Nonlocal Modification Research Articles

Nonlocal Modification of the Kerr Metric

In the present paper, we discuss a nonlocal modification of the Kerr metric. Our starting point is the Kerr–Schild form of the Kerr metric gμν=ημν+Φlμlμ. Using Newman’s approach, we identify a shear free null congruence l with the generators of the null cone with apex at a point p in the complex space. The Kerr metric is obtained if the potential Φ is chosen to be a solution of the flat Laplace equation for a point source at the apex p. To construct the nonlocal modification of the Kerr metric, we modify the Laplace operator ▵ by its nonlocal version exp(−ℓ2▵)▵. We found the potential Φ in such an infinite derivative (nonlocal) model and used it to construct the sought-for nonlocal modification of the Kerr metric. The properties of the rotating black holes in this model are discussed. In particular, we derived and numerically solved the equation for a shift of the position of the event horizon due to nonlocality. AlbertaThy 5–23.

On a Different Vision of Kerr Law in Nonlinear Optical Waveguide Theory

This paper focuses on electromagnetic transverse-electric wave propagation in a planar shielded waveguide filled with nonlinear medium. Instead of using the standard local Kerr (cubic) nonlinearity, we suggest a (nonlocal) modification of this law. In comparison with the standard formula, this modification does not produce infinitely many nonperturbative guided modes. In this research, we present the dispersion equation for propagation constants, eigenwaves and propagation constants via explicit formulas. The found results are compared with the ones relating to the corresponding linear problem and the nonlinear one with the classical Kerr’s law. Numerical results are also presented and discussed.

Ghost-free infinite-derivative dilaton gravity in two dimensions

We present the ghost-free infinite-derivative extensions of the Spherically-Reduced Gravity (SRG) and Callan-Giddings-Harvey-Strominger (CGHS) theories in two space-time dimensions. For the case of SRG, we specify the Schwarzschild-type gauge and diagonalise the quadratic action for field perturbations after taking the background fields to be those of the flat-space solution with a linear dilaton. Using the obtained diagonalisation, we construct ghost-free infinite-derivative modifications of the SRG theory. In the context of this modified SRG theory we derive a non-local modification of the linearised spherically-reduced Schwarzschild solution. For the case of CGHS gravity, we work in the conformal gauge and diagonalise the quadratic action associated with this theory for a general background solution. Using these results, we construct the ghost-free infinite-derivative modifications of the CGHS theory and examine non-local modifications to the linearised CGHS black-hole solution.

Non-local mathematical models for aggregation processes in dispersive media

Particles aggregation is widespread in different technological processes and nature, and there are many approaches to modeling this phenomenon. However, the time non-locality effects with witch these processes are often   accompanied leave to be none well elaborated at present. This problem is justified especially in reference to nano-technological processes. The paper is devoted to the non-local modification of Smoluchowski equation that is the key point for describing influence of synchrony and asynchrony delays in aggregation processes for clusters of different orders. The main scientific contribution consists in deriving the non-linear wave equation describing the evolution of different orders clusters concentration under aggregation processes in polydispersed systems with following for the mentioned non-locality. The practical significance lies in the fact that the results obtained can serve as the basis for the engineering calculation of the kinetics of aggregation in polydisperse nano-systems. The research methodology is based on mathematical modeling with the help of the relaxation transfer kernels approach. Succeeding analysis of aggregation processes on the base of submitted ideology can be directed to generalizing master equations with allowing for space non-locality too. The submitted approach opens up fresh opportunities for detailed study of influence of relaxation times hierarchy on the intensity of aggregation and gelation processes in non-crystalline media containing dispersed solid phase.

Non-local averaging filter adaptation for heart sounds amplification on fetus and humans’ phonocardiograms

The design and substantiation of the pNLF filter based on a non-local averaging filter modification is presented. The filter is used for solving the problem of heart sounds amplification on fetal and human phonocardiograms for further tone segmentation and heart rate calculation relevant for fetal monitoring. The parameters for choosing the filter and the prospects for its optimization for specific tasks are presented. The data and results of filtration performed by the pNLF on fetus and human phonocardiograms recorded by using different acoustic sensors are provided.

