Curvature Expansion Research Articles

Unitarity analysis of general Born-Infeld gravity theories

We develop techniques of analyzing the unitarity of general Born-Infeld gravity actions in $D$-dimensional spacetimes. The determinantal form of the action allows us to find a compact expression quadratic in the metric fluctuations around constant curvature backgrounds. This is highly nontrivial since for the Born-Infeld actions, in principle, infinitely many terms in the curvature expansion should contribute to the quadratic action in the metric fluctuations around constant curvature backgrounds, which would render the unitarity analysis intractable. Moreover in even dimensions, unitarity of the theory depends only on finite number of terms built from the powers of the curvature tensor. We apply our techniques to some four-dimensional examples.

Low energy quantum gravity from the effective average action

Within the effective average action approach to quantum gravity, we recover the low energy effective action as derived in the effective field theory framework, by studying the flow of possibly non-local form factors that appear in the curvature expansion of the effective average action. We restrict to the one-loop flow where progress can be made with the aid of the non-local heat kernel expansion. We discuss the possible physical implications of the scale dependent low energy effective action through the analysis of the quantum corrections to the Newtonian potential.

Born-Infeld-Hořava gravity

We define various Born-Infeld gravity theories in $3+1$ dimensions which reduce to Ho\ifmmode \check{r}\else \v{r}\fi{}ava's model at the quadratic level in small curvature expansion. In their exact forms, our actions provide $z\ensuremath{\rightarrow}\ensuremath{\infty}$ extensions of Ho\ifmmode \check{r}\else \v{r}\fi{}ava's gravity, but when small curvature expansion is used, they reproduce finite $z$ models, including some half-integer ones.

Schwinger-DeWitt technique for quantum effective action in brane induced gravity models

We develop the Schwinger-DeWitt technique for the covariant curvature expansion of the quantum effective action for brane induced gravity models in curved spacetime. This expansion has a part nonanalytic in DGP type scale parameter, leading to the cutoff scale which is given by the geometric average of the mass of the quantum field in the bulk and DGP scale. This cutoff is much higher than the analogous strong coupling scale of the DGP model treated by weak field expansion in the tree-level approximation. The lowest orders of this curvature expansion are calculated for the case of the scalar field in the $(d+1)$-dimensional bulk with the brane carrying the $d$-dimensional kinetic term of this field. The ultraviolet divergences in this model are obtained for a particular case of $d=4$.

Cuscuton and low-energy limit of Hořava-Lifshitz gravity

Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz theory has been recently put forth as a proposal for a renormalizable theory of quantum gravity [1]. It explicitly breaks Lorentz invariance, introducing an apparent extra scalar degree of freedom. I show that the low energy limit of (non-projectible) Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz gravity is uniquely given by the quadratic cuscuton model: a covariant scalar field theory with an infinite speed of sound and a quadratic potential, minimally coupled to Einstein gravity. This implies that the extra scalar is nondynamical to all orders in perturbation theory. Cosmological constraints on the quadratic cuscuton model constrain the low energy Lorentz breaking parameter of Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz theory to $|\ensuremath{\lambda}\ensuremath{-}1|<0.014$. We also point out that the spatial hypersurfaces are constant mean curvature or uniform expansion surfaces and introduce geometrical symmetries that can protect the nondynamical nature of these theories.

Entropy crossover from molecular to macroscopic cavity hydration

The entropies of hydrating molecular and macroscopic non-polar surfaces differ in sign at room temperature, suggesting a size scale at which hydration transitions between these behaviors. Following a curvature expansion for the surface tension, we derive an expression for the radius of a cavity-like solute at which the solvation entropy is zero. This expression accurately predicts the crossover radii observed in a simulation/scaled-particle theory analysis of cavity solvation in water and n-hexane along their saturation curves. Our results indicate differences between water and organic solvents are encoded in the temperature dependence of the surface tension and its leading curvature correction.

Solvation of a Spherical Cavity in Simple Liquids: Interpolating between the Limits

Dissolution of a solute molecule into a solvent necessitates the creation of a cavity devoid of solvent molecules. The cavity solvation free energy is exactly known at both very small and large length scales, but in between it can only be estimated by various approximations. Guided by simulation results for the solvation of small cavities and density functional theory, we analyze the size dependence of the solvation free energy, contact density of solvent molecules, and the interfacial tension for a spherical cavity in a Lennard-Jones fluid or a system of hard spheres. Unlike cavity formation in the hard-sphere system, a quadratic curvature expansion is insufficient to connect smoothly the exact results in the microscopic and macroscopic limits for the cavity surface tension (or equivalently, the contact solvent density) in Lennard-Jones fluids. Considering the sensitivity of solvation to molecular details at small length scales, we conjecture that, for practical purposes, a heuristic approach may be sufficient to link the thermodynamic limit at large length scales and the exact results of cavity formation at very small length scales.

