Curvature Terms Research Articles

Quasi-topological gravities on general spherically symmetric metric

In this work we study a more restricted class of quasi-topological gravity theories where the higher curvature terms have no contribution to the equation of motion on general static spherically symmetric metric where gttgrr ≠ constant. We construct such theories up to quintic order in Riemann tensor and observe an important property of these theories: the higher order term in the Lagrangian vanishes identically when evaluated on the most general non-stationary spherically symmetric metric ansatz. This not only signals the higher terms could only have non-trivial effects when considering perturbations, but also makes the theories quasi-topological on a much wider range of metrics. As an example of the holographic effects of such theories, we consider a general Einstein-scalar theory and calculate it’s holographic shear viscosity.

Covariant Wick rotation: action, entropy, and holonomies

Given an arbitrary Lorentzian metric g_{ab} and a nowhere vanishing, timelike vector field u^a, one can construct a class of metrics {widehat{g}}_{ab} which have Euclidean signature in a specific domain, with a transition to Lorentzian regime occurring on some hypersurface Sigma orthogonal to u^a. Geometry associated with {{{widehat{g}}}}_{ab} has been shown to yield some remarkable insights for classical and quantum gravity. In this work, we focus on studying the implications of this geometry for thermal effects in curved spacetimes and compare and contrast the results with those obtained through conventional Euclidean methods. We show that the expression for entropy computed using {widehat{g}}_{ab} for simple field theories and Lanczos–Lovelock actions differ from Wald entropy by additional terms depending on extrinsic curvature. We also compute the holonomy associated with loops lying partially or wholly in the Euclidean regime in terms of extrinsic curvature and acceleration and compare it with the well-known expression for temperature.

What Is the Fate of Hawking Evaporation in Gravity Theories with Higher Curvature Terms?

During the final stages of black hole evaporation, ultraviolet deviations from general relativity eventually become dramatic, potentially affecting the end state. We explore this problem by performing nonlinear simulations of wave packets in Einstein-dilaton-Gauss-Bonnet gravity, the only gravity theory with quadratic curvature terms which can be studied at a fully nonperturbative level. Black holes in this theory have a minimum mass but also a nonvanishing temperature. This poses a puzzle concerning the final fate of Hawking evaporation in the presence of high-curvature nonperturbative effects. By simulating the mass loss induced by evaporation at the classical level using an auxiliary phantom field, we study the nonlinear evolution of black holes past the minimum mass. We observe a runaway shrink of the horizon (a nonperturbative effect forbidden in general relativity) which eventually unveils a high-curvature elliptic region. While this might hint to the formation of a naked singularity (and hence to a violation of the weak cosmic censorship) or of a pathological spacetime region, a different numerical formulation of the initial-value problem in this theory might be required to rule out other possibilities, including the transition from the critical black hole to a stable horizonless remnant. Our Letter is relevant in the context of the information-loss paradox, dark-matter remnants, and for constraints on microscopic primordial black holes.

Nonperturbative gedanken experiments in Einstein-dilaton-Gauss-Bonnet gravity: Nonlinear transitions and tests of the cosmic censorship beyond general relativity

As the only gravity theory with quadratic curvature terms and second-order field equations, Einstein-dilaton-Gauss-Bonnet gravity is a natural testbed to probe the high-curvature regime beyond General Relativity in a fully nonperturbative way. Due to nonperturbative effects of the dilatonic coupling, black holes in this theory have a minimum mass which separates a stable branch from an unstable one. The minimum mass solution is a double point in the phase diagram of the theory, wherein the critical black hole and a wormhole solution coexist. We perform extensive nonlinear simulations of the spherical collapse onto black holes with scalar hair in this theory, especially focusing on the region near the minimum mass. We study the nonlinear transition from the unstable to the stable branch and assess the nonlinear stability of the latter. Furthermore, motivated by modeling the mass loss induced by Hawking radiation near the minimum mass at the classical level, we study the collapse of a phantom field onto the black hole. When the black-hole mass decreases past the critical value, the apparent horizon shrinks significantly, eventually unveiling a high-curvature elliptic region. We argue that evaporation in this theory is bound to either violate the weak cosmic censorship or produce horizonless remnants. Addressing the end-state might require a different evolution scheme.

