Showing papers on "Singularity published in 1999"
TL;DR: In this paper, a simple semiclassical method based on the method of complex paths was used to obtain particle production in Schwarzschild-like spacetimes with a horizon. But this method was not suitable for the case of a purely time-dependent gauge.
Abstract: This paper discusses particle production in Schwarzschild-like spacetimes and in a uniform electric field. Both problems are approached using the method of complex path analysis which is used to describe tunnelling processes in semiclassical quantum mechanics. Particle production in Schwarzschild-like spacetimes with a horizon is obtained here by a new and simple semiclassical method based on the method of complex paths. Hawking radiation is obtained in the $(t,r)$ coordinate system of the standard Schwarzschild metric without requiring the Kruskal extension. The coordinate singularity present at the horizon manifests itself as a singularity in the expression for the semiclassical propagator for a scalar field. We give a prescription whereby this singularity is regularized with Hawking's result being recovered. The equation satisfied by a scalar field is also reduced to solving a one-dimensional effective Schr\"odinger equation with a potential $(\ensuremath{-}{1/x}^{2})$ near the horizon. Constructing the action for a fictitious nonrelativistic particle moving in this potential and applying the above mentioned prescription, one again recovers Hawking radiation. In the case of the electric field, standard quantum field theoretic methods can be used to obtain particle production in a purely time-dependent gauge. In a purely space-dependent gauge, however, the tunnelling interpretation has to be resorted to in order to recover the previous result. We attempt, in this paper, to provide a tunnelling description using the formal method of complex paths for both the time and space dependent gauges. The usefulness of such a common description becomes evident when ``mixed'' gauges, which are functions of both space and time variables, are analyzed. We report, in this paper, certain mixed gauges which have the interesting property that mode functions in these gauges are found to be a combination of elementary functions unlike the standard modes which are transcendental parabolic cylinder functions. Finally, we present an attempt to interpret particle production by the electric field as a tunnelling process between the two sectors of the Rindler spacetime.
701 citations
TL;DR: In this article, the Coulomb Branch of = 4 super Yang-Mills theory is described in supergravity by multi-center solutions with D3-brane charge, and the low energy excitations of the system appear to be governed by an effective string theory which is related to the singularity in spacetime.
Abstract: At zero temperature the Coulomb Branch of = 4 super Yang-Mills theory is described in supergravity by multi-center solutions with D3-brane charge. At finite temperature and chemical potential the vacuum degeneracy is lifted, and minima of the free energy are shown to have a supergravity description as rotating black D3-branes. In the extreme limit these solutions single out preferred points on the moduli space that can be interpreted as simple distributions of branes - for instance, a uniformly charged planar disc. We exploit this geometrical representation to study the thermodynamics of rotating black D3-branes. The low energy excitations of the system appear to be governed by an effective string theory which is related to the singularity in spacetime.
306 citations
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TL;DR: In this article, the authors introduce complex singularity exponents of plurisubharmonic functions and prove a general semi-continuity result for them, based on a reduction to the algebraic case, taking into account more quantitative informations of great interest for complex analysis and complex differential geometry.
Abstract: We introduce complex singularity exponents of plurisubharmonic functions and prove a general semi-continuity result for them. This concept contains as a special case several similar concepts which have been considered e.g. by Arnold and Varchenko, mostly for the study of hypersurface singularities. The plurisubharmonic version is somehow based on a reduction to the algebraic case, but it also takes into account more quantitative informations of great interest for complex analysis and complex differential geometry. We give as an application a new derivation of criteria for the existence of K\"ahler-Einstein metrics on certain Fano orbifolds, following Nadel's original ideas (but with a drastic simplication in the technique, once the semi-continuity result is taken for granted). In this way, 3 new examples of rigid K\"ahler-Einstein Del Pezzo surfaces with quotient singularities are obtained.
300 citations
12 Mar 1999
TL;DR: In this article, the authors discuss a particular class of rational Gorenstein singularities, which they call symplectic, which are in one-to-one correspondence with simple complex Lie algebras.
Abstract: We discuss a particular class of rational Gorenstein singularities, which we call symplectic A normal variety V has symplectic singularities if its smooth part carries a closed symplectic 2-form whose pull-back in any resolution X --> V extends to a holomorphic 2-form on X Our main result is the classification of isolated symplectic singularities with smooth projective tangent cone They are in one-to-one correspondence with simple complex Lie algebras: to a Lie algebra g corresponds the singularity at 0 of the closure of the minimal (nonzero) nilpotent adjoint orbit in g
253 citations
TL;DR: In this article, a class of non-critical superstring vacua is shown to be holographically related to the non-gravitational superstring theory obtained by studying string theory on a singular Calabi-Yau manifold in the decoupling limit gs→0.