Critical adsorption on nonspherical colloidal particles

We consider a nonspherical colloidal particle immersed in a fluid close to its critical point. The temperature dependence of the corresponding order parameter profile is calculated explicitly. We perform a systematic expansion of the order parameter profile in powers of the local curvatures of the surface of the colloidal particle. This curvature expansion reduces to the short distance expansion of the order parameter profile in the case that the solvent is at the critical composition.

Depletion forces between nonspherical objects

We extend the insertion approach for calculating depletion potentials to the case of nonspherical solutes. We suggest to employ the recently developed curvature expansion of density profiles close to complexly shaped walls. The approximations introduced in the calculation by the use of the curvature expansion and of weight functions for nonspherical objects can be tested independently. As an application for our approach we calculate and discuss the depletion potential between two hard oblate ellipsoids in a solvent of hard spheres. For this system we calculate the entropic force and torque acting on the objects.

Curvature Effects in Ocean Surface Scattering

Curvature effects in EM scattering from ocean surface are described using a generalized curvature expansion of the fields at an elevated nonperfect conducting surface. The new expansion formalism allows us to describe analytically and in general, without separating into different scales, the scattering of EM waves from an undulated ocean surface. The model is exact to first order in curvature for nonshadowing imaging geometry, and obeys the law of reciprocity and tilt invariance. Explicit expressions for EM fields at the surface, including both the projection and the self induced fields, are derived up to first order in surface curvature. Analytic closed form expressions for the scattered fields are derived from the surface field solutions, and applied to the case of backscattering, providing a general expression for the normalized radar cross section. The analytic expression for the normalized radar cross section is implemented for a linear surface model using both the Eulerian and the Lagrangian frame of reference. The results show that the model is capable of describing the expected dependency on polarization, incidence angle, and wind field with minimal restrictions in terms of range of validity. Comparison of polarization ratio shows good agreement between the model and measurements from the Envisat ASAR instrument

Black holes: Quantum trapping and singularity resolution

We describe recent progress on the problem of gravitational collapse in quantum gravity. The model we study is the gravity-scalar field theory in spherical symmetry, which is the original setting for Hawking's semiclassical work on black-hole radiation. We present an approach to full quantization of this model in a Hamiltonian framework, with a view to understanding the late time behaviour of collapsing matter. We give operator realizations of curvature and null expansion variables. The first of these operators has a bounded spectrum indicating curvature singularity avoidance; the second provides a "quantum trapping" criterion for detecting whether a quantum state describes a black hole. It leads to the physical result that the boundary of a quantum black hole is subject to quantum fluctuations. We describe an approach to quantum dynamics, whereby an initial state can be evolved, and tracked to the point of quantum trapping and beyond.PACS Nos.: 04.60.–m, 04.60.Ds, 04.70.Dy

Covariant long-distance modifications of Einstein theory and strong coupling problem

We present generic form of the covariant nonlocal action for infrared modifications of Einstein theory recently suggested within the weak-field curvature expansion. In the lowest order it is determined by two nonlocal operators -- kernels of Ricci tensor and scalar quadratic forms. In models with a low strong-coupling scale this action also incorporates the strongly coupled mode which cannot be perturbatively integrated out in terms of the metric field. This mode enters the action as a Lagrange multiplier for the constraint on metric variables which reduces to the curvature scalar and enforces the latter to vanish on shell. Generic structure of the action is demonstrated on the examples of the Fierz-Pauli and Dvali-Gabadadze-Porrati models and their extensions. The gauge-dependence status of the strong-coupling and VDVZ problems is briefly discussed along with the manifestly gauge-invariant formalism of handling the braneworld gravitational models at classical and quantum levels.

Higher impurity AdS/CFT correspondence in the near-BMN limit

The pp-wave/BMN limit of the AdS/CFT correspondence has exposed the Maldacena conjecture to a new regimen of direct tests. In one line of pursuit, finite-radius curvature corrections to the Penrose limit (which appear in inverse powers of the string angular momentum J) have been found to induce a complicated system of interaction perturbations to string theory on the pp-wave; these have been successfully matched to corresponding corrections to the BMN dimensions of N = 4 super-Yang–Mills (SYM) operators to two loops in the 't Hooft coupling λ. This result is tempered by a well-established breakdown in the correspondence at three loops. Notwithstanding the third-order mismatch, we proceed with this line of investigation by subjecting the string and gauge theories to new and significantly more rigorous tests. Specifically, we extend our earlier results at O ( 1 / J ) in the curvature expansion to include string states and SYM operators with three worldsheet or R-charge impurities. In accordance with the two-impurity problem, we find a perfect and intricate agreement between both sides of the correspondence to two-loop order in λ and, once again, the string and gauge theory predictions fail to agree at third order.

