Events and Observables in Generally Invariant Spacetime Theories

We address the problem of observables in generally invariant spacetime theories such as Einstein’s general relativity. Using the refined notion of an event as a “point-coincidence” between scalar fields that completely characterise a spacetime model, we propose a generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a four-dimensional manifold, that is naturally identified with the physical spacetime.     

Kinematics and dynamics off(R) theories of gravity

We generalise the equations governing relativistic fluid dynamics given by Ehlers and Ellis for general relativity, and by Maartens and Taylor for quadratic theories, to generalisedf(R) theories of gravity. In view of the usefulness of this alternative framework to general relativity, its generalisation can be of potential importance for deriving analogous results to those obtained in general relativity. We generalise, as an example, the results of Maartens and Taylor to show that within the framework of generalf(R) theories, a perfect fluid spacetime with vanishing vorticity, shear and acceleration is Friedmann-Lemaître-Robertson-Walker only if the fluid has in addition a barotropic equation of state. It then follows that the Ehlers-Geren-Sachs theorem and its almost extension also hold forf(R) theories of gravity.     

Regular spherical dust spacetimes

Physical (and weak) regularity conditions are used to determine and classify all the possible types of spherically symmetric dust spacetimes in general relativity. This work unifies and completes various earlier results. The junction conditions are described for general non-comoving (and non-null) surfaces, and the limits of kinematical quantities are given on all comoving surfaces where there is Darmois matching. We show that an inhomogeneous generalisation of the Kantowski-Sachs metric may be joined to the Lema?tre-Tolman-Bondi metric. All the possible spacetimes are explicitly divided into four groups according to topology, including a group in which the spatial sections have the topology of a 3-torus. The recollapse conjecture (for these spacetimes) follows naturally in this approach.     

Does a varying speed of light solve the cosmological problems?

We propose a new generalisation of general relativity which incorporates a variation in both the speed of light in vacuum (c) and the gravitational constant (G) and which is both covariant and Lorentz invariant. We solve the generalised Einstein equations for Friedmann universes and show that arbitrary time-variations of c and G never lead to a solution to the flatness, horizon or Λ problems for a theory satisfying the strong energy condition. In order to do so, one needs to construct a theory which does not reduce to the standard one for any choice of time, length and energy units. This can be achieved by breaking a number of invariance principles such as covariance and Lorentz invariance.     

The physical meaning of canonical quantization in terms of reference systems

The canonical approach to general relativity in terms of reference systems is discussed to show that Einstein's principles of equivalence and general relativity imply the physical insignificance of quantized general relativity. In particular it is demonstrated that even the (anholonomic) flat-space canonical formalism leads to physically uninterpretable results. This lack of quantum content of general relativity is reflected by Rosenfeld's uncertainty relations and can especially be removed by modifying general relativity in the spirit of classical Einstein-Cartan theory with teleparallelism.     

Coordinates, observables and symmetry in relativity

We investigate the interplay and connections between symmetry properties of equations, the interpretation of coordinates, the construction of observables, and the existence of physical relativity principles in spacetime theories. Using the refined notion of an event as a “point-coincidence” between scalar fields that completely characterise a spacetime model, we also propose a natural generalisation of the relational local observables that does not require the existence of four everywhere invertible scalar fields. The collection of all point-coincidences forms in generic situations a four-dimensional manifold, which is naturally identified with the physical spacetime.     

A non-covariant theory of gravitation,I

Homogeneous isotropic models of the universe, based on the general theory of relativity, lead to the existence of a preferred frame of reference, which is similar to the absolute space of, Newton, and a preferred time coordinate, which resembles the absolute time of Newton. These concepts seem to be in contradiction to the principle of covariance on which the general relativity theory is based. A theory of gravitation is therefore proposed which uses the world picture of general relativity but is not covariant. In the three crucial tests, the proposed theory gives the same results as the general relativity theory. However, in contrast to general relativity, the present theory predicts the emission of gravitational waves by spherically symmetric systems, and gravitational waves are found, in general, to have both transverse and longitudinal components.     

The General-Relativistic and Covariant Form of the First Helmholtz Vorticity Theorem

The general relativistic and covariant differential form of Helmholtz's first vorticity theorem is presented. We prove in relation with it an invariant kinematic identity which is the generalisation of the Helmholtz theorem for general continua.     

Fundamentals of the nonholonomically covariant formulation of the general theory of relativity

The physical foundations of the nonholonomic formulation of general relativity are determined, and the role of the Fock-Ivanenko coefficients in setting up and developing the tetrad formalism in general relativity is discussed. The physical and geometrical meaning of the nonholonomic transformations used in general relativity is determined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 55–60, December, 1974.     