Morphological Behavior of Liposomes and Lipid Nanoparticles.

Liposomes, which consist of bilayer lipids surrounding interior aqueous compartment(s), were first characterized nearly 60 years ago. Remarkably, many fundamental properties of liposomes and their micellar-like "solid core" counterparts (a lipid monolayer surrounding a hydrophobic core) and transitions between these structures remain poorly understood. In this work, we examine the effects of basic variables on the morphology adopted by lipid-based systems produced by rapid mixing of lipids in ethanol with aqueous media. We show that, for lipids such as distearolyphosphatidylcholine (DSPC)-cholesterol mixtures that form bilayer vesicles on hydration, osmotic stress can induce regions of high positive membrane curvature, leading to fusion between unilamellar vesicles to produce bilamellar vesicles. Addition of lyso PC, an "inverted cone"-shaped lipid that supports regions of high positive curvature, can inhibit the formation of these bilamellar vesicles by stabilizing a hemifused intermediate structure. Conversely, the presence of "cone"-shaped lipids such as dioleoylphosphatidylethanolamine (DOPE) that results in negative membrane curvature promotes fusion events subsequent to vesicle formation (during the ethanol dialysis stage), leading to bilamellar and multilamellar systems even in the absence of osmotic stress. Alternatively, the presence of increasing amounts of triolein, a lipid that is insoluble in lipid bilayers, results in increasing internal solid core structures until micellar-like systems with a hydrophobic core of triolein are achieved. These results are interpreted in terms of the intrinsic membrane curvature that bilayer vesicles can stably maintain as well as the ability of bilayer lipids to first form a monolayer around a solid core of hydrophobic material such as triolein and then, as the proportion of bilayer lipids is increased, progressively form bilayer structures that can eventually form a complete bilayer encapsulating both a hydrophobic core and an aqueous compartment. These hybrid intermediate structures may have utility as novel drug delivery systems.

Reinterpreting deformed Heisenberg algebras

Minimal and maximal uncertainties of position measurements are widely considered possible hallmarks of low-energy quantum as well as classical gravity. While General Relativity describes interactions in terms of spatial curvature, its quantum analogue may also extend to the realm of curved momentum space as suggested, e.g. in the context of Relative Locality in Deformed Special Relativity. Drawing on earlier work, we show in an entirely Born reciprocal, i.e. position and momentum space covariant, way that the quadratic Generalized Extended Uncertainty principle can alternatively be described in terms of quantum dynamics on a general curved cotangent manifold. In the case of the Extended Uncertainty Principle the curvature tensor in position space is proportional to the noncommutativity of the momenta, while an analogous relation applies to the curvature tensor in momentum space and the noncommutativity of the coordinates for the Generalized Uncertainty Principle. In the process of deriving this map, the covariance of the approach constrains the admissible models to an interesting subclass of noncommutative geometries which has not been studied before. Furthermore, we reverse the approach to derive general anisotropically deformed uncertainty relations from general background geometries. As an example, this formalism is applied to (anti)-de Sitter spacetime.

R2 corrections to the black string instability and the boosted black string

We consider a perturbative Gauss-Bonnet term supplementing the Einstein-Hilbert action, and evaluate its effect on the spectrum of the scalar mode that triggers the Gregory-Laflamme instability of black strings in five dimensional General Relativity. After studying some properties of the static black string, we provide the correction to the Lichnerowicz operator up to $\mathcal{O}(\alpha^2)$. For the scalar mode of the gravitational perturbation, we find a master variable and study its spectrum, providing an analysis of the regime of validity of our scheme. We show that the instability persists under the inclusion of the $R^2$-correction, and that the critical wavelength increases with the value of $\alpha/r_+^2<<1$, providing new evidence of the phenomenon which was already observed in other approaches. We also construct the boosted black strings and compute the correction to the mass, the momentum and the tension due to the higher curvature term. The presence of the dimensionful coupling $\alpha$ spoils the validity of the Smarr relation, which is the gravitational version of the Euler relation which must hold for every homogeneous, thermodynamic system. We show that this identity can be restored by working in an extended thermodynamic setup that includes variations of the Gauss-Bonnet coupling.

