Showing papers in "International Journal of Modern Physics D in 1994"
TL;DR: In this article, a cosmological model describing the evolution of n Einstein spaces (n>1) with m-component perfect-fluid matter is considered, and the Einstein and Wheeler-DeWitt equations are integrated in the cases: (i) m = 1, for all ; (ii) m>1, for some special sets of.
Abstract: A cosmological model describing the evolution of n Einstein spaces (n>1) with m- component perfect-fluid matter is considered. When all spaces are Ricci-flat and for any α-th component the pressures in all spaces are proportional to the density: , the Einstein and Wheeler-DeWitt equations are integrated in the cases: (i) m=1, for all ; (ii) m>1, for some special sets of . For m=1 the quantum wormhole solutions are also obtained.
69 citations
TL;DR: In this paper, it was shown that there is a unique Poincare invariant cubic vertex for free gauge vector fields which preserves the number of gauge symmetries to first order in the coupling constant.
Abstract: Recent results on the cohomological reformulation of the problem of consistent interactions between gauge fields are illustrated in the case of the Yang-Mills models. By evaluating the local BRST cohomology through descent equation techniques, it is shown (i) that there is a unique local, Poincare invariant cubic vertex for free gauge vector fields which preserves the number of gauge symmetries to first order in the coupling constant; and (ii) that consistency to second order in the coupling constant requires the structure constants appearing in the cubic vertex to fulfill the Jacobi identity. The known uniqueness of the Yang-Mills coupling is therefore rederived through cohomological arguments.
60 citations
TL;DR: In this article, a wave-like class of exact cosmological solutions of the apparently empty 5D Kaluza-Klein field equations are derived. But the authors only consider the case where the equation of state is p = γρ, where γ is an arbitrary constant.
Abstract: We derive a “wave-like” class of exact cosmological solutions of the apparently empty 5D Kaluza-Klein field equations. Here by “wave-like” we mean that the solutions look like plane waves propagating in the fifth dimension. In the interpretation that the fifth dimension in Kaluza-Klein theory may induce matter in four dimensions, we then calculate the effective energy density ρ and pressure p, and study in detail the case for which the equation of state is p=γρ (where γ is an arbitrary constant). We show that for both the matter-dominated (γ=0) and radiation-dominated (γ=1/3) eras of the universe, the 4D spacetime defined by hypersurfaces of the 5D metrics are just the same as those of the standard Friedmann-Robertson-Walker models of general relativity. However, in our models the big bang is like a shock wave propagating along the fifth dimension, and different observers can measure different ages for the universe. This property may be tested using the spread in ages of astrophysical objects such as globular clusters.
42 citations
TL;DR: In this article, a non-linear generalization of the theory of cylindrical measures on topological vector spaces is introduced, and a faithfull, diffeomorphism invariant measure is introduced on a suitable completion of.
Abstract: Integral calculus on the space of gauge equivalent connections is developed. By carring out a non-linear generalization of the theory of cylindrical measures on topological vector spaces, a faithfull, diffeomorphism invariant measure is introduced on a suitable completion of . The strip (i.e. momentum) operators are densely-defined in the resulting Hilbert space and interact with the measure correctly
39 citations
TL;DR: The moduli space of the Calabi-Yau three-folds, which play a role as superstring ground states, exhibits the same special geometry that is known from nonlinear sigma models in N = 2 supergravity theories.
Abstract: The moduli space of the Calabi-Yau three-folds, which play a role as superstring ground states, exhibits the same special geometry that is known from nonlinear sigma models in N=2 supergravity theories. We discuss the symmetry structure of special real, complex and quaternionic spaces. Maps between these spaces are implemented via dimensional reduction. We analyze the emergence of extra and hidden symmetries. This analysis is then applied to homogeneous special spaces and the implications for the classification of homogeneous quaternionic spaces are discussed.
37 citations
TL;DR: In this article, the super-Hamiltonian constraint assumes the form of the Dirac equation with an intrinsic time tied to the signature of the supermetric, and a perturbation scheme about an unusual background which is inaccessible to conventional variables is presented.
Abstract: Superspace parametrized by gauge potentials instead of metric three-geometries is discussed in the context of the Ashtekar variables. Gauge-fixing conditions which lead to the natural geometrical separation of physical from gauge modes are derived with the use of the supermetric in connection-superspace. A perturbation scheme about an unusual background which is inaccessible to conventional variables is presented. The resultant expansion retains much of the simplicity of Ashtekar’s formulation of General Relativity. Quantum mechanically, the super-Hamiltonian constraint assumes the form of the Dirac equation with an “intrinsic time” tied to the signature of the supermetric.