Energy and Momentum Densities of Cosmological Models,with Equation of State <Emphasis Type="Italic">ρ</Emphasis>=<Emphasis Type="Italic">μ</Emphasis>, in General Relativity and Teleparallel Gravity

We calculated the energy and momentum densities of stiff fluid solutions, using Einstein, Bergmann–Thomson and Landau–Lifshitz energy-momentum complexes, in both general relativity and teleparallel gravity. In our analysis we get different results comparing the aforementioned complexes with each other when calculated in the same gravitational theory, either this is in general relativity and teleparallel gravity. However, interestingly enough, each complex’s value is the same either in general relativity or teleparallel gravity. Our results sustain that (i) general relativity or teleparallel gravity are equivalent theories (ii) different energy-momentum complexes do not provide the same energy and momentum densities neither in general relativity nor in teleparallel gravity. In the context of the theory of teleparallel gravity, the vector and axial-vector parts of the torsion are obtained. We show that the axial-vector torsion vanishes for the space-time under study.     

A golden age of general relativity? Some remarks on the history of general relativity

This article deals with the concepts “renaissance” and “low water mark between 1925 and 1955” of general relativity suggested in the literature. By empirical data, it is shown that no such period did exist. Research on general relativity continued continuously since the 1920s interrupted only by the second world war. On a broad scale, research on general relativity started only after 1945.     

Quantum Gauge General Relativity

Based on gauge principle, a new model on quantum gravity is proposed in the frame work of quantum gauge theory of gravity. The model has local gravitational gauge symmetry, and the field equation of the gravitational gauge field is just the famous Einstein‘s field equation. Because of this reason, this model is called quantum gauge general relativity, which is the consistent unification of quantum theory and general relativity. The model proposed in this paper is a perturbatively renormalizable quantum gravity, which is one of the most important advantage of the quantum gauge general relativity proposed in this paper. Another important advantage of the quantum gauge general relativity is that it can explain both classical tests of gravity and quantum effects of gravitational interactions, such as gravitational phase effects found in COW experiments and gravitational shielding effects found in Podkletnov experiments.     

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.     

Path integral measure in Regge calculus from the functional Fourier transform

The problem of fixing measure in the path integral for the Regge-discretised gravity is considered from the viewpoint of it is “best approximation” to the already known formal continuum general relativity (GR) measure. A rigorous formulation may consist in treating the measure as functional on the space of the metric functionals. We require coincidence of the measures for the discrete and continuous versions of the theory on some sufficiently large (dense) set of metric functionals which exist and admit exact definitions and calculation in the both versions. This set consists of generalisation of the usual finite-dimensional plane waves to the functional space so that the discrete measure follows by means of the functional Fourier transform. The possibility for such set to exist is due to the Regge manifold being a particular case of general Riemannian one (Regge calculus is a minisuperspace theory). Only a certain continuum measure among the local ones (the scale invariant Misner measure) is found to be reduciable in this way to the well defined Regge discretisation, and we find the two versions for the latter depending on what metric tensor, covariant or contravariant one, is taken as fundamental field variable. The closed expressions for the measure are obtained in the two simple cases of Regge manifold. These turn out to be quite reasonable one of them indicating to possibility of passing in backward direction when appropriately defined continuum limit of the Regge measure would reproduce the original continuum GR measure.     

Numerical modeling of black holes as sources of gravitational waves in a nutshell

These notes summarize basic concepts underlying numerical relativity and in particular the numerical modeling of black hole dynamics as a source of gravitational waves. Main topics are the 3+1 decomposition of general relativity, the concept of a well-posed initial value problem, the construction of initial data for general relativity, trapped surfaces and gravitational waves. Also, a brief summary is given of recent progress regarding the numerical evolution of black hole binary systems.     

Axisymmetric vacuum fields in general projective relativity

A method has been derived which enables one to obtain solutions to the stationary, axially symmetric vacuum fields in general projective relativity developed by Arcidiacono from known solutions of the vacuum field in Einstein's theory. The analogue of the Kerr solution in general projective relativity has been obtained as an example. Finally, a relation between the stationary and static axially symmetric vacuum fields in general projective relativity has been derived.     

Equations of the electromagnetic field in the chronometric-radial invariant formulation of the general theory of relativity

Chronometric-radial invariant (CRI) vectors of the electromagnetic field are introduced in the CRI formulation of the general theory of relativity proposed by Vladimirov. The general theory of relativity Maxwell equations for the electromagnetic field are transformed into equations for CRI quantities. It is postulated that the CRI components of vectors and tensors are the physically measurable quantities of the general theory of relativity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 110–115, February, 1992.The author is grateful to Yu. S. Vladimirov for useful discussions and interest in this work.     

Jordan-Fock type uncertainty relations and cut-off lengths in quantum general relativity

It is demonstrated that in quantized general relativity one is led to Jordan-Fock type uncertainty relations implying the occurrence of cut-off lengths. We argue that these lengths (i) represent limitations on the measurability of quantum effects of general relativity and (ii) provide a cut-off length of quantum divergences.     

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 space-time 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.     

On the precision of a length measurement

We show that quantum mechanics and general relativity imply the existence of a minimal length. To be more precise, we show that no operational device subject to quantum mechanics, general relativity and causality could exclude the discreteness of spacetime on lengths shorter than the Planck length. We then consider the fundamental limit coming from quantum mechanics, general relativity and causality on the precision of length measurement. PACS 04.20.-q; 03.65.-w