Showing papers on "Singularity published in 2012"
TL;DR: This work presents the most general covariant ghost-free gravitational action in a Minkowski vacuum and includes a large class of nonlocal actions with improved UV behavior, which nevertheless recover Einstein's general relativity in the IR.
Abstract: We present the most general covariant ghost-free gravitational action in a Minkowski vacuum. Apart from the much studied f(R) models, this includes a large class of non-local actions with improved UV behavior, which nevertheless recover Einstein's general relativity in the IR.
720 citations
TL;DR: In this article, an extension of the Stelle higher derivative gravity involving an infinite number of derivative terms was studied at both the classical and quantum level, and the theory was shown to be ghost-free, since the introduction of two entire functions in the model with the property does not introduce new poles in the propagator.
Abstract: In this paper we study perturbatively an extension of the Stelle higher derivative gravity involving an infinite number of derivative terms. We know that the usual quadratic action is renormalizable but suffers from the unitarity problem because of the presence of a ghost (state of negative norm) in the theory. In this paper, we reconsider the theory first introduced by Tomboulis in 1997, but we expand and extensively study it at both the classical and quantum level. This theory is ghost-free, since the introduction of (in general) two entire functions in the model with the property does not introduce new poles in the propagator. The local high derivative theory is recovered expanding the entire functions to the lowest order in the mass scale of the theory. Any truncation of the entire functions gives rise to the unitarity violation, but if we keep all the infinite series, we do not fall into these troubles. The theory is renormalizable at one loop and finite from two loops on. Since only one-loop Feynman diagrams are divergent, then the theory is super-renormalizable. We analyze the fractal properties of the theory at high energy showing a reduction of the spacetime dimension at short scales. Black hole spherical symmetric solutions are also studied omitting the high curvature corrections in the equation of motions. The solutions are regular and the classical singularity is replaced by a ``de Sitter-like core'' in $r=0$. Black holes may show a ``multihorizon'' structure depending on the value of the mass. We conclude the paper with a generalization of the Tomboulis theory to a multidimensional spacetime.
556 citations
TL;DR: In this article, it was shown that spheres, cylinders, and planes are the only stable self-shrinkers under the mean curvature of R 3, and that every singularity other than spheres and cylinders can be perturbed away.
Abstract: It has long been conjectured that starting at a generic smooth closed embedded surface in R 3 , the mean curvature ow remains smooth until it arrives at a singularity in a neighborhood of which the ow looks like concentric spheres or cylinders. That is, the only singularities of a generic ow are spherical or cylindrical. We will address this conjecture here and in a sequel. The higher dimensional case will be addressed elsewhere. The key to showing this conjecture is to show that shrinking spheres, cylinders, and planes are the only stable self-shrinkers under the mean curvature ow. We prove this here in all dimensions. An easy consequence of this is that every singularity other than spheres and cylinders can be perturbed away.
449 citations
TL;DR: Recently, an explicit, recursive formula for the all-loop integrand of planar scattering amplitudes in planar SYM has been described, generalizing the BCFW formula for tree amplitudes, and making manifest the Yangian symmetry as discussed by the authors.
Abstract: Recently, an explicit, recursive formula for the all-loop integrand of planar scattering amplitudes in $ \mathcal{N} = {4} $
SYM has been described, generalizing the BCFW formula for tree amplitudes, and making manifest the Yangian symmetry of the theory. This has made it possible to easily study the structure of multi-loop amplitudes in the theory. In this paper we describe a remarkable fact revealed by these investigations: the integrand can be expressed in an amazingly simple and manifestly local form when represented in momentum-twistor space using a set of chiral integrals with unit leading singularities. As examples, we present very-concise expressions for all 2- and 3-loop MHV integrands, as well as all 2-loop NMHV integrands. We also describe a natural set of manifestly IR-finite integrals that can be used to express IR-safe objects such as the ratio function. Along the way we give a pedagogical introduction to the foundations of the subject. The new local forms of the integrand are closely connected to leading singularities — matching only a small subset of all leading singularities remarkably suffices to determine the full integrand. These results strongly suggest the existence of a theory for the integrand directly yielding these local expressions, allowing for a more direct understanding of the emergence of local spacetime physics.
418 citations
TL;DR: In this article, the Luttinger liquid theory has been used for the description of one-dimensional (1D) quantum fluids beyond the low-energy limit, where the nonlinearity of the dispersion relation becomes essential.
