Scalar hairy black holes and solitons in a gravitating Goldstone model

We study black hole solutions of Einstein gravity coupled to a specific global symmetry breaking Goldstone model described by an O(3) isovector scalar field in four spacetime dimensions. Our configurations are static and spherically symmetric, approaching at infinity a Minkowski spacetime background. A set of globally regular, particle-like solutions are found in the limit of vanishing event horizon radius. These configurations can be viewed as ‘regularised’ global monopoles, since their mass is finite and the spacetime geometry has no deficit angle. As an unusual feature, we notice the existence of extremal black holes in this model defined in terms of gravity and scalar fields only.     

Realisation of a Lorentz algebra in Lorentz violating theory

A Lorentz non-invariant higher derivative effective action in flat spacetime, characterised by a constant vector, can be made invariant under infinitesimal Lorentz transformations by restricting the allowed field configurations. These restricted fields are defined as functions of the background vector in such a way that background dependence of the dynamics of the physical system is no longer manifest. We show here that they also provide a field basis for the realisation of a Lorentz algebra and allow the construction of a Poincaré invariant symplectic two-form on the covariant phase space of the theory.     

The energy distribution for a spherically symmetric isolated system in general relativity

The problems of the tolal energy and quasilocalenergy density or an isolated spherically symmetric static system in general relativity (GR) are considered with examples of some exact suintions. The field formulation of GR dereloped earlier hy L. P. Grishchuk. el al. (1984). in ihe framework of which all the dynamical fields, including the gravitation field, are considered in a fixed background spacetime is used intensively. The exact Schwarzschild and Reissner Nordstrom solutions are investigated in detail, and the results are compared with those in the recent work by J. D. Brown and J. W. York. Jr. (1993) as well as discussed with respect to the principle of nonlocalization of the gravitational energy in GR. Those examples are illustrative and simple because the background is selected as Minkowski spacetime and, in fact, the field configurations are studied in the framework of special relativity. It is shown that some problems of the Schwarzschild solution which are difficult to resolve in the standard geometrical framework of GR are resolved in the framework of the field formulation.     

Magnetic Field Effects on Spacetime Around?a?Magnetized Spherical Star

We investigate the effects of magnetic field on the background spacetime of a spherically symmetric relativistic star. Using the general relativistic Maxwell equations coupled to the Einstein field equations for the gravitational field, it is shown that not only the backreaction of the spacetime modifies the magnetic field of the star, but also the magnetic field of the star molds the spacetime in its vicinity. The part played by the poloidal as well as the toroidal components of the magnetic field on the exterior spacetime are investigated.     

Conformally Flat Spacetimes and Weyl Frames

We discuss the concepts of Weyl and Riemann frames in the context of metric theories of gravity and state the fact that they are completely equivalent as far as geodesic motion is concerned. We apply this result to conformally flat spacetimes and show that a new picture arises when a Riemannian spacetime is taken by means of geometrical gauge transformations into a Minkowskian flat spacetime. We find out that in the Weyl frame gravity is described by a scalar field. We give some examples of how conformally flat spacetime configurations look when viewed from the standpoint of a Weyl frame. We show that in the non-relativistic and weak field regime the Weyl scalar field may be identified with the Newtonian gravitational potential. We suggest an equation for the scalar field by varying the Einstein-Hilbert action restricted to the class of conformally-flat spacetimes. We revisit Einstein and Fokker’s interpretation of Nordstr?m scalar gravity theory and draw an analogy between this approach and the Weyl gauge formalism. We briefly take a look at two-dimensional gravity as viewed in the Weyl frame and address the question of quantizing a conformally flat spacetime by going to the Weyl frame.     

Dynamically Generated Inertia

A (Higgs vacuum)–(spacetime geometry) reciprocity principle is proposed and its consequences are explored. While it has been established that configurations of the spacetime metric tensor field, associated with acceleration with respect to local inertial frames, cause the vacuum to become thermalized, it is asserted that the converse is also possible. An appropriate thermal vacuum, through dynamical mass generation, can cause particles to propagate in a spacetime with a Minkowski metric, as if they were in a spacetime with a non-Minkowski metric. The two points of view are equivalent and interchangeable. Invoking the reciprocity principle in the case of the Unruh effect in an accelerated frame, a mechanism is analyzed whereby in the context of the minimal standard model a gradient in the vacuum expectation value of the Higgs field in the direction of acceleration produces an effective inertial force on an accelerated material body.     