Non-local imprints of gravity on quantum theory

During the last two decades or so much effort has been devoted to the discussion of quantum mechanics (QM) that in some way incorporates the notion of a minimum length. This upsurge of research has been prompted by the modified uncertainty relation brought about in the framework of string theory. In general, the implementation of minimum length in QM can be done either by modification of position and momentum operators or by restriction of their domains. In the former case we have the so called soccer-ball problem when the naive classical limit appears to be drastically different from the usual one. Starting with the latter possibility, an alternative approach was suggested in the form of a band-limited QM. However, applying momentum cutoff to the wave-function, one faces the problem of incompatibility with the Schrödinger equation. One can overcome this problem in a natural fashion by appropriately modifying Schrödinger equation. But incompatibility takes place for boundary conditions as well. Such wave-function cannot have any more a finite support in the coordinate space as it simply follows from the Paley–Wiener theorem. Treating, for instance, the simplest quantum-mechanical problem of a particle in an infinite potential well, one can no longer impose box boundary conditions. In such cases, further modification of the theory is in order. We propose a non-local modification of QM, which has close ties to the band-limited QM, but does not require a hard momentum cutoff. In the framework of this model, one can easily work out the corrections to various processes and discuss further the semi-classical limit of the theory.

Nonlocal SU(5) GUT

We show that in nonlocal generalization of standard nonsupersymmetric SU(5) GUT, it is possible to solve the problems with the proton lifetime and the Weinberg angle without introduction of additional particles in the spectrum of the theory. Nonlocal scale [Formula: see text] responsible for ultraviolet cutoff coincides (up to some factor) with GUT scale [Formula: see text]. We find that in the simplest nonlocal modification of the SU(5) model, [Formula: see text]GeV. In the general case, the value of [Formula: see text] is an arbitrary and the most interesting option [Formula: see text] could be realized.

Ultrarelativistic charged and magnetized objects in nonlocal ghost-free electrodynamics

We study a non-local ghost-free Lorentz invariant modification of the Maxwell equations in four- and higher-dimensional flat spacetimes. We construct solutions of these equations for stationary charged and magnetized objects and use them to find the field created by such objects moving with the speed of light.

Analytic infinite derivative gravity, R2-like inflation, quantum gravity and CMB

Emergence of [Formula: see text] inflation, which is the best fit framework for CMB observations till date, comes from the attempts to attack the problem of quantization of gravity which in turn have resulted in the trace anomaly discovery. Further developments in trace anomaly and different frameworks aiming to construct quantum gravity indicate an inevitability of nonlocality in fundamental physics at small time and length scales. A natural question would be to employ the [Formula: see text] inflation as a probe for signatures of nonlocality in the early Universe physics. Recent advances of embedding [Formula: see text] inflation in a string theory inspired nonlocal gravity modification provide very promising theoretical predictions connecting the nonlocal physics in the early Universe and the forthcoming CMB observations.

On the Kuzmin model in fractional Newtonian gravity

Fractional Newtonian gravity, based on the fractional generalization of Poisson's equation for Newtonian gravity, is a novel approach to Galactic dynamics aimed at providing an alternative to the dark matter paradigm through a non-local modification of Newton's theory. We provide an in-depth discussion of the gravitational potential for the Kuzmin disk within this new approach. Specifically, we derive an integral and a series representation for the potential, we verify its asymptotic behavior at large scales, and we provide illuminating plots of the resulting equipotential surfaces.

