Gravitational Configurations Research Articles

Duality Identities for Moduli Functions of Generalized Melvin Solutions Related to Classical Lie Algebras of Rank 4

We consider generalized Melvin-like solutions associated with nonexceptional Lie algebras of rank 4 (namely, A4, B4, C4, and D4) corresponding to certain internal symmetries of the solutions. The system under consideration is a static cylindrically symmetric gravitational configuration in D dimensions in presence of four Abelian 2-forms and four scalar fields. The solution is governed by four moduli functions Hs(z) (s=1,…,4) of squared radial coordinate z=ρ2 obeying four differential equations of the Toda chain type. These functions turn out to be polynomials of powers (n1,n2,n3,n4)=(4,6,6,4),(8,14,18,10),(7,12,15,16),(6,10,6,6) for Lie algebras A4, B4, C4, and D4, respectively. The asymptotic behaviour for the polynomials at large distances is governed by some integer-valued 4×4 matrix ν connected in a certain way with the inverse Cartan matrix of the Lie algebra and (in A4 case) the matrix representing a generator of the Z2-group of symmetry of the Dynkin diagram. The symmetry properties and duality identities for polynomials are obtained, as well as asymptotic relations for solutions at large distances. We also calculate 2-form flux integrals over 2-dimensional discs and corresponding Wilson loop factors over their boundaries.

Holographic subregion complexity under a thermal quench

We study the evolution of holographic subregion complexity under a thermal quench in this paper. From the subregion CV proposal in the AdS/CFT correspondence, the subregion complexity in the CFT is holographically captured by the volume of the codimension-one surface enclosed by the codimension-two extremal entanglement surface and the boundary subregion. Under a thermal quench, the dual gravitational configuration is described by a Vaidya-AdS spacetime. In this case we find that the holographic subregion complexity always increases at early time, and after reaching a maximum it decreases and gets to saturation. Moreover we notice that when the size of the strip is large enough and the quench is fast enough, in AdSd+1(d ≥ 3) spacetime the evolution of the complexity is discontinuous and there is a sudden drop due to the transition of the extremal entanglement surface. We discuss the effects of the quench speed, the strip size, the black hole mass and the spacetime dimension on the evolution of the subregion complexity in detail numerically.

Starobinsky inflation and dark energy and dark matter effects from quasicrystal like spacetime structures

The goal of this work on mathematical cosmology and geometric methods in modified gravity theories, MGTs, is to investigate Starobinsky-like inflation scenarios determined by gravitational and scalar field configurations mimicking quasicrystal, QC, like structures. Such spacetime aperiodic QCs are different from those discovered and studied in solid state physics but described by similar geometric methods. We prove that a inhomogeneous and locally anisotropic gravitational and matter field effective QC mixed continuous and discrete “ether” can be modelled by exact cosmological solutions in MGTs and Einstein gravity. The coefficients of corresponding generic off-diagonal metrics and generalized connections depend (in general) on all spacetime coordinates via generating and integration functions and, certain smooth and discrete parameters. Imposing additional nonholonomic constraints, prescribing symmetries for generating functions and solving the boundary conditions for integration functions and constants, we can model various nontrivial torsion QC structures or extract cosmological Levi-Civita configurations with diagonal metrics reproducing de Sitter (inflationary) like and other type homogeneous inflation and acceleration phases. Finally, we speculate how various dark energy and dark matter effects can be modelled by off-diagonal interactions and deformations of a nontrivial QC like gravitational vacuum structure and analogous scalar matter fields.

Constant curvature black holes in Einstein AdS gravity: Euclidean action and thermodynamics

We compute the Euclidean action for constant curvature black holes (CCBHs), as an attempt to associate thermodynamic quantities to these solutions of Einstein anti-de Sitter (AdS) gravity. CCBHs are gravitational configurations obtained by identifications along isometries of a $D$-dimensional globally AdS space, such that the Riemann tensor remains constant. Here, these solutions are interpreted as extended objects, which contain a $(D-2)$-dimensional de-Sitter brane as a subspace. Nevertheless, the computation of the free energy for these solutions shows that they do not obey standard thermodynamic relations.

LensFlow: A Convolutional Neural Network in Search of Strong Gravitational Lenses

Abstract In this work, we present our machine learning classification algorithm for identifying strong gravitational lenses from wide-area surveys using convolutional neural networks; LensFlow. We train and test the algorithm using a wide variety of strong gravitational lens configurations from simulations of lensing events. Images are processed through multiple convolutional layers that extract feature maps necessary to assign a lens probability to each image. LensFlow provides a ranking scheme for all sources that could be used to identify potential gravitational lens candidates by significantly reducing the number of images that have to be visually inspected. We apply our algorithm to the HST/ACS i-band observations of the COSMOS field and present our sample of identified lensing candidates. The developed machine learning algorithm is more computationally efficient and complimentary to classical lens identification algorithms and is ideal for discovering such events across wide areas from current and future surveys such as LSST and WFIRST.