Nonlocal action for long-distance modifications of gravity theory

We construct the covariant nonlocal action for recently suggested long-distance modifications of gravity theory motivated by the cosmological constant and cosmological acceleration problems. This construction is based on the special nonlocal form of the Einstein–Hilbert action explicitly revealing the fact that this action within the covariant curvature expansion begins with curvature-squared terms. Nonlocal form factors in the action of both quantum and brane-induced nature are briefly discussed. In particular, it is emphasized that for certain class of quantum initial value problems nonlocal nature of the Euclidean action does not contradict the causality of effective equations of motion.

Chaotic diffusion on periodic orbits: the perturbed Arnold cat map.

Chaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnold cat map on a cylinder, in a range of perturbation parameters corresponding to an extended structural-stability regime of the system on the torus. The diffusion coefficient is calculated, using the following PO formulas: (1). the curvature expansion of the Ruelle zeta function; (2). the average of the PO winding-number squared, w(2), weighted by a stability factor; (3). the uniform (nonweighted) average of w(2). The results from formulas (1). and (2). agree very well with those obtained by standard methods, for all the perturbation parameters considered. Formula (3). gives reasonably accurate results for sufficiently small parameters corresponding also to cases of a considerably nonuniform hyperbolicity. This is due to uniformity sum rules satisfied by the PO Lyapunov eigenvalues at fixed w. These sum rules follow from general arguments and are supported by much numerical evidence.

Quantum production of black holes

We give a path integral expression for the quantum amplitude to produce a black hole from particle collisions. When expanded about an appropriate classical solution it yields the leading order contribution to the production amplitude in a curvature expansion. Classical solutions describing black hole production resulting from two particle scattering at non-zero impact parameter, combined with our formalism, indicate a geometric cross section for the quantum process. In TeV gravity scenarios these solutions may exhibit large curvatures, but (modulo a mild assumption about quantum gravity) corrections to the semi-classical cross section are small.

Doubletons and 5D higher spin gauge theory

We use Grassmann even spinor oscillators to construct a bosonic higher spin extension hs(2,2) of the five-dimensional anti-de Sitter algebra SU(2,2), and show that the gauging of hs(2,2) gives rise to a spectrum S of physical massless fields with spin s=0,2,4,... that is a UIR of hs(2,2). In addition to a master gauge field which contains the massless s=2,4,.. fields, we construct a scalar master field containing the massless s=0 field, the generalized Weyl tensors and their derivatives. We give the appropriate linearized constraint on this master scalar field, which together with a linearized curvature constraint produces the correct linearized field equations. A crucial step in the construction of the theory is the identification of a central generator K which is eliminated by means of a coset construction. Its charge vanishes in the spectrum S, which is the symmetric product of two spin zero doubletons. We expect our results to pave the way for constructing an interacting theory whose curvature expansion is dual to a CFT based on higher spin currents formed out of free doubletons in the large N limit. Thus, extending a recent proposal of Sundborg (hep-th/0103247), we conjecture that the hs(2,2) gauge theory describes a truncation of the bosonic massless sector of tensionless Type IIB string theory on AdS_5 x S^5 for large N. This implies AdS/CFT correspondence in a parameter regime where both boundary and bulk theories are perturbative.

On curvature expansion of higher-spin gauge theory

We examine the curvature expansion of the field equations of afour-dimensional higher-spin gauge theory extension of anti-de Sittergravity. The theory contains massless particles of spin 0,2,4,... thatarise in the symmetric product of two spin-0 singletons. We cast thecurvature expansion into manifestly covariant form and elucidate thestructure of the equations and observe a significant simplification.

BLACK HOLES OF A MINIMAL SIZE IN STRING GRAVITY

A lower limit for a neutral black hole size is obtained in the frames of the string gravity model with the second order curvature correction. It is shown that this effect remains when the third order curvature correction is also taken into account and argued that such restriction does exist in all perturbative orders of curvature expansions.

Magnetic-field-induced anisotropic curvature elasticity of a vesicle membrane containing magnetic polyions.

Interaction between a charged membrane and the electrolyte solution containing magnetic polyions is considered. A self-magnetic field, which arises due to the nonhomogeneous magnetic particle distribution near a charged membrane increases the effective charge screening length for the parts of a membrane normal to a magnetic field. The anisotropy of elastic properties of a membrane depending on the screening length is calculated on the basis of the curvature expansion. It is shown that due to diminishing of the spontaneous curvature for the parts of a membrane normal to a magnetic field there are two competing mechanisms of the ferrovesicle shape transformation under the influence of a magnetic field-the formation of a prolate shape orientated along a field due to the diminishing action of the demagnetizing field energy and the deformation to a oblate shape due to the decrease in the spontaneous curvature of the parts of a membrane normal to a field.