27 citations
TL;DR: In this paper, a two-level spin 1/2 atom interacting with laser fields in a gravitational background is considered. And a possible application to gravitational wave detection is outlined. But the application of spin-gravitation effects is not discussed.
Abstract: We give covariant equations for a two-level spin 1/2 atom interacting with laser fields in a gravitational background. Some gravitational effects of interest for atomic interferometry are derived, including spin-gravitation effects. A possible application to gravitational wave detection is outlined.
27 citations
TL;DR: In this article, the commutative algebra of functions on a manifold is extended to a non-commutative one by considering its tensor product with the algebra of n×n complex matrices.
Abstract: The commutative algebra of functions on a manifold is extended to a noncommutative algebra by considering its tensor product with the algebra of n×n complex matrices. Noncommutative geometry is used to formulate an extension of the Einstein-Hilbert action. The result is shown to be equivalent to the usual Kaluza-Klein theory with the manifold SUn as an internal space, in a truncated approximation.
24 citations
22 citations
TL;DR: In this paper, the canonical treatment and quantization of matter coupled supergravity in three dimensions, with special emphasis on N = 2 supergravity, is discussed, and the quantum constraint algebra is analyzed.
Abstract: We discuss the canonical treatment and quantization of matter coupled supergravity in three dimensions, with special emphasis on N = 2 supergravity. We then analyze the quantum constraint algebra; certain operator ordering ambiguities are found to be absent due to local supersymmetry. We show that the supersyinmetry constraints can be partially solved by a functional analog of the method of characteristics. We also consider extensions of Wilson loop integrals of the type previously found in ordinary gravity, but now with connections involving the bosonic and fermionic matter fields in addition to the gravitational connection. In a separate section of this paper, the canonical treatment and quantization of non-linear coset space sigma models are discussed in a self-contained way.
21 citations
TL;DR: In this paper, it was shown that when a Nother symmetry exists, it is always possible to integrate the Wheeler-DeWitt equation and recover the semiclassical regime for the wave function of the universe.
Abstract: We construct minisuperspace models for a class of theories of gravity nonminimally coupled with a scalar field. We show that when a Nother symmetry exists, it is always possible to integrate the Wheeler-DeWitt equation and recover the semiclassical regime for the wave function of the universe. In this sense, we can interpret the Nother symmetries as a selection rule in the philosophy of the so called Hartle criterion: when they exist, it is possible to select classical universes.
TL;DR: In this article, the authors introduce a theory for Yang-Mills phase space that is well defined for an arbitrary gauge group with an invariant bilinear form, it contains only first class constraints and has a simple form in terms of the phase space variables.
Abstract: We introduce a gauge and diffeomorphism invariant theory on the Yang-Mills phase space The theory is well defined for an arbitrary gauge group with an invariant bilinear form, it contains only first class constraints, and the spacetime metric has a simple form in terms of the phase space variables With gauge group SO(3, C), the theory equals the Ashtekar formulation of gravity with a cosmological constant For Lorentzian signature, the theory is complex, and we have not found any good reality conditions In the Euclidean signature case, everything is real In a weak field expansion around de Sitter spacetime, the theory is shown to give the conventional Yang-Mills theory to the lowest order in the fields We show that the coupling to a Higgs scalar is straightforward, while the naive spinor coupling does not work We have not found any way of including spinors that gives a closed constraint algebra For gauge group U(2), we find a static and spherically symmetric solution
TL;DR: In this paper, the gamma-ray bursters (GRBs) are examples of these naked singularity solutions, and according to solutions involving spherically symmetric collapse of pure radiation field, the energy Eγ and the observed duration Δt0 of a GRB should satisfy, being the fraction (10−2 to 10−3) of energy released as gamma rays and the rest possibly as gravitational waves.
Abstract: Naked singularities appear naturally in dynamically evolving solutions of Einstein equations involving gravitational collapse of radiation, dust, and perfect fluids provided the rate of accretion is less than a critical value. We propose that the gamma-ray bursters (GRBs) are examples of these naked singularity solutions. For illustration, we show that according to solutions involving spherically symmetric collapse of pure radiation field, the energy Eγ and the observed duration Δt0 of a GRB should satisfy, being the fraction (10−2 to 10−3) of energy released as gamma rays and the rest possibly as gravitational waves. All the presently observed GRBs satisfy this condition; those satisfying the condition close to equality must necessarily be of cosmological origin with the red-shift factor z not exceeding ~1−10 depending on exact observed flux, red-shift and conversion efficiency of gamma rays. If GRBs are indeed from naked singular regions, they should also be accompanied by a strong burst of gravitational waves which, if detectible, will constitute a basic test for our model.