Mimicking the [formula omitted]CDM universe through inhomogeneous space–time

Starting from an inhomogeneous space–time model of the universe we could recreate a scenario of recent time accelerating universe dominated by Dark Energy type of fluid. The background matter component of such a universe was considered to be made up of a combination of an anisotropic fluid, a barotropic fluid and the pressure less cold dark matter. It was found that inhomogeneity exhibits itself as the curvature term in such a universe. We corroborated our model with recent supernova Ia-JLA data together with H0 data and BAO data. Cosmographic analysis of the dynamical variables further show that the model can mimic the ΛCDM cosmology very closely.

Berry Population Analysis: Atomic Charges from the Berry Curvature in a Magnetic Field.

The Berry curvature is essential in Born-Oppenheimer molecular dynamics, describing the screening of the nuclei by the electrons in a magnetic field. Parts of the Berry curvature can be understood as the external magnetic field multiplied by an effective charge so that the resulting Berry force behaves like a Lorentz force during the simulations. Here, we investigate whether these effective charges can provide insight into the electronic structure of a given molecule or, in other words, whether we can perform a population analysis based on the Berry curvature. To develop our approach, we first rewrite the Berry curvature in terms of charges that partially capture the effective charges and their dependencies on the nuclear velocities. With these Berry charges and charge fluctuations, we then construct our population analysis yielding atomic charges and overlap populations. Calculations at the Hartree-Fock level reveal that the atomic charges are similar to those obtained from atomic polar tensors. However, since we additionally obtain an estimate for the fluctuations of the charges and a partitioning of the atomic charges into contributions from all atoms, we conclude that the Berry population analysis is a useful alternative tool to analyze the electronic structures of molecules.

Approximate treatment of noncommutative curvature in quartic matrix model

We study a Hermitian matrix model with the standard quartic potential amended by a tr(RΦ2) term for fixed external matrix R. This is motivated by a curvature term in the truncated Heisenberg algebra formulation of the Grosse-Wulkenhaar model — a renormalizable noncommutative field theory. The extra term breaks the unitary symmetry of the action and leads, after perturbative calculation of the unitary integral, to an effective multitrace matrix model. Accompanying the analytical treatment of this multitrace approximation, we also study the model numerically by Monte Carlo simulations. The phase structure of the model is investigated, and a modified phase diagram is identified. We observe a shift of the transition line between the 1-cut and 2-cut phases of the theory that is consistent with the previous numerical simulations and also with the removal of the noncommutative phase in the Grosse-Wulkenhaar model.

Poisson Doubly Warped Product Manifolds

This article generalizes some geometric structures on warped product manifolds equipped with a Poisson structure to doubly warped products of pseudo-Riemannian manifolds equipped with a doubly warped Poisson structure. First, we introduce the notion of Poisson doubly warped product manifold (fB×bF,Π=μvΠBh+νhΠFv,g) and express the Levi-Civita contravariant connection, curvature and metacurvature of (fB×bF,Π,g) in terms of Levi-Civita connections, curvatures and metacurvatures of components (B,ΠB,gB) and (F,ΠF,gF). We also study compatibility conditions related to the Poisson structure Π and the contravariant metric g on fB×bF, so that the compatibility conditions on (B,ΠB,gB) and (F,ΠF,gF) remain consistent in the Poisson doubly warped product manifold (fB×bF,Π,g).

Post-inflationary GW production in generic higher (infinite) derivative gravity

Gravity can be embedded into a renormalizable theory by means of adding quadratic in curvature terms. However, this at first leads to the presence of the Weyl ghost. It is possible to get rid of this ghost if the locality assumption is weakened and the propagator of the graviton is represented by an entire function of the d'Alembertian operator without new poles and zeros. Models of this type admit a cosmological solution describing the R2, or Starobinsky, inflation. We study graviton production after inflation in this model and show that it is negligible despite the presence of the higher derivative operators which could potentially cause instabilities.

