontation between General Relativity and Experiment

We review the experimental evidence for Einstein's general relativity. Tests of the Einstein Equivalence Principle support the postulates of curved spacetime and bound variations of fundamental constants in space and time, while solar-system experiments strongly confirm weak-field general relativity. The Binary Pulsar provides tests of gravitational-wave damping and of strong-field general relativity. Future experiments, such as the Gravity Probe B Gyroscope Experiment, a satellite test of the Equivalence principle, and tests of gravity at short distance to look for extra spatial dimensions could further constrain alternatives to general relativity. Laser interferometric gravitational-wave observatories on Earth and in space may provide new tests of scalar-tensor gravity and graviton-mass theories via the properties of gravitational waves. This revised version was published online in July 2006 with corrections to the Cover Date.     

Solution of the equation of transfer with general phase function by a modified spherical-harmonic method

The equation of transfer with general phase function has been solved by a modified form of spherical-harmonic method. The solutions in case of certain particular phase functions are then derived from the general one.     

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.     

Stability of general relativistic Miyamoto–Nagai galaxies

The stability of a recently proposed general relativistic model of galaxies is studied in some detail. This model is a general relativistic version of the well-known Miyamoto–Nagai model that represents well a thick galactic disc. The stability of the disc is investigated under a general first-order perturbation keeping the space–time metric frozen (no gravitational radiation is taken into account). We find that the stability is associated with the thickness of the disc. We find that flat galaxies have more non-stable modes than the thick ones, i.e. flat galaxies have a tendency to form more complex structures like rings, bars and spiral arms.     

Hill stability of the general problem of three bodies

We discuss Hill stability in the general three-body problem. The Hill curves in the general problem are the same as in the planar problem. We show that the bifurcation points correspond to the five equilibrium solutions, and derive the criterion for stability in the general case. Application of this criterion to 19 natural satellites of the Solar system leads to the result that, apart from Neptune 1, all the other 18 satellites are unstable in the sense of Hill. The dominant factor in producing this result is the finite eccentricity of the planetary orbits around the Sun.     

Robertson-Walker Lyttleton-Bondi universe with cosmological constant — A comment

It is shown that the exterior solutions of the Robertson-Walker metric in the Lyttleton-Bondi universe with cosmological constant are, in general, those space-times which represent stiff matter fluids in general relativity theory. This shows that a result stated by Varma and Roy is incorrect.     

What does the Sun tell and hint now？

Some historical records, which have held since the beginning of modern solar activity cycles, are being broken by the present Sun： cycle 23 records the longest cycle length and fall time; latitudes of high-latitude sunspots belonging to a new cycle around the minimum time of the cycle are statistically the lowest at present, compared with those of other cycles; there are only one or no sunspots in a month appearing at high latitudes for 58 months, which is the first time that such a long duration has been observed. The solar dynamo is believed to be slowing down due to： （1） the minimum smoothed monthly mean sunspot number is the smallest since cycle 16 onwards, and even probably among all modern solar cycles; and （2） once the time interval between the first observations of two neighboring sunspot groups is larger than 14 d, it should be approximately regarded as an observation of no sunspots on the visible solar disk, called a spotless event. Spotless events occur with the highest frequency around the minimum time of cycle 24, and the longest spotless event also appears around the minimum time for observations of the Sun since cycle 16. Cycle 24 is expected to have the lowest level of sunspot activity from cycle 16 onwards and even probably for all of the modern solar cycles.     

The kilosecond variability of X-ray sources in nearby galaxies

Chandra observations of 17 nearby galaxies were analyzed and 166 bright sources with X-ray counts 〉 100 were chosen for temporal analysis. Fractional root mean square （rms） variability amplitudes were estimated for light curves, binned at 4 kilosecond （ks）, with length 〈 40 ks. While there are nine ultra-luminous X- ray sources （ULXs） with unabsorbed luminosity （in the 0.3-8.0 keV band） L 〉 1039 erg s-1 in the sample for which the fractional rms variability is constrained to be 〈 10%, only two of them show variability. One of the variable ULXs exhibits a secular transition and has an ultra-soft spectrum with temperature - 0.3 keV while the other is a rapidly varying source in NGC 0628, which has previously been com- pared to the Galactic microquasar GRS 1915＋105. These results seem to indicate that ULXs are typically not highly variable on ks timescales, except for some ultra-soft ones. Among the relatively low luminosity sources （L - 10^38 erg s-1）, we find five of them to be variable. Apart from an earlier known source in NGC 1569, we identify a source in NGC 2403 that exhibits persistent high amplitude fluctuations. In general, the variability of the sources does not seem to be correlated with hardness, which indicates that they may not be due to variations in any absorbing material, but instead could reflect instabilities in the inner accretion disk.     