TL;DR: In this article, the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) model is modified to include particle production processes and the influence of these processes on the dynamics of the early universe is investigated.
Abstract: The standard Friedmann-Lemaitre-Robertson-Walker (FLRW) model is modified to include particle production processes. The influence of these processes on the dynamics of the early Universe is investigated. We argue that a sufficiently high creation rate may give rise to an inflationary period. A stability analysis about this background yields growing energy density perturbations during the de Sitter stage.
TL;DR: In this article, the Schrodinger equation with higher-derivative terms in the Friedmann space-time ds2=dt2−e2α(t)dx2, where the M-space dx2 has curvature K, was shown to be classically stable if the spin-2 tachyon is also absent.
Abstract: Quantization of the D(=M+1)-dimensional gravitational theory with higher-derivative terms in the Friedmann space-time ds2=dt2−e2α(t)dx2, where the M-space dx2 has curvature K, yields the Schrodinger equation (Wheeler-DeWitt equation) i∂Ψ/∂t=[−AMe−Mα∂2/∂ξ2+VM,K(α, ξ)]Ψ, where ξ≡dα/dt, provided that differs from the Euler-number density. The coefficient AM is positive if there is no spin-0 tachyon in and the potential VM,K is positive semi-definite if M=3 and K=0. The theory is classically stable if the spin-2 tachyon is also absent. All of these conditions are satisfied by the heterotic superstring, after reduction to four dimensions, but not by the bosonic string, which contains a spin-2 tachyon, nor by the type-II superstring, which contains a spin-0 tachyon. After generalization to the anisotropic space-time ds2= dt2−e2β(t)dy2−e2γ(t)dz2, where dy2 and dz2 have dimensions one and two, respectively, the Schrodinger equation becomes i∂Ψ/∂t=[–(4B)−1e−(β+2γ) (X∂2/∂ζ2+Y∂2+ 2Z∂2/∂ζ∂η)+…+V(β, γ; ζ, η)]Ψ, where ζ≡dβ/dt, η≡dγ/dt. The potential V is unbounded both from above and from below for all β≠γ, for all three superstring theories, and in fact for all dimensionalities. This explains why the Universe is isotropic, and why dimensional reduction and compactification occur.
TL;DR: In this article, the authors consider topology changing spacetimes with domains of non-Lorentzian signature and show that these domains may be Riemannian or Kleinian (+ + − − −).
Abstract: Some recent ideas about topology and signature changing spacetimes are described. If spacetime is everywhere Lorentzian but non-orientable, one can sometimes avoid closed timelike curves, but one must must consider pinors rather than spinors. One finds that there is now an important distinction between signature (+ + + −) and (− − − +). In some cases one signature may be excluded and the other allowed. Topology changing spacetimes with domains of non-Lorentzian signature are considered. These domains may be Riemannian or Kleinian (+ + − −). It is argued that our present signature, together with the idea of time must have arisen as the consequence of physical processes. This emergence of the idea of time is also connected with the origin of the complex numbers in Quantum Mechanics which should also be regarded as the consequence of the evolution of the universe.
TL;DR: In this paper, a self-contained treatment of the linearization procedure for constrained Hamiltonian systems is first presented in a general setting, then applied to general relativity using triads and self-dual connections as the basic canonical variables.
Abstract: A self-contained treatment of the linearization procedure for constrained Hamiltonian systems is first presented in a general setting. The procedure is then applied to general relativity using triads and self-dual connections as the basic canonical variables. These results have paved the way to the quantization of weak gravitational waves in the connection and loop representations and to a study of the relation between these quanta and nonperturbative canonical gravity. In the classical theory, they suggest a new approach to the treatment of gravitational perturbations and may be useful also to the theory underlying weak gravity waves.
TL;DR: A comparison between the proposals made to measure Hawking-like effects and the Unruh effect in the laboratory is given at the level of their estimates.
Abstract: A comparison between the proposals made to measure Hawking-like effects and the Unruh effect in the laboratory is given at the level of their estimates. No satisfactory scheme exists as yet for their detection.
TL;DR: In this article, the influence of quantum effects on the properties of large-scale inhomogeneities of metric is analyzed and a model with short-distance fluctuations omitted is considered.