Abstract: For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the particles constituting the fluid. Recent progress in understanding 1D quantum fluids beyond the low-energy limit is reviewed, where the nonlinearity of the dispersion relation becomes essential. The novel methods which have been developed to tackle such systems combine phenomenology built on the ideas of the Fermi-edge singularity and the Fermi-liquid theory, perturbation theory in the interaction strength, and new ways of treating finite-size properties of integrable models. These methods can be applied to a wide variety of 1D fluids, from 1D spin liquids to electrons in quantum wires to cold atoms confined by 1D traps. Existing results for various dynamic correlation functions are reviewed, in particular, the dynamic structure factor and the spectral function. Moreover, it is shown how a dispersion nonlinearity leads to finite particle lifetimes and its impact on the transport properties of 1D systems at finite temperatures is discussed. The conventional Luttinger liquid theory is a special limit of the new theory, and the relation between the two is explained.
381 citations
TL;DR: In this paper, a comprehensive definition of relaxors is proposed: relaxors are defined as ferroelectrics in which the maximum in the temperature dependence of static susceptibility occurs within the temperature range of dielectric relaxation, but does not coincide with the temperature of singularity of relaxation time or soft mode frequency.
Abstract: In this review the dielectric properties of relaxor ferroelectrics are discussed and compared with the properties of normal dielectrics and ferroelectrics. We try to draw a general picture of dielectric relaxation starting from a textbook review of the underlying concepts and pay attention to common behavior of relaxors rather than to the features observed in specific materials. We hope that this general approach is beneficial to those physicists, chemists, material scientists and device engineers who deal with relaxors. Based on the analysis of dielectric properties, a comprehensive definition of relaxors is proposed: relaxors are defined as ferroelectrics in which the maximum in the temperature dependence of static susceptibility occurs within the temperature range of dielectric relaxation, but does not coincide with the temperature of singularity of relaxation time or soft mode frequency.
266 citations
TL;DR: The overall approach proposed in the present work is able to provide the proper accuracy to support experimental investigations even for large molecular systems of biotechnological interest in a fully automated manner, without any ad hoc scaling procedure.
Abstract: A general second-order perturbative approach based on resonance- and threshold-free computations of vibrational properties is introduced and validated. It starts from the evaluation of accurate anharmonic zero-point vibrational energies for semirigid molecular systems, in a way that avoids any singularity. Next, the degeneracy corrected second-order perturbation theory (DCPT2) is extended to a hybrid version (HDCPT2), allowing for reliable computations even in cases where the original formulation faces against severe problems, including also an automatic treatment of internal rotations through the hindered-rotor model. These approaches, in conjunction with the so-called simple perturbation theory (SPT) reformulated to treat consistently both energy minima and transition states, allow one to evaluate degeneracy-corrected partition functions further used to obtain vibrational contributions to properties like enthalpy, entropy, or specific heat. The spectroscopic accuracy of the HDCPT2 model has been also va...
238 citations
TL;DR: In this paper, the authors introduced new recursion relations to compute correlation functions of the stress-tensor or a conserved current at tree-level, which can be used in all dimensions including $d = 3.
Abstract: We consider correlation functions of the stress-tensor or a conserved current in ${\mathrm{AdS}}_{d+1}/{\mathrm{CFT}}_{d}$ computed using the Hilbert or the Yang-Mills action in the bulk. We introduce new recursion relations to compute these correlators at tree-level. These relations have an advantage over the Britto-Cachazo-Feng-Witten (BCFW)-like relations described in arXiv:1102.4724 and arXiv:1011.0780 because they can be used in all dimensions including $d=3$. We also introduce a new method of extracting flat-space $S$-matrix elements from AdS/CFT correlators in momentum space. We show that the ($d+1$)-dimensional flat-space amplitude of gravitons or gluons can be obtained as the coefficient of a particular singularity of the $d$-dimensional correlator of the stress-tensor or a conserved current; this technique is valid even at loop-level in the bulk. Finally, we show that our recursion relations automatically generate correlators that are consistent with this observation: they have the expected singularity and the flat-space gluon, or graviton amplitude appears as its coefficient.
200 citations
TL;DR: In this paper, stable finite time blow up regimes for the energy critical co-rotational Wave Map with the S 2 target in all homotopy classes and for the critical equivariant SO(4) Yang-Mills problem were derived.