Gravitational waves in Poincaré gauge gravity theory

We derive the exact gravitational wave solutions in a general class of quadratic Poincar\'e gauge gravity models. The Lagrangian includes all possible linear and quadratic invariants constructed from the torsion and the curvature, including the parity odd terms. The Ansatz for the gravitational wave configuration and the properties of the wave solutions are patterned following the corresponding Ansatz and the properties of the plane-fronted electromagnetic wave.

Stealths on $$(1+1)$$ ( 1 + 1 ) -dimensional dilatonic gravity

We study gravitational stealth configurations emerging on a charged dilatonic $(1+1)$-D black hole spacetime. We accomplish this by considering the coupling of a non-minimally scalar field $\phi$ and a self-interacting scalar field $\Psi$ living in a $(1+1)$-D charged black hole background. In addition, the self-interacting potential for $\Psi$ is obtained which exhibits transitions for some specific values of the non-minimal parameter. Atypically, we found that the solutions for these stealth scalar fields do not have a dependence on the temporal coordinate.

Time transfer functions in Schwarzschild-like metrics in the weak-field limit: A unified description of Shapiro and lensing effects

We present a complete analysis of the light rays within the linearized, weak-field approximation of a Schwarzschild-like metric describing the gravitational field of an isolated, spherically symmetric body. We prove in this context the existence of two time transfer functions and we obtain these functions in an exact closed-form. We are led to distinguish two regimes. In the first regime, the two time transfer functions correspond to rays which are confined in regions of spacetime where the weak-field approximation is valid. Such a regime occurs in gravitational lensing configurations with double images of a given source. We find the general expressions of the angular separation and the difference in light travel time between the two images. In the second regime, there exists only one time transfer function corresponding to a light ray remaining in a region of weak field. Performing a Taylor expansion of this function with respect to the gravitational constant, we obtain the Shapiro time delay completed by a series of so-called "enhanced terms". The enhanced terms beyond the third order are new.

Vacuum structure and gravitational bags produced by metric-independent space–time volume-form dynamics

We propose a new class of gravity-matter theories, describing [Formula: see text] gravity interacting with a nonstandard nonlinear gauge field system and a scalar “dilaton,” formulated in terms of two different non-Riemannian volume-forms (generally covariant integration measure densities) on the underlying space–time manifold, which are independent of the Riemannian metric. The nonlinear gauge field system contains a square-root [Formula: see text] of the standard Maxwell Lagrangian which is known to describe charge confinement in flat space–time. The initial new gravity-matter model is invariant under global Weyl-scale symmetry which undergoes a spontaneous breakdown upon integration of the non-Riemannian volume-form degrees of freedom. In the physical Einstein frame we obtain an effective matter-gauge-field Lagrangian of “k-essence” type with quadratic dependence on the scalar “dilaton” field kinetic term [Formula: see text], with a remarkable effective scalar potential possessing two infinitely large flat regions as well as with nontrivial effective gauge coupling constants running with the “dilaton” [Formula: see text]. Corresponding to each of the two flat regions we find “vacuum” configurations of the following types: (i) [Formula: see text] and a nonzero gauge field vacuum [Formula: see text], which corresponds to a charge confining phase; (ii) [Formula: see text] (“kinetic vacuum”) and ordinary gauge field vacuum [Formula: see text] which supports confinement-free charge dynamics. In one of the flat regions of the effective scalar potential we also find: (iii) [Formula: see text] (“kinetic vacuum”) and a nonzero gauge field vacuum [Formula: see text], which again corresponds to a charge confining phase. In all three cases, the space–time metric is de Sitter or Schwarzschild–de Sitter. Both “kinetic vacuums” (ii) and (iii) can exist only within a finite-volume space region below a de Sitter horizon. Extension to the whole space requires matching the latter with the exterior region with a nonstandard Reissner–Nordström–de Sitter geometry carrying an additional constant radial background electric field. As a result, we obtain two classes of gravitational bag-like configurations with properties, which on one hand partially parallel some of the properties of the solitonic “constituent quark” model and, on the other hand, partially mimic some of the properties of MIT bags in QCD phenomenology.