Abstract: The question on the influence of quantum effects on the properties of large-scale inhomogeneities of metric is analyzed. A model with short-distance fluctuations omitted is considered. An assumption of absence of short-scale perturbations allows one to solve the Wheeler-DeWitt equation exactly, for the case of asymptotical closeness to a singularity. Probability interpretation of the wave function is discussed. In the framework of the model it is possible to define the stationary states. It is found that the metric inhomogeneities are spatially delta-correlated in a stationary state. In contrast to the classical theory, the properties of inhomogeneities are essentially dependent upon the choice of initial conditions.
TL;DR: In this paper, the authors consider density perturbations of non-flat Robertson-Walker universes with a general imperfect fluid which can also be taken to represent a scalar field.
Abstract: Given that observations seem to favour a density parameter Ω0<1, corresponding to an open universe, we consider gauge-invariant perturbations of nonflat Robertson-Walker universes filled with a general imperfect fluid which can also be taken to represent a scalar field. Our aim is to set up the equations that govern the evolution of the density perturbations Δ so that it can be determined through a first order differential equation with a quantity which is conserved at any length scale, even in nonflat universe models, acting as a source term. The quantity generalizes other variables that are conserved in specific cases (for example at large scales in a flat universe) and is useful to connect different epochs in the evolution of density perturbations via a transfer function. We show that the problem of finding a conserved can be reduced to determining two auxiliary variables X and Y, and illustrate the method with two simple examples.
TL;DR: In this paper, the authors calculated the total masses and radii of neutron stars from the Tolman-Oppenheimer-Volkoff (TOV) equations and different equations of state for neutron-star matter.
Abstract: We have calculated total masses and radii of neutron stars from the Tolman-Oppenheimer-Volkoff (TOV) equations (for matter in equilibrium in gravitational fields) and different equations of state for neutron-star matter. The calculations are done for different input central densities. We have also obtained pressure and density as functions of distance from the centre of the star, and moments of inertia and surface gravitational redshifts as functions of the total mass of the star. The maximum mass Mmax is for all equations of state in our calculations given by 1.65M⊙
TL;DR: In this paper, it is shown that Dirac constraints can be solved exactly in the momentum representation, the path integral can be integrated out, and the constraint algebra can be explicitely canonically abelianized, thus allowing also for a reduced phase space quantization.
Abstract: It is shown that the models of 2D Liouville Gravity, 2D Black Hole- and R2-Gravity are embedded in the Katanaev-Volovich model of 2D NonEinsteinian Gravity. Different approaches to the formulation of a quantum theory for the above systems are then presented: The Dirac constraints can be solved exactly in the momentum representation, the path integral can be integrated out, and the constraint algebra can be explicitely canonically abelianized, thus allowing also for a (superficial) reduced phase space quantization. Non-trivial dynamics are obtained by means of time dependent gauges. All of these approaches lead to the same finite dimensional quantum mechanical system.
TL;DR: In this article, the authors survey recent attempts to understand the nature of these effects using idealized models, and present a survey of the most popular models for modeling the effects of nonspherical collapse to a black hole.
Abstract: Nonspherical collapse to a black hole leaves a wake of gravitational waves. Externally, this rapidly dies away. But it has a marked effect on the hole’s internal structure as it is blueshifted near the inner horizon. This article surveys recent attempts to understand the nature of these effects using idealized models.
TL;DR: In this paper, the problem of separation of variables for the Dirac square equation on a curved space-time in the presence of electromagnetic potential is considered, and it is shown that the necessary condition for the separation of the variables in this equation is the complete separation in the related Hamilton-Jacobi equation, i.e. the Riemann space should be Stackel.
Abstract: The problem of separation of variables for the Dirac square equation on a curved space-time in the presence of electromagnetic potential is considered. It is shown that the necessary condition for the separation of variables in the Dirac square equation is the complete separation of variables in the related Hamilton-Jacobi equation, i.e. the Riemann space should be Stackel. The constructive scheme for separation procedure is presented.
TL;DR: In this article, the authors generalized this analysis to the two-dimensional theory, which subsumes the spherical black holes formulated in D≥4 dimensions, when A = ½ (D - 2) (D- 3)ϕ2 (D − 4)/(D − 2), B = 2(D−3)/( D−2), C=1, and also the twodimensional black hole identified by Witten and by Gautam et al.