Abstract: We exhibit stable finite time blow up regimes for the energy critical co-rotational Wave Map with the S
2 target in all homotopy classes and for the critical equivariant SO(4) Yang-Mills problem. We derive sharp asymptotics on the dynamics at blow up time and prove quantization of the energy focused at the singularity.
197 citations
TL;DR: In this article, the authors prove well-posedness for the three-dimensional compressible Euler equations with moving physical vacuum boundary, with an equation of state given by p(ρ) = Cγργ for γ > 1.
Abstract: We prove well-posedness for the three-dimensional compressible Euler equations with moving physical vacuum boundary, with an equation of state given by p(ρ) = Cγργ for γ > 1. The physical vacuum singularity requires the sound speed c to go to zero as the square-root of the distance to the moving boundary, and thus creates a degenerate and characteristic hyperbolic free-boundary system wherein the density vanishes on the free-boundary, the uniform Kreiss–Lopatinskii condition is violated, and manifest derivative loss ensues. Nevertheless, we are able to establish the existence of unique solutions to this system on a short time-interval, which are smooth (in Sobolev spaces) all the way to the moving boundary, and our estimates have no derivative loss with respect to initial data. Our proof is founded on an approximation of the Euler equations by a degenerate parabolic regularization obtained from a specific choice of a degenerate artificial viscosity term, chosen to preserve as much of the geometric structure of the Euler equations as possible. We first construct solutions to this degenerate parabolic regularization using a higher-order version of Hardy’s inequality; we then establish estimates for solutions to this degenerate parabolic system which are independent of the artificial viscosity parameter. Solutions to the compressible Euler equations are found in the limit as the artificial viscosity tends to zero. Our regular solutions can be viewed as degenerate viscosity solutions. Our methodology can be applied to many other systems of degenerate and characteristic hyperbolic systems of conservation laws.
187 citations
TL;DR: In this article, the structure of matter representations arising from codimension two singularities in F-theory, focusing on gauge groups SU(N), is analyzed. And a detailed local description of the geometry associated with several types of singularities and the associated matter representations is given.
Abstract: We analyze the structure of matter representations arising from codimension two singularities in F-theory, focusing on gauge groups SU(N). We give a detailed local description of the geometry associated with several types of singularities and the associated matter representations. We also construct global F-theory models for 6D and 4D theories containing these matter representations. The codimension two singularities encountered in- clude examples where the apparent Kodaira singularity type does not need to be completely resolved to produce a smooth Calabi-Yau, examples with rank enhancement by more than one, and examples where the 7-brane configuration is singular. We identify novel phase transitions, in some of which the gauge group remains fixed but the singularity type and associated matter content change along a continuous family of theories. Global analysis of 6D theories on P 2 with 7-branes wrapped on curves of small degree reproduces the range of 6D supergravity theories identified through anomaly cancellation and other consistency conditions. Analogous 4D models are constructed through global F-theory compactifica- tions on P 3 , and have a similar pattern of SU(N) matter content. This leads to a constraint on the matter content of a limited class of 4D supergravity theories containing SU(N) as a local factor of the gauge group.
TL;DR: In this article, a non-isotropy norm is defined to capture the dissipation in the linearized collision operator of the Boltzmann equation and a new and precise coercivity estimate for general physical cross sections is given.
TL;DR: In this article, the authors used the acceleration signal instead of the deflection signal, employing a vehicle-bridge finite element interaction model, and developing a novel wavelet-based approach using wavelet energy content at each bridge section, which proves to be more sensitive to damage than a wavelet coefficient line plot at a given scale as employed by others.
TL;DR: In this article, it was shown that the eigenvectors of the PT-symmetric imaginary cubic oscillator are complete, but do not form a Riesz basis.
Abstract: We show that the eigenvectors of the PT-symmetric imaginary cubic oscillator are complete, but do not form a Riesz basis. This results in the existence of a bounded metric operator having intrinsic singularity reflected in the inevitable unboundedness of the inverse. Moreover, the existence of non-trivial pseudospectrum is observed. In other words, there is no quantum-mechanical Hamiltonian associated with it via bounded and boundedly invertible similarity transformations. These results open new directions in physical interpretation of PT-symmetric models with intrinsically singular metric, since their properties are essentially different with respect to self-adjoint Hamiltonians, for instance, due to spectral instabilities.
TL;DR: In this paper, the authors construct phantom energy models with the equation of state parameter w which is less than −1, w − 1, but finite-time future singularity does not occur.