Abstract: We argue that a class of ``non-critical superstring'' vacua is holographically related to the (non-gravitational) theory obtained by studying string theory on a singular Calabi-Yau manifold in the decoupling limit gs→0. In two dimensions, adding fundamental strings at the singularity of the CY manifold leads to conformal field theories dual to a recently constructed class of AdS3 vacua. In four dimensions, special cases of the construction correspond to the theory on an NS5-brane wrapped around a Riemann surface.
223 citations
TL;DR: In this article, the authors presented a coordinate-invariant differential geometric analysis of kinematic singularities for closed chains containing both active and passive joints, and classified closed chain singularities into three basic types: (i) those corresponding to singular points of the joint configuration space, (ii) those induced by the choice of actuated joints (actuator singularities), and (iii) those configurations in which the end effector loses one or more degrees of freedom of available motion (end-effector singularities).
Abstract: This paper presents a coordinate-invariant differential geometric analysis of kinematic singularities for closed kinematic chains containing both active and passive joints. Using the geometric framework developed in Park and Kim (1996) for closed chain manipulability analysis, we classify closed chain singularities into three basic types: (i) those corresponding to singular points of the joint configuration space (configuration space singularities), (ii) those induced by the choice of actuated joints (actuator singularities), and (iii) those configurations in which the end-effector loses one or more degrees of freedom of available motion (end-effector singularities). The proposed geometric classification provides a high-level taxonomy for mechanism singularities that is independent of the choice of local coordinates used to describe the kinematics, and includes mechanisms that have more actuators than kinematic degrees of freedom.
222 citations
TL;DR: This paper describes a systematic approach to the enumeration of ‘non-crossing’ geometric congurations built on vertices of a convex n-gon in the plane that relies on generating functions, symbolic methods, singularity analysis, and singularity perturbation.
211 citations
200 citations
TL;DR: In this article, an approach to regularity and singularity of the obstacle problem is presented, by means of an epiperimetric inequality and a monotonicity formula, which leads to uniqueness of blow-up limits and regularity in that order.
Abstract: This paper contains a new approach to regularity and singularity of the obstacle problem: by means of an epiperimetric inequality and a monotonicity formula an energy decay estimate is derived. As a consequence, the increase in the solution’s homogeneity when passing to a smaller ball can be estimated. This leads to uniqueness of blow-up limits and regularity in that order.
171 citations
TL;DR: In this paper, a set of parallel 3-brane probes near a conifold singularity can be mapped onto a configuration of intersecting branes in type IIA string theory.
164 citations
TL;DR: In this paper, a general field theory of a scalar field coupled to gravity through a quadratic Gauss-Bonnet term was studied and it was shown that the singularity-free cosmological solutions are confined in a part of the phase space of the theory allowing the non-singular solutions to fill the rest of the space.
Abstract: We study a general field theory of a scalar field coupled to gravity through a quadratic Gauss-Bonnet term $\ensuremath{\xi}(\ensuremath{\varphi}{)R}_{\mathrm{GB}}^{2}.$ The coupling function has the form $\ensuremath{\xi}(\ensuremath{\varphi})={\ensuremath{\varphi}}^{n},$ where n is a positive integer. In the absence of the Gauss-Bonnet term, the cosmological solutions for an empty universe and a universe dominated by the energy-momentum tensor of a scalar field are always characterized by the occurrence of a true cosmological singularity. By employing analytical and numerical methods, we show that, in the presence of the quadratic Gauss-Bonnet term, for the dual case of even n, the set of solutions of the classical equations of motion in a curved FRW background includes singularity-free cosmological solutions. The singular solutions are shown to be confined in a part of the phase space of the theory allowing the non-singular solutions to fill the rest of the space. We conjecture that the same theory with a general coupling function that satisfies certain criteria may lead to non-singular cosmological solutions.
TL;DR: In this article, the moduli space of a D-brane at a point is studied, and it is shown that closed string moduli do not fully resolve the singularity, but the resulting space contains n-1 conifold singularities.