Heterotic NS5-branes from closed string tachyon condensation

We show how to construct the familiar heterotic NS5 brane as a topological soliton in a supercritical version of heterotic string theory. Closed string tachyon condensation removes the extra dimensions, leaving the NS5 in ten dimensions, in a process highly reminiscent of the K-theoretical description of type II D-branes, but linking nontrivial gauge bundles and geometry. This establishes a new kind of equivalence between gravitational and gauge configurations, reminiscent of the gauge/geometry correspondence. We also use the K-theory description to build other heterotic branes as solitons of closed string tachyons. The construction requires a modification of the anomalous Bianchi identity for ${H}_{3}$ in supercritical heterotic string theory. We give various proofs for the existence of this modification.

Geroch group description of black holes

On one hand the Geroch group allows one to associate spacetime independent matrices with gravitational configurations that effectively only depend on two coordinates. This class includes stationary axisymmetric four- and five-dimensional black holes. On the other hand, a recently developed inverse scattering method allows one to factorize these matrices to explicitly construct the corresponding spacetime configurations. In this work we demonstrate the construction as well as the factorization of Geroch group matrices for a wide class of black hole examples. In particular, we obtain the Geroch group SL(3, ℝ) matrices for the five-dimensional Myers-Perry and Kaluza-Klein black holes and the Geroch group SU(2, 1) matrix for the four-dimensional Kerr-Newman black hole. We also present certain non-trivial relations between the Geroch group matrices and charge matrices for these black holes.

A type of Levi–Civita solution in modified Gauss–Bonnet gravity

Herein we obtain an exact solution for cylindrically symmetric modified Gauss–Bonnet gravity. This metric is a generalization of the vacuum solution of Levi–Civita in general relativity. It describes an isotropic perfect fluid one-parameter family of the gravitational configurations, which can be interpreted as the exterior metric of a cosmic string. By setting the Gauss–Bonnet coupling parameter to zero, we recover the vacuum solution in the Einstein gravity as well.

Theoretical Limits on the Efficiency of a Quantum Vacuum Thruster

Theory and experiments show that vacuum fluctuations in quantum gravity can be abnormally strong, also at the micrometer or nanometer scale, for the following reasons: (1) the Einstein action is not positive-definite; (2) it is the only possible effective gravitational action; (3) quantum mechanics, in the form of the Feynman path integral, must apply to it, because any natural process is the result of all its possible quantum amplitudes; (4) due to (1), there are important non-classical virtual gravitational field configurations which can agree on a common phase. These field configurations can only interact directly with coherent matter, but can emit virtual gravitons which are absorbed by ordinary matter. All this makes possible, in principle, a vacuum thruster much more efficient than those based on the electromagnetic Casimir effect. We give an estimate of its efficiency based on the mentioned microscopic processes and on some parameters observed in experiments on anomalous forces with superconductors. With the observed energy efficiency of the order of 10-4 and an electric power of 10 W per kilogram of mass to propel, we find that a velocity of 0.1c can be reached in ca. 10 years. Possible improvements and practical limits are outlined. We discuss how the concept of ideal vacuum should be modified in order to allow a consistent description of these phenomena.

Laser interferometric analysis of glucose and sucrose diffusion in agarose gel.

The paper presents the investigation results of glucose and sucrose diffusion in agarose gel studied with laser interferometry method and the results of fluorescence analysis of the macroscopic gel structure. The diffusion kinetics of these substances released from aqueous solutions of a molar concentration of 0.05 M into the agarose solutions of concentrations of 0.5% and 3% in two gravitational configurations of measuring system was analysed. In the first configuration the solute diffused according, whereas in the second one - opposite to the gravitational force. The diffusion was analysed in the time period between 120 and 2400 s with a time interval of Δt = 120 s. We observed that the convective instabilities were damped well by the agarose gel, which gives the possibility of the interferometric studies of the diffusive transport for other substances in different gravitational configurations of the system. The time characteristics of glucose and sucrose fluxes in both configurations of the system and the gravitational polarisation coefficient values were obtained. The substantial differences in fluxes of glucose and sucrose diffused according and opposite to the gravitational force were observed. Additionally, we observed the differences between the diffusive fluxes of these substances in both configurations in dependence on the gel solution concentration (which is associated with gel porosity dependent on its concentration) and the kind of diffused substance.

