Flat Spacetime Background Research Articles

COLLAPSING AND EXPANDING CYLINDRICALLY SYMMETRIC FIELDS WITH LIGHTLIKE WAVE-FRONTS IN GENERAL RELATIVITY

The dynamics of collapsing and expanding cylindrically symmetric gravitational and matter fields with lightlike wave-fronts is studied in General Relativity, using the Barrabés–Israel method. As an application of the general formulae developed, the collapse of a matter field that satisfies the condition RABgAB =0, (A,B = z, φ), in an otherwise flat spacetime background is studied. In particular, it is found that the gravitational collapse of a purely gravitational wave or a null dust fluid cannot be realized in a flat spacetime background. The studies are further specified to the collapse of purely gravitational waves and the general conditions for such collapse are found. It is shown that after the waves arrive at the axis, in general, part of them is reflected to spacelike infinity along the future light cone, and part of it is focused to form spacetime singularities on the symmetry axis. The cases where the collapse does not result in the formation of spacetime singularities are also identified.

Supersymmetric pair correlation function of Wilson loops

We give a path integral derivation of the annulus diagram in a supersymmetric theory of open and closed strings with Dbranes. We compute the pair correlation function of Wilson loops in the generic weakly coupled supersymmetric flat spacetime background with Dbranes. We obtain a -u^4/r^9 potential between heavy nonrelativistic sources in a supersymmetric gauge theory at short distances.

Matrix theory star products from the Born–Infeld action

We conjecture that the Sen-Seiberg limit of the Type IIA D2-brane action in a flat spacetime background can be resummed, at all orders in \alpha', to define an associative star product on the membrane. This star product can be independently constrained from the equivalent Matrix theory description of the corresponding M2-brane, by carefully analyzing the known BPS conditions. Higher derivative corrections to the Born-Infeld action on the IIA side are reinterpreted, after the Sen-Seiberg limit, as higher derivative corrections to a field theory on the membrane, which itself can be resummed to yield the known Matrix theory quantum mechanics action. Conversely, given the star product on the membrane as a formal power series in \alpha', one can constrain the higher derivative corrections to the Born-Infeld action, in the Sen-Seiberg limit. This claim is explicitly verified to first order. Finally, we also comment on the possible application of this method to the derivation of the Matrix theory action for membranes in a curved background.

Dynamics and integrability property of the chiral string model

The effect of fermionic string conductivity by purely right (or purely left) moving “zero modes” is shown to be governed by a simple Lagrangian characterizing a certain “chiral” (null current carrying) string model whose dynamical equations of motion turn out to be explicitly integrable in a flat spacetime background.

Gravity, gauge theories and geometric algebra

A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the positions and orientations of the matter fields. In this manner all properties of the background spacetime are removed from physics, and what remains are a set of `intrinsic' relations between physical fields. The properties of the gravitational gauge fields are derived from both classical and quantum viewpoints. Field equations are then derived from an action principle, and consistency with the minimal coupling procedure selects an action that is unique up to the possible inclusion of a cosmological constant. This in turn singles out a unique form of spin-torsion interaction. A new method for solving the field equations is outlined and applied to the case of a time-dependent, spherically-symmetric perfect fluid. A gauge is found which reduces the physics to a set of essentially Newtonian equations. These equations are then applied to the study of cosmology, and to the formation and properties of black holes. The existence of global solutions enables one to discuss the properties of field lines inside the horizon due to a point charge held outside it. The Dirac equation is studied in a black hole background and provides a quick derivation of the Hawking temperature.

Gravitational radiation and the photon rocket

The absence of gravitational radiation in Kinnersley's `photon rocket' solution of Einstein's equations is explained by the fact that in Kerr - Schild coordinates the pseudo-energy - momentum tensor vanishes everywhere. As a result the energy and momentum of the rocket and null fluid is conserved without any contribution to or from the gravitational field. A description is presented in terms of energy and momentum flow in a flat background spacetime.

CONFORMAL INVARIANCE, N-EXTENDED SUPERSYMMETRY AND MASSLESS SPINNING PARTICLES IN ANTI-DE SITTER SPACE

Starting with a manifestly conformal (O(d, 2) invariant) mechanics model in d space and two time dimensions, we derive the action for a massless spinning particle in d-dimensional anti-de Sitter space. The action obtained possesses both gauge N-extended worldline supersymmetry and local O(N) invariance. Thus we improve the old statement by Howe et al. that the spinning particle model with extended worldline supersymmetry admits only flat spacetime background for N>2 (spin greater one). The original (d+2)-dimensional model is characterized by rather unusual property that the corresponding supersymmetry transformations do not commute with the conformal ones, in spite of the explicit O(d, 2) invariance of the action.

Kleinian signature change

We study the propagation of plane-waves in a fixed flat background spacetime whose metric changes from a Lorentzian signature to a Kleinian signature . When the change of signature is discontinuous there is an apparent difference in wave behaviour depending upon whether the wave describes matter with integer or half-integer spin. A more detailed study of the Dirac equation shows that, while it is possible to decrease this disparity, the two matter classes still do not behave identically. A more consistent picture finally emerges when the same problem is attempted with a metric which changes signature continuously. This leads to the prediction of some surprising physical phenomena.

String model of the early Universe.