Abstract: We derive D-brane gauge theories for C^3/Z_n x Z_n orbifolds with discrete torsion and study the moduli space of a D-brane at a point. We show that, as suggested in previous work, closed string moduli do not fully resolve the singularity, but the resulting space -- containing n-1 conifold singularities -- is somewhat surprising. Fractional branes also have unusual properties.
We also define an index which is the CFT analog of the intersection form in geometric compactification, and use this to show that the elementary D6-brane wrapped about T^6/Z_n x Z_n must have U(n) world-volume gauge symmetry.
TL;DR: In this article, two singularities inherent to the operator are demonstrated: the k-singularity, related to the phase shift between the exact and the numerical waves, and the λ -singularity corresponding to the singularity at the eigenfrequencies.
TL;DR: In this paper, the authors study the three-dimensional Edwards-Anderson model with binary interactions by Monte Carlo simulations, and show that the infinite volume data are consistent with a conventional power law singularity at finite temperature Tc.
Abstract: We study the three-dimensional Edwards-Anderson model with binary interactions by Monte Carlo simulations. Direct evidence of finite-size scaling is provided, and the universal finite-size scaling functions are determined. Monte Carlo data are extrapolated to infinite volume with an iterative procedure up to correlation lengths xi \approx 140. The infinite volume data are consistent with a conventional power law singularity at finite temperature Tc. Taking into account corrections to scaling, we find Tc = 1.156 +/- 0.015, nu = 1.8 +/- 0.2 and eta = -0.26 +/- 0.04. The data are also consistent with an exponential singularity at finite Tc, but not with an exponential singularity at zero temperature.
TL;DR: In this paper, the authors focus on the integration of a system that is known to be closely related to so-called linear complementary problem (LCP) and show that the eventual divergence of the contact forces does not call into question the wellposedness of the model.
Abstract: In this note, we deal with the dynamics of a mechanical system subject to unilateral constraints. In particular, we shall focus on the integration of such a system that is known to be closely related to so-called linear complementary problem (LCP). Except a in very simple case like codimension 1, frictionless constraints, the problem of well-posedness (existence and uniqueness of solution) to such hybrid dynamic systems (smooth dynamics + LCP + shock dynamics) is a big challenge. We concentrate on the well-known Painleve example the dynamics of which in a sliding regime may be singular, depending on the friction coefficient. A new critical friction coefficient is presented below, the contact forces of which remain bounded. Moreover, a detailed analysis of the vector field near the singularity shows that the eventual divergence of the contact forces does not call into question the well-posedness of the model.
TL;DR: Theorem 3.2 as discussed by the authors shows that any Qp-cohomology class on the link of the singularity extends to the resolution, more precisely, the resolution of singularities.
Abstract: In this paper we prove four theorems: one on surface singularities, two on Fcrystals, and one on moduli of p-divisible groups. The reason we put together these results in one paper is that the proofs, as given here, show how these theorems are related. Let us first describe our results. Let (S, 0) be a normal surface singularity over an algebraically closed field of characteristic p. Let S S be a resolution of singularities. Our first result is Theorem 3.2: (1) Any Qp-cohomology class on the link of the singularity extends to the resolution, more precisely
TL;DR: In this paper, the correlation-consistent basis set convergence of the electric dipole moments of BH and HF is examined by comparison with results obtained with explicitly correlated wave function models.
Abstract: The electric dipole moments (μ) of BH and HF are computed in conventional calculations employing different correlation-consistent basis sets at the levels of Hartree–Fock theory, second-order perturbation theory, and coupled cluster theory with single and double excitations, and single and double excitations with a perturbative triples correction. The basis-set convergence of μ is examined by comparison with results obtained with explicitly correlated wave function models. Inclusion of diffuse functions in the basis set is essential for accurate calculations of μ. They speed up the convergence at the Hartree–Fock level significantly and make the convergence at the correlated levels systematic. Once the outer valence regions important for μ are described accurately via the diffuse functions, the convergence at the correlated levels is governed by the interelectronic Coulomb singularity. For the aug-cc-pVXZ basis sets, the correlation contribution to μ follows μXcorr=μlimcorr+aX−3, which is similar to the f...
TL;DR: The method developed extends the range of applicability of singularity analysis techniques to combinatorial sums involving transcendental elements like logarithms or fractional powers.
TL;DR: In this article, the authors studied the well posedness of initial value problems for test scalar fields with finite energy so that the natural function space of initial data is the Sobolev space.