TL;DR: The hypothesis of this paper is that the results obtained by applying traditional similarities measures can be improved by taking contextual information, drawn from the entire body of users, and using it to calculate the singularity which exists, for each item, in the votes cast by each pair of users that you wish to compare.
Abstract: Recommender systems play an important role in reducing the negative impact of information overload on those websites where users have the possibility of voting for their preferences on items. The most normal technique for dealing with the recommendation mechanism is to use collaborative filtering, in which it is essential to discover the most similar users to whom you desire to make recommendations. The hypothesis of this paper is that the results obtained by applying traditional similarities measures can be improved by taking contextual information, drawn from the entire body of users, and using it to calculate the singularity which exists, for each item, in the votes cast by each pair of users that you wish to compare. As such, the greater the measure of singularity result between the votes cast by two given users, the greater the impact this will have on the similarity. The results, tested on the Movielens, Netflix and FilmAffinity databases, corroborate the excellent behaviour of the singularity measure proposed.
TL;DR: In this paper, the authors provided new exact solutions to the Einstein-Maxwell system of equations which are physically reasonable and showed that the spacetime is static and spherically symmetric with a charged matter distribution.
Abstract: We provide new exact solutions to the Einstein–Maxwell system of equations which are physically reasonable. The spacetime is static and spherically symmetric with a charged matter distribution. We utilise an equation of state which is quadratic relating the radial pressure to the energy density. Earlier models, with linear and quadratic equations of state, are shown to be contained in our general class of solutions. The new solutions to the Einstein–Maxwell are found in terms of elementary functions. A physical analysis of the matter and electromagnetic variables indicates that the model is well behaved and regular. In particular there is no singularity in the proper charge density at the stellar centre unlike earlier anisotropic models in the presence of the electromagnetic field.
TL;DR: In this paper, the authors explore the possibility of producing a logarithmic violation of the usual area law behavior by analyzing the IR regions of the bulk geometries dual to such theories.
Abstract: The entanglement entropy in theories with a Fermi surface is known to pro- duce a logarithmic violation of the usual area law behavior. We explore the possibility of producing this logarithmic violation holographically by analyzing the IR regions of the bulk geometries dual to such theories. The geometry of Ogawa, Takayanagi, and Ugajin is explored and shown to have a null curvature singularity for all values of parameters, except for dynamical critical exponent z = 3=2 (the hyperscaling violation parameter = 1 for this geometry) in four dimensions. The results are extended to general hyperscaling viola- tion exponent. We explore strings propagating through the singularity and show that they become innitely excited, suggesting the singularity is not resolved by stringy eects and
TL;DR: In this paper, a dual description of AdS spacetimes is proposed, where the reduced density matrix encoding the state of the degrees of freedom in one of these CFTs describes the physics in a single wedge, which can be viewed as the region of spacetime accessible to an accelerated observer in AdS.
Abstract: In this note, we explain how asymptotically globally AdS spacetimes can be given an alternate dual description as entangled states of a pair of hyperbolic space CFTs, which are associated with complementary Rindler wedges of the AdS geometry. The reduced density matrix encoding the state of the degrees of freedom in one of these CFTs describes the physics in a single wedge, which we can think of as the region of spacetime accessible to an accelerated observer in AdS. For pure AdS, this density matrix is thermal, and we argue that the microstates in this thermal ensemble correspond to spacetimes that are almost indistinguishable from a Rindler wedge of pure AdS away from the horizon, but with the horizon replaced by some kind of singularity where the geometrical description breaks down. This alternate description of AdS, based on patches associated with particular observers, may give insight into the holographic description of cosmologies where no observer has access to the full spacetime.
TL;DR: The method presented provides a unified framework for optimizing both the element size and anisotropy distribution using an a posteriori error estimate and enables efficient adaptation of anisotropic simplex meshes for high-order discretizations.
TL;DR: In this article, the authors constructed the first family of microstate geometries of near-extremal black holes, by placing metastable supertube probes inside certain scaling supersymmetric smooth microstate geometry, which differs from the classical black hole solution macroscopically at the horizon scale and for certain probes the fluctuations between various fuzzballs will be visible as thermal noise far away from the horizon.
