On the inertial mass concept in special and general relativity

Inertial mass in relativity theory is discussed from a conceptual view. It is shown that though relativistic dynamics implies a particular dependence of the momentum of a free particle on its velocityin special relativity, which diverges as v approaches c, the inertial mass itself of a moving body remains constant, from any frame of observation. However, extension to general relativity does conceptually introduce variability of the inertial mass of a body, through a necessarily generally covariant field theory of inertia, when the Mach principle is incorporated into the theory of general relativity, as a theory of matter.     

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.     

Bianchi type I inflationary universe in general relativity

In this paper, we have investigated Bianchi type I inflationary universe in the presence of massless scalar field with a flat potential. To get an inflationary solution, we have considered a flat region in which potential V is constant. The inflationary scenario of the model is discussed in detail.     

Summary of classical general relativity workshop

This is a summary of the presentations at the parallel session in the classical general relativity workshop of the ICGC-2004.     

Generalized uncertainty principle and the maximum mass of ideal white dwarfs

The effects of a generalized uncertainty principle on the structure of an ideal white dwarf star is investigated. The equation describing the equilibrium configuration of the star is a generalized form of the Lane–Emden equation. It is proved that the star always has a finite size. It is then argued that the maximum mass of such an ideal white dwarf tends to infinity, as opposed to the conventional case where it has a finite value.     

Role of general relativity in accretion disk dynamics

In this we briefly review the discussions on accretion dynamics, the standard scenario and the ones including the effects of electromagnetic fields. The emphasis throughout is to show the relevance of general relativistic formalism in discussing the dynamics of magnetofluid around compact objects.     

Repulsive effects in steady axisymmetric fields

In this paper the repulsive effects in the Kerr and Kerr--Newman fields are discussed. The contributions made by all parameters of the fields and test particles to the repulsive effects are also discussed, and the accretive effect on interstellar dust, i.e. the distribution of dust is calculated. The discussion is also carried out on the slow rotation of the Kerr field in which the effect is related to the positions and velocities of the particles and the orientations of their trajectories as well.     

Spherically symmetric solutions with heat flow in general relativity

Some new solutions of shear-free imperfect fluid spheres with heat flux in the radial direction are obtained. They have isotropic pressure and could be the generalizations of earlier solutions of Nariai and of Banerjee and Banerji for perfect fluid without dissipation.     

Some applications of differential topology in general relativity

Recently, there have been several applications of differential and algebraic topology to problems concerned with the global structure of spacetimes. In this paper, we derive obstructions to the existence of spin-Lorentz and pin-Lorentz cobordisms and we show that for compact spacetimes with non-empty boundary there is no relationship between the homotopy type of the Lorentz metric and the casual structure. We also point out that spin-Lorentz and tetrad cobordisms are equivalent. Furthermore, because the original work on metric homotopy and causality may not be known to a wide audience, we present an overview of the results here.     

A canonical dynamics view of the Newtonian limit of general relativity

The Newtonian limit of general relativity was Jürgen Ehlers favourite model for limit relations between theories of physics. In this contribution, for the case of isolated systems, the Newtonian limit of general relativity will be illuminated from a canonical dynamics point of view. The canonical dynamics approach naturally supplies a post-Newtonian expansion of general relativity.     

Scalar-tensor cosmologies with a potential in the general relativity limit: Time evolution

We consider Friedmann–Lemaître–Robertson–Walker flat cosmological models in the framework of general Jordan frame scalar-tensor theories of gravity with arbitrary coupling function and potential. For the era when the cosmological energy density of the scalar potential dominates over the energy density of ordinary matter, we use a nonlinear approximation of the decoupled scalar field equation for the regime close to the so-called limit of general relativity where the local weak field constraints are satisfied. We give the solutions in cosmological time with a particular attention to the classes of models asymptotically approaching general relativity. The latter can be subsumed under two types: (i) exponential convergence, and (ii) damped oscillations around general relativity. As an illustration we present an example of oscillating dark energy.     

以广义相对论为例谈实验检验的总体方案设计

以广义相对论为例，论述了如何根据物理理论的逻辑体系设计实验，以检验理论的正确性，对于广义相对论，检验实验应包括对等效原理的检验实验，对牛顿极限的检验实验，以及对广义相对论推论的检验实验。     

The logic of quantum mechanics derived from classical general relativity

For the first time it is shown that the logic of quantum mechanics can be derived from classical physics. An orthomodular lattice of propositions characteristic of quantum logic, is constructed for manifolds in Einstein’s theory of general relativity. A particle is modelled by a topologically non-trivial 4-manifold with closed timelike curves—a 4-geon, rather than as an evolving 3-manifold. It is then possible for both the state preparationand measurement apparatus to constrain the results of experiments. It is shown that propositions about the results of measurements can satisfy a non-distributive logic rather than the Boolean logic of classical systems. Reasonable assumptions about the role of the measurement apparatus leads to an orthomodular lattice of propositions characteristic of quantum logic.     