Spinning test particle in Kalb-Ramond background

In this work we explore the geodesic deviations of spinning test particles in a string inspired Einstein-Kalb-Ramond background. Such a background is known to be equivalent to a spacetime geometry with torsion. We have shown here that the antisymmetric Kalb-Ramond field has a significant effect on the geodesic deviation of a spinning test particle. A search for observational evidence of such an effect in astrophysical experiments may lead to a better understanding of the geometry of the background spacetime.Received: 5 April 2005, Revised: 19 May 2005, Published online: 8 July 2005     

Non-trivial field configurations in five-dimensional relativity

We note the possibility of the existence of “twisted” real scalar field configurations in certain Kaluza-Klein five-dimensional spacetime models, and propose, as a consequence of the requirement of classical field stability, that they must be considered in preference to the corresponding untwisted structure when modelling charge quantization in terms of the five- dimensional Klein - Gordon equation.     

The Conformal Metric Associated with the U(1) Gauge of the Stueckelberg–Schrödinger Equation

We review the relativistic classical and quantum mechanics of Stueckelberg, and introduce the compensation fields necessary for the gauge covariance of the Stueckelbert–Schrödinger equation. To achieve this, one must introduce a fifth, Lorentz scalar, compensation field, in addition to the four vector fields with compensate the action of the space-time derivatives. A generalized Lorentz force can be derived from the classical Hamilton equations associated with this evolution function. We show that the fifth (scalar) field can be eliminated through the introduction of a conformal metric on the spacetime manifold. The geodesic equation associated with this metric coincides with the Lorentz force, and is therefore dynamically equivalent. Since the generalized Maxwell equations for the five dimensional fields provide an equation relating the fifth field with the spacetime density of events, one can derive the spacetime event density associated with the Friedmann–Robertson–Walker solution of the Einstein equations. The resulting density, in the conformal coordinate space, is isotropic and homogeneous, decreasing as the square of the Robertson–Walker scale factor. Using the Einstein equations, one see that both for the static and matter dominated models, the conformal time slice in which the events which generate the world lines are contained becomes progressively thinner as the inverse square of the scale factor, establishing a simple correspondence between the configurations predicted by the underlying Friedmann–Robertson–Walker dynamical model and the configurations in the conformal coordinates.     

Cosmic string in the NUT-Kerr-Newman spacetime

We study the equilibrium configurations of a cosmic string described by the Nambu action in the NUT-Kerr-Newman spacetime which includes as special cases the Kerr-Newman black hole spacetime as well as the NUT spacetime which is considered as a cosmological model. In this study it is interesting to note that one can obtain parallel results for the Kerr-Newman black hole as well as the NUT spacetime.     

Axiomatic Quantum Field Theory in Curved Spacetime

The usual formulations of quantum field theory in Minkowski spacetime make crucial use of features—such as Poincaré invariance and the existence of a preferred vacuum state—that are very special to Minkowski spacetime. In order to generalize the formulation of quantum field theory to arbitrary globally hyperbolic curved spacetimes, it is essential that the theory be formulated in an entirely local and covariant manner, without assuming the presence of a preferred state. We propose a new framework for quantum field theory, in which the existence of an Operator Product Expansion (OPE) is elevated to a fundamental status, and, in essence, all of the properties of the quantum field theory are determined by its OPE. We provide general axioms for the OPE coefficients of a quantum field theory. These include a local and covariance assumption (implying that the quantum field theory is constructed in a local and covariant manner from the spacetime metric and other background structure, such as time and space orientations), a microlocal spectrum condition, an “associativity” condition, and the requirement that the coefficient of the identity in the OPE of the product of a field with its adjoint have positive scaling degree. We prove curved spacetime versions of the spin-statistics theorem and the PCT theorem. Some potentially significant further implications of our new viewpoint on quantum field theory are discussed.     