Abstract: We construct the first family of microstate geometries of near-extremal black holes, by placing metastable supertube probes inside certain scaling supersymmetric smooth microstate geometries. These fuzzballs differ from the classical black hole solution macroscopically at the horizon scale, and for certain probes the fluctuations between various fuzzballs will be visible as thermal noise far away from the horizon. We discuss whether these fuzzballs appear to infalling observers as fuzzballs of fuzz or as fuzzballs of fire. The existence of these solutions suggests that the singularity of non-extremal black holes is resolved all the way to the outer horizon and this “backwards in time” singularity resolution can shed light on the resolution of spacelike cosmological singularities.
TL;DR: In this article, a new approach for singularity analysis of parallel manipulators by taking into account motion/force transmissibility is presented, where several performance indices are introduced to measure the closeness to singularities.
Abstract: Singularity analysis is one of the most important issues in the field of parallel manipulators. An approach for singularity analysis should be able to not only identify all possible singularities but also explain their physical meanings. Since a parallel manipulator is always out of control at a singularity and its neighborhood, it should work far from singular configurations. However, how to measure the closeness between a pose and a singular configuration is still a challenging problem. This paper presents a new approach for singularity analysis of parallel manipulators by taking into account motion/force transmissibility. Several performance indices are introduced to measure the closeness to singularities. By using these indices, a uniform “metric” can be found to represent the closeness to singularities for different types of nonredundant parallel manipulators.
TL;DR: In this paper, the authors conjecture that the generating function of Euler characteristics of refined punctual Hilbert schemes is the HOMFLY polynomial of the link of a complex plane curve with a small three-sphere surrounding one of its singularities.
Abstract: The intersection of a complex plane curve with a small three-sphere surrounding one of its singularities is a nontrivial link. The refined punctual Hilbert schemes of the singularity parameterize subschemes supported at the singular point of fixed length and whose defining ideals have a fixed number of generators. We conjecture that the generating function of Euler characteristics of refined punctual Hilbert schemes is the HOMFLY polynomial of the link. The conjecture is verified for irreducible singularities yk=xn whose links are the (k,n) torus knots, and for the singularity y4=x7−x6+4x5y+2x3y2 whose link is the (2,13) cable of the trefoil.
TL;DR: In this paper, the effects of the underlying quantum geometry in loop quantum cosmology on spacetime curvature invariants and the extendibility of geodesics in the Bianchi-I model for matter with a vanishing anisotropic stress were investigated.
Abstract: We investigate the effects of the underlying quantum geometry in loop quantum cosmology on spacetime curvature invariants and the extendibility of geodesics in the Bianchi-I model for matter with a vanishing anisotropic stress. Using the effective Hamiltonian approach, we find that even though quantum geometric effects bound the energy density and expansion and shear scalars, divergences of curvature invariants are potentially possible under special conditions. However, as in the isotropic models in LQC, these do not necessarily imply a physical singularity. Analysis of geodesics and strength of such singular events, point towards a general resolution of all known types of strong singularities. We illustrate these results for the case of a perfect fluid with an arbitrary finite equation of state $w > -1$, and show that curvature invariants turn out to be bounded, leading to the absence of strong singularities. Unlike classical theory, geodesic evolution does not break down. We also discuss possible generalizations of sudden singularities which may arise at a non-vanishing volume, causing a divergence in curvature invariants. Such finite volume singularities are shown to be weak and harmless.
TL;DR: In this paper, the authors derived qualitatively different optical properties of hyperbolic media, due to the free-electron nonlocal optical response of their metal constituents, and showed that non-local response gives rise to a large-wavevector cutoff in the dispersion that is inversely proportional to the Fermi velocity of the electron gas.
Abstract: We study metamaterials known as hyperbolic media that in the usual local-response approximation exhibit hyperbolic dispersion and an associated broadband singularity in the density of states. Instead, from the more microscopic hydrodynamic Drude theory we derive qualitatively different optical properties of these metamaterials, due to the free-electron nonlocal optical response of their metal constituents. We demonstrate that nonlocal response gives rise to a large-wavevector cutoff in the dispersion that is inversely proportional to the Fermi velocity of the electron gas, but also for small wavevectors we find differences for the hyperbolic dispersion. Moreover, the size of the unit cell influences effective parameters of the metamaterial even in the deep subwavelength regime. Finally, instead of the broadband supersingularity in the local density of states, we predict a large but finite maximal enhancement proportional to the inverse cube of the Fermi velocity.
TL;DR: In this paper, the authors compute four point functions of the stress tensor and conserved currents in AdS_4/CFT_3 using bulk perturbation theory.