Abstract: To probe naked spacetime singularities with waves rather than with particles we study the well posedness of initial value problems for test scalar fields with finite energy so that the natural function space of initial data is the Sobolev space. In the case of static and conformally static spacetimes we examine the essential self-adjointness of the time translation operator in the wave equation defined in the Hilbert space. For some spacetimes the classical singularity becomes regular if probed with waves while stronger classical singularities remain singular. If the spacetime is regular when probed with waves we may say that the spacetime is ``globally hyperbolic.''
TL;DR: In this article, an extended local Born Fourier migration method was proposed that circumvents the singularity problem of the local Born solution and makes it possible to choose the average slowness as a reference SLOWess.
Abstract: A migration approach based on a local application of the Born approximation within each extrapolation interval contains a singularity that can make direct application unstable. Previous authors have suggested adding an imaginary part to the vertical wavenumber to eliminate the singularity. However, their method requires that the reference slowness must be the maximum slowness of a given layer; consequently, the slowness perturbations are larger than those when the average slowness is selected as a reference slowness. Therefore, its applicability is limited. We develop an extended local Born Fourier migration method that circumvents the singularity problem of the local Born solution and makes it possible to choose the average slowness as a reference slowness. It is computationally efficient because of the use of a fast Fourier transform algorithm. It can handle wider angles (or steeper interfaces) and scattering effects of heterogeneities more accurately than the split‐step Fourier (SSF) method, which acco...
TL;DR: In this article, it was shown that all two degree of freedom quantum integrable systems with a focus-focus singularity have the same non-trivial quantum monodromy.
Abstract: Let P1(h),...,Pn(h) be a set of commuting self-adjoint h-pseudo-differential operators on an n-dimensional manifold. If the joint principal symbol p is proper, it is known from the work of Colin de Verdiere [6] and Charbonnel [3] that in a neighbourhood of any regular value of p, the joint spectrum locally has the structure of an affine integral lattice. This leads to the construction of a natural invariant of the spectrum, called the quantum monodromy. We present this construction here, and show that this invariant is given by the classical monodromy of the underlying Liouville integrable system, as introduced by Duistermaat [9]. The most striking application of this result is that all two degree of freedom quantum integrable systems with a focus-focus singularity have the same non-trivial quantum monodromy. For instance, this proves a conjecture of Cushman and Duistermaat [7] concerning the quantum spherical pendulum.
TL;DR: In this article, a consistent asymptotic solution to the problem posed by Moore is presented, which includes the shape of the vortex sheet as the curvature singularity forms, and for a wide class of initial conditions (including perturbations of finite amplitude), the 3/2-power singularities can spontaneously form at t = 0+ in the complex plane.
Abstract: Moore (1979) demonstrated that the cumulative influence of small nonlinear effects on the evolution of a slightly perturbed vortex sheet is such that a curvature singularity can develop at a large, but finite, time. By means of an analytical continuation of the problem into the complex spatial plane, we find a consistent asymptotic solution to the problem posed by Moore. Our solution includes the shape of the vortex sheet as the curvature singularity forms. Analytic results are confirmed by comparison with numerical solutions. Further, for a wide class of initial conditions (including perturbations of finite amplitude), we demonstrate that 3/2-power singularities can spontaneously form at t=0+ in the complex plane. We show that these singularities propagate around the complex plane. If two singularities collide on the real axis, then a point of infinite curvature develops on the vortex sheet. For such an occurrence we give an asymptotic description of the vortex-sheet shape at times close to singularity formation.
TL;DR: In this paper, a solution of the equations of motion of five-dimensional gauged type IIB supergravity was discussed, which describes confining SU(N) gauge theories at large N and large 't Hooft parameter.
Abstract: We discuss a solution of the equations of motion of five-dimensional gauged type IIB supergravity that describes confining SU(N) gauge theories at large N and large 't Hooft parameter. We prove confinement by computing the Wilson loop, and we show that our solution is generic, independent of most of the details of the theory. In particular, the Einstein-frame metric near its singularity, and the condensates of scalar, composite operators are universal. Also universal is the discreteness of the glueball mass spectrum and the existence of a mass gap. The metric is also identical to a generically confining solution recently found in type 0B theory.
TL;DR: In this paper, the conformal Einstein equations for polytropic perfect fluid cosmologies admit an isotropic singularity, and it is shown that the Cauchy problem for these equations is wellposed, that solutions exist, are unique, and depend smoothly on the data, with data consisting of simply the 3metric of the singularity.