Exact Brans-Dicke cosmologies with a cosmological constant

We present the general Brans-Dicke-Friedmann-Robertson-Walker (k=0) vacuum solutions with a cosmological constant. The space-times considered here are the generalizations of the de Sitter models of the general theory of relativity.     

Why the concepts of a cosmic potential and gravitational force need not be redundant in the general relativity and cosmology

A reply is given to the critique that the introduction of the cosmic potential and gravitational force into the general relativity is, at least, redundant, if not wrong. The introduction is both motivated and necessary, in order to make Mach's principle and the general relativity compatible.     

Brightness temperature for 166 radio sources

Using the database of the University of Michigan Radio Astronomy Observatory （UMRAO） at three radio frequencies （4.8, 8 and 14.5 GHz）, we determined the short-term variability timescales for 166 radio sources. The timescales are 0.15d （2007＋777） to 176.17 d （0528-250） with an average timescale of Atobs = 17.1 4- 16.5 d for the whole sample. The timescales are used to calculate the brightness temperatures, TB. The value of log TB is in the range of log TB = 10.47 to 19.06 K. In addition, we also estimated the boosting factor for the sources. The correlation between the polarization and the Doppler factor is also discussed.     

An analysis of the optical light curve of the X-ray binary 3U 1653+35

The purpose of this paper is to provide an estimate of several parameters of X-ray binary system 3U 1653+35, based a study of the optical light curve of the companion of HZ Her.The introductory section gives a general outline of the problem and deals with the general method of estimation of the parameters. In Section 2, the reflection effect in close binary systems is demonstrated in the end of this section we first introduce a new method of evaluation of reflection effect in close binary systems. Section 3 gives an analysis of the optical curve of the X-ray binary system 3U 1653+35, and general discussion.     

On the restricted three-body problem with generalized forces

By introducing general functions which depend on distance, a general scheme which determines the equilibrium solutions for the generalized restricted three-body problem is given. Applications to problems such as primaries considered as rigid bodies, influence of the radiation pressure of the primaries, and a combination of radiation pressure and rigid body are presented.     

Analysis of interval constants in calendars affiliated with the Shoushili

We study interval constants that are related to motions of the Sun and Moon,i.e., the Qi, Intercalation, Revolution and Crossing interval, in calendars affiliated with the Shoushi calendar(Shoushili), such as Datongli and Chiljeongsannaepyeon. It is known that these interval constants were newly introduced in the Shoushili calendar and revised afterward, except for the Qi interval constant, and the revised values were adopted in later calendars affiliated with the Shoushili. We first investigate the accuracy of these interval constants and then the accuracy of calendars affiliated with the Shoushili in terms of these constants by comparing times for the new moon and the maximum solar eclipse calculated by each calendar with modern methods of calculation. During our study, we found that the Qi and Intercalation interval constants used in the early Shoushili were well determined, whereas the Revolution and Crossing interval constants were relatively poorly measured. We also found that the interval constants used by the early Shoushili were better than those of the later one, and hence better than those of Datongli and Chiljeongsannaepyeon. On the other hand, we found that the early Shoushili is, in general, a worse calendar than Datongli for use in China but a better one than Chiljeongsannaepyeon for use in Korea in terms of times for the new moon and when a solar eclipse occurs, at least for the period 1281 – 1644.Finally, we verified that the times for sunrise and sunset in the Shoushili-Li-Cheng and Mingshi are those at Beijing and Nanjing, respectively.     

Spontaneous magnetic reconnection mechanisms in plasma

Using the kinetic theory and model collision integral of Bhatnagar-Gross-Krook we obtain the general dispersion relation for different regimes of the tearing-mode instability development in configuration with sheared magnetic field. Thus, we can construct the general picture of the applicability of different mechanisms of the tearing-mode dependent on collision frequency and value of the shear.