Magnetized cylindrically symmetric universe in general relativity

A magnetized cylindrically symmetric universe with two degrees of freedom in which the free gravitational field is Petrov type I degenerate, is obtained. The magnetic field is due to an electric current produced along the x-axis. The distribution consists of an electrically neutral perfect fluid with an infinite electrical conductivity. The behaviour of the model when magnetic field tends to zero and other physical aspects of the model are also discussed.     

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.     

Singular densities,test particles and generalized Hamiltonian systems in general relativity

We derive the motion equations and the structure equations of neutral and charged test particles, starting from the gravitational field equations. The method consists in the application of conservation laws to singular tensor densities, which represent regions of strong matter concentration. Moreover, a Hamiltonian formulation of the particle equations is given, in the form of implicit differential equations generated by Hamiltonian Morse families.     

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.     

Exact solutions for the massless plane symmetric scalar field in general relativity,with cosmological constant

The Klein–Gordon equations are solved for the case of a plane-symmetric static massless scalar field in general relativity with cosmological constant, generalizing the solutions found by Taub, Novotny and Horsky, and Singh. A separate class of solutions is obtained in which the metrics reduce to flat space in the limit that .The static solutions can be used to generate time-dependent cosmological solutions, one of which exhibits rapid inflation followed by continued exponential expansion at all later times.     

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.     

Geodesically equivalent metrics in general relativity

We discuss whether it is possible to reconstruct a metric from its nonparameterized geodesics, and how to do it effectively. We explain why this problem is interesting for general relativity. We show how to understand whether all curves from a sufficiently big family are nonparameterized geodesics of a certain affine connection, and how to reconstruct algorithmically a generic 4-dimensional metric from its nonparameterized geodesics. The algorithm works most effectively if the metric is Ricci-flat. We also prove that almost every metric does not allow nontrivial geodesic equivalence, and construct all pairs of 4-dimensional geodesically equivalent metrics of Lorentz signature.     

Why solve the Hamiltonian constraint in numerical relativity?

The indefinite sign of the Hamiltonian constraint means that solutions to Einstein's equations must achieve a delicate balance – often among numerically large terms that nearly cancel. If numerical errors cause a violation of the Hamiltonian constraint, the failure of the delicate balance could lead to qualitatively wrong behavior rather than just decreased accuracy. This issue is different from instabilities caused by constraint-violating modes. Examples of stable numerical simulations of collapsing cosmological spacetimes exhibiting local mixmaster dynamics with and without Hamiltonian constraint enforcement are presented.     

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.     

A new Hamiltonian structure for the dynamics of general relativity

A new compact form of the dynamical equations of relativity is proposed. The new form clarifies the covariance of the equations under coordinate transformations of the space-time. On a deeper level, we obtain new insight into the infinite-dimensional symplectic geometry behind the dynamical equations, the decompositions of gravitational perturbations, and the space of gravitational degrees of freedom. Prospects for these results in studying fields coupled to gravity and the quantization of gravity are outlined.This essay was awarded the second prize for 1976 by the Gravity Research Foundation.     

The string coupling accelerates the expansion of the universed

Generic cosmological models in non-critical string theory have a time-dependent dilaton background at a late epoch. The cosmological deceleration parameter q ₀ is given by the square of the string coupling, g _s ², up to a negative sign. Hence the expansion of the Universe must accelerate eventually, and the observed value of q ₀ corresponds to g _s ² ∼ 0.6. In this scenario, the string coupling is asymptotically free at large times, but its present rate of change is imperceptibly small. First Award in the 2005 Essay Competition of the Gravity Research Foundation. - Ed.     

Improved Hamiltonian for general relativity

A Hamiltonian formalism for asymptotically flat spaces in general relativity which is manifestly covariant under Poincaré transformations at infinity is proposed and some of its implications are briefly discussed.     

Non-local equations for general relativity

The field equations for two non-local variables, equivalent to the Einstein vacuum equations, are presented. These variables are the holonomy operator associated with special paths and the light cone cut function.

Starting from these equations, one shows via a perturbation argument that a single, fourth-order equation for the cut function can be derived. This single equation encodes the entire conformal structure of a vacuum space—time. The same perturbation technique yields, via quadratures, solutions to the vacuum Einstein equations to any order.     

Is Dark Energy an illusion?

Much evidence has accumulated that within the context of general relativistic Friedmann-Robertson-Walker (FRW) cosmology there must exist a new, and gravitationally repulsive, substance in the Universe. The effect of this new type of energy density on the expansion of the Universe is to cause its acceleration, and the name that is given to it is ‘Dark Energy’. To say whether or not Dark Energy really exists, however, requires a definite model for the Universe. That is, to be sure of the existence of Dark Energy, and the cosmological acceleration it causes, we must first be sure of the cosmological model we are using to interpret our observations. This is the subject of the present contribution, which will concentrate on the observational status of the Copernican Principle, which is at the heart of the FRW model. In particular, we will outline recent progress that has been made toward answering the question ‘can the observations usually requiring the existence of Dark Energy be accounted for without introducing any new and exotic types of energy density, if we are prepared to give up some of the assumptions of the standard cosmological model?’, or, alternatively, ‘is Dark Energy an illusion?’.     

The Mössbauer rotor experiment and the general theory of relativity

In the recent paper Yarman et al. (2015), the authors claim that our general relativistic analysis in Corda (2015), with the additional effect due to clock synchronization, cannot explain the extra energy shift in the Mössbauer rotor experiment. In their opinion, the extra energy shift due to the clock synchronization is of order 10⁻¹³ and cannot be detected by the detectors of γ$\gamma$-quanta which are completely insensitive to such a very low order of energy shifts. In addition, they claim to have shown that the extra energy shift can be explained in the framework of the so-called YARK gravitational theory. They indeed claim that such a theory should replace the general theory of relativity (GTR) as the correct theory of gravity.     

Bianchi cosmologies with anisotropic matter: Locally rotationally symmetric models

The dynamics of cosmological models with isotropic matter sources (perfect fluids) is extensively studied in the literature; in comparison, the dynamics of cosmological models with anisotropic matter sources is not. In this paper we consider spatially homogeneous locally rotationally symmetric solutions of the Einstein equations with a large class of anisotropic matter models including collisionless matter (Vlasov), elastic matter, and magnetic fields. The dynamics of models of Bianchi types I, II, and IX are completely described; the two most striking results are the following. (i) There exist matter models, compatible with the standard energy conditions, such that solutions of Bianchi type IX (closed cosmologies) need not necessarily recollapse; there is an open set of forever expanding solutions. (ii) Generic type IX solutions associated with a matter model like Vlasov matter exhibit oscillatory behavior toward the initial singularity. This behavior differs significantly from that of vacuum/perfect fluid cosmologies; hence “matter matters”. Finally, we indicate that our methods can probably be extended to treat a number of open problems—in particular, the dynamics of Bianchi type VIII and Kantowski-Sachs solutions.     

The nearly flat universe

We study here what it means for the Universe to be nearly flat, as opposed to exactly flat. We give three definitions of nearly flat, based on density, geometry and dynamics; all three definitions are equivalent and depend on a single constant flatness parameter ɛ that quantifies the notion of nearly flat. Observations can only place an upper limit on ɛ, and always allow the possibility that the Universe is infinite with k = −1 or finite with k = 1. We use current observational data to obtain a numerical upper limit on the flatness parameter and discuss its implications, in particular the “naturalness” of the nearly flat Universe.