Perusing Buchbinder–Lyakhovich Canonical Formalism for Higher-Order Theories of Gravity

Ostrogradsky’s, Dirac’s, and Horowitz’s techniques in terms of higher-order theories of gravity produce identical phase-space structures. The problem with these techniques is manifested in the case of Gauss–Bonnet–dilatonic coupled action in the presence of higher-order term, in which case, classical correspondence cannot be established. Here, we explore another technique developed by Buchbinder and their collaborators (BL) and show that it also suffers from the same disease. However, when expressing the action in terms of the three-space curvature, and removing ‘the total derivative terms’, if Horowitz’s formalism or even Dirac’s constraint analysis is pursued, all pathologies disappear. Here, we show that the same is true for BL formalism, which appears to be the simplest of all the techniques to handle.

A quantum complexity lower bound from differential geometry

The Bishop-Gromov bound -- a cousin of the focusing lemmas that Hawking and Penrose used to prove their black hole singularity theorems -- is a differential geometry result that upperbounds the rate of growth of volume of geodesic balls in terms of the Ricci curvature. In this paper, I apply the Bishop-Gromov bound to Nielsen's complexity geometry to prove lowerbounds on the quantum complexity of a typical unitary. For a broad class of penalty schedules, the typical complexity is shown to be exponentially large in the number of qubits. This technique gives results that are tighter than all known lowerbounds in the literature, as well as establishing lowerbounds for a much broader class of complexity geometry metrics than has hitherto been bounded. For some metrics, I prove these lowerbounds are tight. This method realizes the original vision of Nielsen, which was to apply the tools of differential geometry to study quantum complexity.

Molecular Berry curvatures and the adiabatic response tensors.

Adiabatic transport in a many-electron system is expressed in terms of the appropriate Berry curvature, owing to the Niu-Thouless theory [J. Phys. A: Math. Gen. 17, 2453 (1984)]; the main equation is very compact and very general. I address here three paradigmatic adiabatic response tensors-the atomic polar tensor, the atomic axial tensor, and the rotational g factor-and I show that, for all of them, the known formulas do not need an independent proof. They are just case studies of the general expression, for different choices of the curvature's two arguments.

A phase-field model without artificial curvature effect for the crystal growth simulation

In this study, we present a novel phase-field model without artificial curvature effect for the crystal growth simulation. Most phase-field models for dendritic growth are based on the anisotropic Allen–Cahn (AC) equation which models anti-phase domain coarsening in a binary alloy. However, the AC equation intrinsically contains the motion by mean curvature term, i.e., curvature flow, which may have effect on the phases transition. In this work, we remove the artificial curvature effect and propose a novel phase-field model without artificial curvature effect for the dendritic growth simulation. Both two- and three-dimensional numerical tests show that, in the case of the new phase-field model, dendritic growth develops faster than the conventional phase-field model because of the absence of artificial motion by mean curvature effect. In addition, we show that the proposed model has applicability to polycrystal growth.

On the Initialization Problem for Timed-Elastic Bands

Path planning is an important part of navigation for mobile robots. Several approaches have been proposed in the literature based on a discretisation of the map, including A*, Theta*, and RRT*. While these approaches have been widely adopted also in real applications, they tend to generate non-smooth paths, which can be difficult to follow, based on the kinematic and dynamic constraints of the robot. Time-Elastic-Bands (TEB) have also been used in the literature, to deform an original path in real-time to produce a smoother path, and to handle potential local changes in the environment, such as the detection of an unknown obstacle. This work analyses the effects on the overall path for different choices of initial paths fed to TEB. In particular, the produced paths are compared in terms of total distance, curvature, and variation in the desired heading. The optimised version of the solution produced by Theta* shows the highest performance among the considered methods and metrics, and we show that it can be successfully followed by an autonomous bicycle.

Some new characterizations of the Wulff shape

We consider characterizations of a closed orientable connected hypersurface $X:M\to \mathbb R^{n+1}$ in terms of anisotropic higher order mean curvature, which is an extension of the usual mean curvature. On the one hand, we improve the result of Leyla On

Second Curvature Factor and Term Premium in U.S. Yield Curve: Insights from Deep Learning

Second Curvature Factor and Term Premium in U.S. Yield Curve: Insights from Deep Learning

Second Curvature Factor and Term Premium in the U.S. Yield Curve: Insights from Deep Learning

Second Curvature Factor and Term Premium in the U.S. Yield Curve: Insights from Deep Learning