DARK HALOS AND ELLIPTICAL GALAXIES AS MARGINALLY STABLE DYNAMICAL SYSTEMS

The origin of equilibrium gravitational configurations is sought in terms of the stability of their trajectories, as described by the curvature of their Lagrangian configuration manifold of particle positions --- a context in which subtle spurious effects originating from the singularity in the two body potential become particularly clear. We focus on the case of spherical systems, which support only regular orbits in the collisionless limit, despite the persistence of local exponential instability of $N$-body trajectories in the anomalous case of discrete point particle representation even as $N \rightarrow \infty$. When the singularity in the potential is removed, this apparent contradiction disappears. In the absence of fluctuations, equilibrium configurations generally correspond to positive scalar curvature, and thus support stable trajectories. A null scalar curvature is associated with an effective, averaged, equation of state describing dynamically relaxed equilibria with marginally stable trajectories. The associated configurations are quite similar to those of observed elliptical galaxies and simulated cosmological halos, and are necessarily different from the systems dominated by isothermal cores, expected from entropy maximization in the context of the standard theory of violent relaxation. It is suggested that this is the case because a system starting far from equilibrium does not reach a 'most probable state' via violent relaxation, but that this process comes to an end as the system finds and (settles in) a configuration where it can most efficiently wash out perturbations. We explicitly test this interpretation by means of direct simulations.

Spin in an arbitrary gravitational field

We study the quantum mechanics of a Dirac fermion on a curved spacetime manifold. The metric of the spacetime is completely arbitrary, allowing for the discussion of all possible inertial and gravitational field configurations. In this framework, we find the Hermitian Dirac Hamiltonian for an arbitrary classical external field (including the gravitational and electromagnetic ones). In order to discuss the physical content of the quantum-mechanical model, we further apply the Foldy-Wouthuysen transformation, and derive the quantum equations of motion for the spin and position operators. We analyse the semiclassical limit of these equations and compare the results with the dynamics of a classical particle with spin in the framework of the standard Mathisson-Papapetrou theory and in the classical canonical theory. The comparison of the quantum mechanical and classical equations of motion of a spinning particle in an arbitrary gravitational field shows their complete agreement.

The fate of monsters in anti-de Sitter spacetime

Abstract Black hole entropy remains a deep puzzle: where does such enormous amount of entropy come from? Curiously, there exist gravitational configurations that possess even larger entropy than a black hole of the same mass, in fact, arbitrarily high entropy. These are the so-called monsters, which are problematic to the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence paradigm since there is far insufficient degrees of freedom on the field theory side to account for the enormous entropy of monsters in AdS bulk. The physics of the bulk however may be considerably modified at semi-classical level due to the presence of branes. We show that this is especially so since monster spacetimes are unstable due to brane nucleation. As a consequence, it is not clear what the final fate of monsters is. We argue that in some cases there is no real threat from monsters since although they are solutions to Einstein’s Field Equations, they are very likely to be completely unstable when embedded in string theory, and thus probably are not solutions to the full quantum theory of gravity. Our analysis, while suggestive and supportive of the claim that such pathological objects are not allowed in the final theory, by itself does not rule out all monsters. We comment on various kin of monsters such as the “bag-of-gold” spacetime, and also discuss briefly the implications of our work to some puzzles related to black hole entropy.

Trade-off between quantum and thermal fluctuations in mirror coatings yields improved sensitivity of gravitational-wave interferometers

We propose a simple way to improve the laser gravitational-wave detectors sensitivity by means of reduction of the number of reflective coating layers of the core optics mirrors. This effects in the proportional decrease of the coating thermal noise, the most notorious among the interferometers technical noise sources. The price for this is the increased quantum noise, as well as high requirements for the pump laser power and power at the beamsplitter. However, as far as these processes depend differently on the coating thickness, we demonstrate that a certain trade-off is possible, yielding a 20-30% gain (for diverse gravitational wave signal types and interferometer configurations), providing that feasible values of laser power and power on the beamsplitter are assumed.

Fractional Dynamics from Einstein Gravity, General Solutions, and Black Holes

We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical objects and a generalized tensor calculus all being similar to respective integer dimension constructions. Such models of fractional gravity mimic the Einstein gravity theory and various Lagrange-Finsler and Hamilton-Cartan generalizations in nonholonomic variables. The approach suggests a number of new implications for gravity and matter field theories with singular, stochastic, kinetic, fractal, memory etc processes. We prove that the fractional gravitational field equations can be integrated in very general forms following the anholonomic deformation method for constructing exact solutions. Finally, we study some examples of fractional black hole solutions, fractional ellipsoid gravitational configurations and imbedding of such objects in fractional solitonic backgrounds.

Electrically charged black hole solutions in generalized gauge field theories

We summarize the main features of a class of anomalous (asymptotically flat, but non Schwarzschild-like) gravitational configurations in models of gravitating non-linear electrodynamics (G-NED) whose Lagrangian densities are defined as arbitrary functions of the two field invariants and constrained by several physical admissibility conditions. This class of models and their associated electrostatic spherically symmetric black hole (ESSBH) solutions are characterized by the behaviours of the Lagrangian densities around the vacuum and at the boundary of their domain of definition.