Quantum Restrictions on Measurement of Electromagnetic Field

The integration over field configurations is applied for finding quantum restrictions on measurability of electromagnetic field strength. The inequalities are derived demonstrating what precision is available for estimation, with the help of measurements, of the field strength in each point of a spacetime region. The comparison is made of the obtained results with those of the known papers by Landau and Peierls and Bohr and Rosenfeld.     

Vacuum charge and the eta function

The vacuum charge of a second quantized spinor field in a static classical background field on a static spacetime is studied. Wheng ₀₀=1 the vacuum charge is shown to be essentially the eta function of the spinor Hamiltonian ats=0. This is computed for compact and noncompact spaces and a boundary dependence is derived in the latter case.     

The Casimir effect of Reissner-NordstrSm black hole

The stress tensor of a massless scalar field satisfying a mixed boundary condition in a （1 ＋ 1）-dimensional Reissner- Nordstrom black hole background is calculated by using Wald＇s axiom. We find that Dirichlet stress tensor and Neumann stress tensor can be deduced by changing the coefficients of the stress tensor calculated under a mixed boundary condition. The stress tensors satisfying Dirichlet and Neumann boundary conditions are discussed. In addition, we also find that the stress tensor in conformal flat spacetime background differs from that in flat spacetime only by a constant.     

An elliptic complex associated to the Yang-Mills constraint equations

This paper presents an elliptic complex of linear spaces and operators which resolves the linearized constraint equations for the initial data for a Yang-Mills (gauge) field. The complex exists when the background gauge field satisfies a certain condition corresponding to self-duality in the Riemannian case and is defined on a spacetime which has a spacelike Cauchy surface.Partially Supported by NSF Grant MCS 78-01460     

A Model of the Electron in a 6-Dimensional Spacetime

The electron is considered as a massless point-particle which moves in a spacetime with (3+3) dimensions subjected to a field that attracts it towards the (3+1) standard spacetime. This field is assumed to be described by the radial time component of the e.m. 6-potential and to be due to the vacuum polarization arising when the charge of the electron is removed from the (3+1) spacetime. The pertinent Klein-Gordon equitation in 6 dimensions is solved and the right values for the electron magnetic moment and spin are derived. The rest mass of the electron, as it appears in the standard (3+1) spacetime, is obtained as an integration constant from the motion in the two extra time dimensions. The very simple form assumed as a first approximation for the attractive potential does not give quantized rest masses.     

Generally covariant quantization and the Dirac field

Canonical Hamiltonian field theory in curved spacetime is formulated in a manifestly covariant way. Second quantization is achieved invoking a correspondence principle between the Poisson bracket of classical fields and the commutator of the corresponding quantum operators. The Dirac theory is investigated and it is shown that, in contrast to the case of bosonic fields, in curved spacetime, the field momentum does not coincide with the generators of spacetime translations. The reason is traced back to the presence of second class constraints occurring in Dirac theory. Further, it is shown that the modification of the Dirac Lagrangian by a surface term leads to a momentum transfer between the Dirac field and the gravitational background field, resulting in a theory that is free of constraints, but not manifestly hermitian.     

Quantization Conditions in Curved Spacetime and Uncertainty-Driven Inflation

An alternative inflationary model is proposed predicated upon a considerationof the form of the uncertainty principle in a curved background spacetime. Anargument is presented suggesting a possible curvature dependence in the correctcommutator relations for a quantum field in a classical background which cannotbe deduced simply by extrapolation from the flat spacetime theory. To assess thepossible consequences of this dependence, we apply the idea to a scalar field ina closed Friedmann-Robertson-Walker background, using a simple model forthe curvature dependence (along the way, a previous erroneous result obtainedby Bunch for the adiabatically expanded wave function is corrected). The resultis a time-dependent cosmological constant, producing a vast amount of inflationthat is independent of either the mass of the matter field or its effectivepotential.Furthermore, it is seen that the field modes are initially zero for allwavelengthsand come into being as the universe evolves. In this sense, the universe createsits contents out of its own expansion. At the end of the process, the matterfieldis far from equilibrium and essentially reproduces the initial conditions forthe New Inflationary Model.