TL;DR: The extreme Schwarzschild-de Sitter space-time is a spherically symmetric solution of Einstein's equations with a cosmological constant Lambda and mass parameter m > 0 which is characterized by the condition that 9Λm2 = 1 as discussed by the authors.
Abstract: The extreme Schwarzschild-de Sitter space-timeis a spherically symmetric solution of Einstein'sequations with a cosmological constant Lambda and massparameter m > 0 which is characterized by thecondition that 9Λm2 = 1. The globalstructure of this space-time is here analyzed in detail.Conformal and embedding diagrams are constructed, andsynchronous coordinates which are suitable for a discussion of the cosmic no-hair conjecture arepresented. The permitted geodesic motions are alsoanalyzed. By a careful investigation of the geodesicsand the equations of geodesic deviation, it is shown that specific families of observers escape fromfalling into the singularity and approach nonsingularasymptotic regions which are represented by special“points” in the complete conformal diagram.The redshift of signals emitted by particles whichfall into the singularity, as detected by those observers which escape, is also calculated.
TL;DR: McVittie's solution of Einstein's field equations, representing a point mass embedded in an isotropic universe, possesses a scalar curvature singularity at proper radius R = 2m as discussed by the authors.
Abstract: McVittie's solution of Einstein's field equations, representing a point mass embedded in an isotropic universe, possesses a scalar curvature singularity at proper radius R = 2m. The singularity is spacelike and precedes, in the expanding case, all other events in the spacetime. It is shown here that this singularity is gravitationally weak, and the possible structure of the region R2m is investigated. A characterization of this solution which does not involve asymptotics is given.
TL;DR: In this paper, the pairing singularity has been incorporated into the effective field theory framework for low-density fermionic matter, and the BCS theory of pairing is amenable to this approach.
Abstract: In the theory of fermionic matter, the expansion about the low-density limit has been invaluable for understanding the structure of the theory and the role of the interaction. At low densities, the interaction needs only be characterized by its scattering length to get expansions for the energy density, excitation spectrum, etc. @1#. However, to our knowledge the pairing singularity has never been incorporated into this framework. We have for example only the qualitative statement in Ref. @1# that the pairing singularity is logarithmic and unimportant for integrated quantities. A more quantitative statement is needed to have complete understanding of low-density fermionic matter. Another motivation for our study is the general reexamination of nuclear physics with effective field theory which is now taking place @2‐9#. In the effective field theory approach, the interaction is systematically expanded in a power series in momentum with the object of getting relationships between observables such that the details of the shortdistance interaction need not be parameterized. We shall show here that the BCS theory of pairing is amenable to this approach, and the low-energy theory gives finite and analytic results. Within effective field theory many results can be obtained analytically opposed to the numerical treatment of potential models. In this sense our approach complements the large body of literature of pairing in nuclear and neutron matter that is based on potential models @10‐16#. We consider a Fermi gas with two-fold degeneracy interacting with a short-range attractive interaction. Examples are neutron matter or gaseous 3 He. The Hamiltonian is idealized to be of the form
TL;DR: In this article, supersymmetry preserving conditions for infinite M5-branes intersecting on a (3+1)-dimensional space are given. But these conditions are completely localized and cannot be generalized to D3-brane intersections.
Abstract: We write supersymmetry preserving conditions for infinite M5-branes intersecting on a (3+1)-dimensional space. In contrast to previously known solutions, these intersections are completely localized. We solve the equations for a particular class of configurations which in the near-horizon decoupling limit are dual to Nf = 2Nc Seiberg-Witten superconformal field theories with gauge group SU(N) and generalisations to SU(N)n. We also discuss the relationship to D3-branes in the presence of an Ak singularity.
TL;DR: In this paper, supersymmetry preserving conditions for infinite M5-branes intersecting on a (3+1)-dimensional space are given. But these conditions are completely localized and are not applicable to D3-brane intersections.
Abstract: We write supersymmetry preserving conditions for infinite M5-branes intersecting on a (3+1)-dimensional space. In contrast to previously known solutions, these intersections are completely localized. We solve the equations for a particular class of configurations which in the near-horizon decoupling limit are dual to N_f = 2N_c Seiberg-Witten superconformal field theories with gauge group SU(N) and generalisations to SU(N)^n. We also discuss the relationship to D3-branes in the presence of an A_k singularity.
TL;DR: In this article, the extended Clenshaw-Curtis method for finite Fourier integrals is discussed, and a number of timed comparisons are made between the various implementations which appear in the literature.