Abstract: We compute four point functions of the stress tensor and conserved currents in AdS_4/CFT_3 using bulk perturbation theory. We work at treel level in the bulk theory, which we take to be either pure gravity or Yang Mills theory in AdS. We bypass the tedious evaluation of Witten diagrams using recently developed recursion relations for these correlators. In this approach, the four point function is obtained as the sum of residues of a rational function at easily identifiable poles. We write down an explicit formula for the four point correlator with arbitrary external helicities and momenta. We verify that, precisely as conjectured in a companion paper, the Maximally Helicity Violating (MHV) amplitude of gravitons or gluons appears as the coefficient of a specified singularity in the MHV stress-tensor or current correlator. We comment on the remarkably simple analytic structure of our answers in momentum space.
Book•
03 Apr 2012
TL;DR: This paper presents a meta-modelling framework that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive process of map-side approximation that is necessary to study the dynamics of flow.
Abstract: Preface Chapter 1. Introduction Chapter 2. Flow Passability and Tangential Flows Chapter 3. Flow Switching Bifurcations Chapter 4. Transversal Singularity and Bouncing Flows Chapter 5. Real and Imaginary Flows Chapter 6. Discontinuous Vector Fields with Flow Barriers Chapter 7. Transport Laws and Mapping Dynamics Chapter 8. Symmetry and Fragmentized Strange Attractors Appendix References Subject Index
TL;DR: In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values.
Abstract: In this paper, the continuous genetic algorithm is applied for the solution of singular two-point boundary value problems, where smooth solution curves are used throughout the evolution of the algorithm to obtain the required nodal values. The proposed technique might be considered as a variation of the finite difference method in the sense that each of the derivatives is replaced by an appropriate difference quotient approximation. This novel approach possesses main advantages; it can be applied without any limitation on the nature of the problem, the type of singularity, and the number of mesh points. Numerical examples are included to demonstrate the accuracy, applicability, and generality of the presented technique. The results reveal that the algorithm is very effective, straightforward, and simple.
TL;DR: In this paper, a general Kaluza-Klein reduction of a truncated Lovelock theory is considered, and necessary geometric conditions for the reduction to be consistent are given.
Abstract: We consider a general Kaluza-Klein reduction of a truncated Lovelock theory. We find necessary geometric conditions for the reduction to be consistent. The resulting lower-dimensional theory is a higher derivative scalar-tensor theory, depends on a single real parameter and yields second-order field equations. Due to the presence of higher-derivative terms, the theory has multiple applications in modifications of Einstein gravity (Galileon/Horndesky theory) and holography (Einstein-Maxwell-Dilaton theories). We find and analyze charged black hole solutions with planar or curved horizons, both in the ‘Einstein’ and ‘Galileon’ frame, with or without cosmological constant. Naked singularities are dressed by a geometric event horizon originating from the higher-derivative terms. The near-horizon region of the near-extremal black hole is unaffected by the presence of the higher derivatives, whether scale invariant or hyperscaling violating. In the latter case, the area law for the entanglement entropy is violated logarithmically, as expected in the presence of a Fermi surface. For negative cosmological constant and planar horizons, thermodynamics and first-order hydrodynamics are derived: the shear viscosity to entropy density ratio does not depend on temperature, as expected from the higher-dimensional scale invariance.
TL;DR: In this paper, it was shown that for small spherically symmetric perturbations of asymptotically flat two-ended Reissner-Nordstrom data for the real scalar field system, the boundary of the dynamic spacetime which evolves is globally represented by a bifurcate null hypersurface across which the metric extends continuously.
Abstract: It is shown that for small, spherically symmetric perturbations of asymptotically flat two-ended Reissner-Nordstrom data for the Einstein-Maxwell-real scalar field system, the boundary of the dynamic spacetime which evolves is globally represented by a bifurcate null hypersurface across which the metric extends continuously. Under additional assumptions, it is shown that the Hawking mass blows up identically along this bifurcate null hypersurface, and thus the metric cannot be extended twice differentiably, in fact, cannot be extended in a weaker sense characterized at the level of the Christoffel symbols. The proof combines estimates obtained in previous work with an elementary Cauchy stability argument. There are no restrictions on the size of the support of the scalar field, and the result applies to both the future and past boundary of spacetime. In particular, it follows that for an open set in the moduli space of solutions around Reissner-Nordstrom, there is no spacelike component of either the future or the past singularity.