爱丁顿与广义相对论的验证

简单介绍了在广义相对论诞生之初,验证其理论正确性的三个天文实验,并详细介绍了爱丁顿为验证广义相对论,发起并组织的观测1919年5月29日的日全食考察队的具体情况.这是爱丁顿认为他在天文学研究中最激动人心的事件.     

Initial-value problems and singularities in general relativity

Linearized solution of Datta in a non-symmetric and isentropic motion of a perfect fluid is studied by dealing with a Cauchy problem in co-moving coordinates in the framework of general relativity. The problem of singularities is discussed from the standpoint of a local observer both for rotating and non-rotating fluids. It is shown that, whatever the distribution of matter, a singularity which occurred in the past in both the rotating and non-rotating parts of the universe must occur again later after some finite proper time, if the universe is closed. A modification is incorporated in Penrose’s theorem by explicitly exhibiting that the universe defined by Penrose can possess a Cauchy hypersurface.     

Some solutions of the Einstein-Maxwell equations in general relativity

A solution of the Einstein-Maxwell equations corresponding to source-free electromagnetic field plus pure radiation is obtained. The solution is algebraically special. A particular case of the solution is considered which encompasses many known solutions. Among them is a radiating Ruban metric.     

Einstein's ‘Zürich Notebook’ and his journey to general relativity

On the basis of his ‘Zürich Notebook’ I shall describe a particularly fruitful phase in Einstein's struggle on the way to general relativity. These research notes are an extremely illuminating source for understanding Einstein's main physical arguments and conceptual difficulties that delayed his discovery of general relativity by about three years. Together with the ‘Entwurf’ theory in collaboration with Marcel Grossmann, these notes also show that the final theory was missed late in 1912 within a hair's breadth. The Einstein‐Grossmann theory, published almost exactly hundred years ago, contains, however, virtually all essential elements of Einstein's definite gravitation theory.     

The origin of the strongest magnetic fields in dwarfs

White dwarfs have frozen in magnetic fields ranging from below the measurable limit of about 3×10³ to 10⁹ G. White dwarfs with surface magnetic fields in excess of 1 MG are found as isolated single stars and relatively more often in magnetic cataclysmic variables. Some 1253 white dwarfs with a detached low-mass main-sequence companion have been identified in the Sloan Digital Sky Survey (SDSS) but none of these shows sufficient evidence for Zeeman splitting of hydrogen lines for a magnetic field in excess of 1 MG. If such high magnetic fields in white dwarfs result from the isolated evolution of a single star then there should be the same fraction of high field white dwarfs among this SDSS binary sample as among single stars. Thus, we deduce that the origin of such high magnetic fields must be intimately tied to the formation of cataclysmic variables (CVs). The formation of a CV must involve orbital shrinkage from giant star to main-sequence star dimensions. It is believed that this shrinkage occurs as the low-mass companion and the white dwarf spiral together inside a common envelope. CVs emerge as very close but detached binary stars that are then brought together by magnetic braking or gravitational radiation. We propose that the smaller the orbital separation at the end of the common envelope phase, the stronger the magnetic field. The magnetic cataclysmic variables (MCVs) originate from those common envelope systems that almost merge. Those common envelope systems that do merge are the progenitors of the single high field white dwarfs. Thus all highly magnetic white dwarfs, be they single stars or the components of MCVs, have a binary origin. This accounts for the relative dearth of single white dwarfs with fields of 10⁴–10⁶ G. Such intermediate-field white dwarfs are found preferentially in cataclysmic variables. The bias towards higher masses for highly magnetic white dwarfs is expected if a fraction of these form when two degenerate cores merge in a common envelope. From the space density of single highly magnetic white dwarfs we estimate that about three times as many common envelope events lead to a merged core as to a cataclysmic variable.     

Gravitational collapse with standard and dark energy in the teleparallel equivalent of general relativity

A perfect fluid with self-similarity of the second kind is studied within the framework of the teleparallel equivalent of general relativity(TEGR).A spacetime which is not asymptotically flat is derived.The energy conditions of this spacetime are studied.It is shown that after some time the strong energy condition is not enough to satisfy showing a transition from standard matter to dark energy.The singularities of this solution are discussed.