Abstract: Integration over the angular coordinates of the evaporating, four-dimensional Schwarzschild black hole leads to a two-dimensional action, for which the Wheeler-DeWitt equation has been found by Tomimatsu, on the apparent horizon, where the Vaidya metric is valid, using the Hamiltonian formalism of Hajicek. For the Einstein theory of gravity coupled to a massless scalar field ζ, the wave function Ψ obeys the Schrodinger equation , where M is the mass of the hole. The solution is , where k2 is the separation constant, and for k2>0 the hole evaporates at the rate Ṁ=−k2/4M2, in agreement with the result of Hawking. Here, this analysis is generalized to the two-dimensional theory , which subsumes the spherical black holes formulated in D≥4 dimensions, when A = ½ (D - 2) (D - 3)ϕ2 (D - 4)/(D - 2), B=2(D−3)/(D−2), C=1, and also the twodimensional black hole identified by Witten and by Gautam et al., when A=4/α′, B=2, C=1/8π, c=+8/α′ being (minus) the central charge. In all cases an analogous Schrodinger equation is obtained. The evaporation rate is when D≥4 and when D=2. Since Ψ evolves without violation of unitarity, there is no loss of information during the evaporation process, in accord with the principle of black-hole complementarity introduced by Susskind et al. Finally, comparison with the four-dimensional, cosmological Schrodinger equation, obtained by reduction of the ten-dimensional heterotic superstring theory including terms , shows in both cases that there is a positive semi-definite potential which evolves to zero, this corresponding to the ground state, which is Minkowski space.
TL;DR: The reduction of the dreibein formalism of 2+1 General Relativity to the dynamical degrees of freedom for a genus 2 and by extension for an arbitrary genus) two space is outlined.
Abstract: This paper outlines the reduction of the dreibein formalism of 2+1 General Relativity to the dynamical degrees of freedom for a genus 2 (and by extension for an arbitrary genus) two space. The resulting dynamical variables of the reduced theory are global holonomies and are constants of the motion of the original theory. The relation to geometry and closed timelike curves is briefly described.
TL;DR: In this article, computer algebra programs for automatically formulating and solving Killing equations and calculating the corresponding Lie algebra are described and examples are given, and examples of such programs are given.
Abstract: Computer algebra programs, and for automatically formulating and solving Killing equations and calculating the corresponding Lie algebra are described and examples are given.
TL;DR: In this article, it was shown that the two-particle spacetimes admit closed timelike curves provided the center-of-momentum energy exceeds a certain critical value.
Abstract: Multiparticle solutions for sources moving at the speed of light and corresponding to superpositions of single-particle plane-wave solutions are constructed in 2+1 gravity. It is shown that the two-particle spacetimes admit closed timelike curves provided the center-of-momentum energy exceeds a certain critical value. This occurs, however, at the cost of unphysical boundary conditions which are analogous to those affecting Gott’s time machine. As the energy exceeds the critical value, the closed timelike curves first occur at spatial infinity, then migrate inward as the energy is further increased. The total mass of the system also becomes imaginary for particle energies greater than the critical value.
TL;DR: In this paper, it was shown that the renormalised stress tensor is the difference of energy between the physical vacuum and that defined by local modes and local particles at any point in curved space time as those that most resemble Minkowsky modes at that point.
Abstract: Local modes and local particles are defined at any point in curved space time as those that most resemble Minkowsky modes at that point. It is shown that the renormalised stress tensor is the difference of energy between the physical vacuum and that defined by these local modes.
TL;DR: In this article, the authors analyze Lorentzian and Euclidean gravity in vacuum up to a constant conformal transformation and show that the reality conditions are invariant under a Wick rotation of the time, and that the compatibility of the algebra of commutators and constraints with the involution defined by reality conditions restricts the possible values of the conformal factor to be either real or purely imaginary.
Abstract: Using Ashtekar variables, we analyze Lorentzian and Euclidean gravity in vacuum up to a constant conformal transformation. Keeping unaltered the symplectic structure in the full theory of complex gravity, we prove that the reality conditions are invariant under a Wick rotation of the time, and show that the compatibility of the algebra of commutators and constraints with the involution defined by the reality conditions restricts the possible values of the conformal factor to be either real or purely imaginary. In the first case, one recovers real Lorentzian general relativity. For purely imaginary conformal factors, the classical theory can be interpreted as real Euclidean gravity. The reality conditions associated with this Euclidean theory demand the hermiticity of the Ashtekar connection, but the densitized triad is represented by an anti-Hermitian operator. We also demonstrate that the Euclidean and Lorentzian sets of reality conditions lead to inequivalent quantizations of full general relativity. This conclusion also holds in the geometrodynamic formulation. As a consequence, it seems impossible to obtain Lorentzian physical predictions from the quantum theory constructed with the Euclidean reality conditions.