Using the scaling notion of a cosmic string network, we study the evolution of the early Universe, dominated by long strings in a flat background space-time. Defining a parameter r, the radiation fraction of the total energy density, the long strings, loops, and radiation energy densities are obtained in a self-consistent manner. The reconnection of loops into long strings is obtained in a manner consistent with Kibble's one scale hypothesis. It is found that the reconnection of loops to long strings plays an important role in the evolution of the Universe. The string tension or rather G\ensuremath{\mu} is obtained and is found to vary between ${10}^{\mathrm{\ensuremath{-}}2}$ and ${10}^{\mathrm{\ensuremath{-}}4}$ as the Universe evolves from matter domination to radiation domination. It is also found that the radiation fraction is finely tuned with the string tension.

Bimetric formulation of scalar-tensor theories of gravitation and conservation laws

The scalar-tensor theories are formulated against a flat background space-time. Expressions for various energy-momentum tensors of the gravitational field and relations between them are obtained. Integral conservation laws are examined and formulas for four-momentum and angular momentum tensor of the gravitational field together with the matrix are derived.

Gravitational field of a tachyon in a de Sitter universe

An exact solution of Einstein’s equations is interpreted as describing the gravitational field of a tachyon in a de Sitter universe. Switching off the cosmological constant yields the gravitational field of a tachyon in flat spacetime background.

Remarks on squeezed states of a harmonic oscillator in spatially flat Robertson-Walker space-time

We have investigated the time evolution of a non-relativistic harmonic oscillator in a spatially flat Robertson-Walker background space-time. It is found that the time evolution operator of the system is a product of a squeeze operator and a rotation operator, and thus the initial cohrent state evolves into a squeezed state at a later time. In other words, the time evolution of the non-relativistic oscillator in a spatially flat Robertson-Walker background spacetime is a «squeezing» process. The squeezing effect is induced by the continuous scale dilation in expanding space-time, and depends on the specific model for an expanding universe. For instance, there is no squeezing in the de Sitter model, whereas squeezing does occur in the spatially flat Friedmann model.

Supplement to "Some Aspects of Minimally Relativistic Newtonian Gravity"

Abstract This supplement to Z. Naturforsch. 46 a, 1026 (1991) provides additional material that should be combined with the contents of that paper. The combined content then provides a model of gravitation which is complete in essential details. Its main features are that it (i) predicts all the local GR tests accurately but (ii) does not exhibit Schwarzschild singularity, (iii) allows the wellknown Birkhoff's theorem to hold and (iv) has well defined conservation laws in virtue of the maximal group of motions admissible on the flat background spacetime

Absorption and emission of radiation by a sourceless abelian gauge wall in a robertson-walker space-time

A model of a sourceless Abelian «gauge wall» consisting of a singular magnetic field occupying the (y, z)-plane is examined in the context of a flat Robertson-Walker space-time background. Exact solutions are found for the gauge field structure function. The solutions may be static or time dependent. Dynamic solutions exist which describe the absorption and emission of gauge field radiation by the gauge wall.

Vilkovisky-DeWitt effective potential for higher-derivative gravity coupled to scalars.

Using a four-parameter family of gauges, the one-loop Vilkovisky-DeWitt effective potential for higher-derivative gravity coupled to scalars about a flat background spacetime is constructed. It is shown explicitly to be independent of the gauge parameters. The effective potential is then evaluated at finite temperature which is used to investigate the possibility of inducing Einstein gravity spontaneously. The critical temperature for this phase transition is also estimated. This phase transition, if it exists, will occur in the early Universe between the grand-unified-theory and the Planck scales, and may be a candidate for the primordial inflationary universe scenario.

Regular cylindrically symmetric Einstein-Maxwell metrics of Petrov type D

The authors analyse all presently known exact solutions of the vacuum Einstein and Einstein-Maxwell equations sharing the properties of being of Petrov type D, non-stationary, cylindrically symmetric, asymptotically flat and regular everywhere. All these solutions are particular subfamilies of a general one that describes the evolution of a single solitonic perturbation travelling on a flat spacetime background. They also investigate the relationship between these solitonic-type families and analytic extensions from stationary families. In particular they reobtain the Piran, Safier and Katz solution (1986) by performing an analytic extension from the massless Kerr-NUT spacetime.

The eta function in Chern-Simons field theory

We discuss a Schwinger expansion technique for computing the η-function of a first-order operator in the pure Chern-Simons quantum field theory. When evaluated at zero, the η-function of this operator gives essentially the one-loop correction to the partition function. We illustrate this technique by explicitly computing the one-loop two-point function in this theory on a flat spacetime background.

A BRST APPROACH TO MASSLESS GAUGE FIELDS OF HALF-INTEGER SPIN

We present a program based on BRST techniques for how to obtain the conventional equations for totally symmetric tensor-spinors which describe free massless particles of arbitrary half-integer spin. We do so in a wave function representation in a flat space-time background of any even dimension.

A BRST APPROACH TO MASSLESS GAUGE FIELDS OF INTEGER SPIN

We present a method based on BRST techniques for how to obtain the conventional equations for symmetric tensor gauge fields which describe free massless particles of arbitrary integer spin. We do so in a wave function representation in a flat space-time background of any dimension. A fairly straightforward way is also presented for how to obtain the equations from a gauge invariant Lagrangian of the form [Formula: see text].

Hermiticity and CPT in string theory

In the application of conformal field theory to string theory S-matrix elements are obtained from correlation functions of vertex operators. By studying the relation between the vertex operators for the incoming states and those for the outgoing states we obtain two results: First we show that hermiticity of the string vertices is equivalent to the CPT invariance of the corresponding conformal field theory. Secondly we prove that the S-matrix elements in any theory in flat space-time background are invariant under CPT.