Continuum simulation for regularized non-local μ(I) model of dense granular flows

In this work, we implement the local μ(I) rheology law and its non-local modification in a PISO-VOF numerical scheme with a sharp-interface-capturing THINC method for two-dimensional dense granular flows in both steady and transient states. The non-local effect on the constitutive relation is addressed by the gradient expansion model to account for additional momentum transport in view of the spatial variation of flow inertial number and the stress model singularity near the static state, I=0, is handled by the Bercovier-Engelman regularization scheme. Our simulations provide the first numerical evidence for the crucial role of non-local momentum transport on degrading the velocity profiles predicted with a local rheology model as those reported from two-dimensional discrete element simulations. For example, we successfully reproduce the sub-Bagnold velocity profile for steady inclined flows of height comparable to the Hstop and capture how the linear velocity profile in a simple shear creeping flow is degraded to a S-shape. More importantly, we exploit the current solver to study the layer-accumulated deviation, ε, between the local and the non-local velocity profile (Bagnold to its degradation) for inclined flows. For steady flows, ε decays monotonically with flow Froude number Fr and a critical Frc≈0.25 is detected below which ε rises rapidly necessitating a non-local constitutive relation. For a layer developing from rest to its steady state, the time evolution of ε(t) shows further dependence on flow height and can be collapsed into a monotonically growing trend with local instantaneous inertial number I(t). A critical Icr is also determined and the local model prediction can be erroneous whenever I(t)<Icr. Interestingly, the result for simple shear flows without gravity also confirms that non-local effect becomes non-negligible when the macroscopic inertial number drops to the order of Icr. Finally, we simulate the two-dimensional column collapse flows with both local and non-local rheology and find a shorter run-out distance with the presence of non-local momentum transport.

Some Cosmological Solutions of a New Nonlocal Gravity Model

In this paper, we investigate a nonlocal modification of general relativity (GR) with action S = 1 16 π G ∫ [ R − 2 Λ + ( R − 4 Λ ) F ( □ ) ( R − 4 Λ ) ] − g d 4 x , where F ( □ ) = ∑ n = 1 + ∞ f n □ n is an analytic function of the d’Alembertian □. We found a few exact cosmological solutions of the corresponding equations of motion. There are two solutions which are valid only if Λ ≠ 0 , k = 0 , and they have no analogs in Einstein’s gravity with cosmological constant Λ . One of these two solutions is a ( t ) = A t e Λ 4 t 2 , that mimics properties similar to an interference between the radiation and the dark energy. Another solution is a nonsingular bounce one a ( t ) = A e Λ t 2 . For these two solutions, some cosmological aspects are discussed. We also found explicit form of the nonlocal operator F ( □ ) , which satisfies obtained necessary conditions.

Non-Gaussianities and tensor-to-scalar ratio in non-local R2-like inflation

In this paper we will study R2-like inflation in a non-local modification of gravity which contains quadratic in Ricci scalar and Weyl tensor terms with analytic infinite derivative form-factors in the action. It is known that the inflationary solution of the local R + R2 gravity remains a particular exact solution in this model. It was shown earlier that the power spectrum of scalar perturbations generated during inflation in the non-local setup remains the same as in the local R + R2 inflation, whereas the power spectrum of tensor perturbations gets modified due to the non-local Weyl tensor squared term. In the present paper we go beyond 2-point correlators and compute the non-Gaussian parameter fNL related to 3-point correlations generated during inflation, which we found to be different from those in the original local inflationary model and scenarios alike based on a local gravity. We evaluate non-local corrections to the scalar bi-spectrum which give non-zero contributions to squeezed, equilateral and orthogonal configurations. We show that fNL∼ O(1) with an arbitrary sign is achievable in this model based on the choice of form-factors and the scale of non-locality. We present the predictions for the tensor-to-scalar ratio, r, and the tensor tilt, nt. In contrast to standard inflation in a local gravity, here the possibility nt> 0 is not excluded. Thus, future CMB data can probe non-local behaviour of gravity at high space-time curvatures.

Structure formation in the new Deser-Woodard nonlocal gravity model

We consider the structure formation in the nonlocal gravity model proposed recently by Deser and Woodard (DW-2019 model), which can not only reproduce the ΛCDM cosmology without fine-tuning puzzle but also may provide a screening mechanism for free. By using the direct numerical method of the reconstructing technique, the nonlocal distortion function f(Y) is fixed as f(Y)≃e2.153(Y−16.97) which has a small deviation with the fitted function proposed by Deser and Woodard. Based on the numerical results, we plotted the curve of the growth rate fσ8(z) under the DW-2019 model, which shows this model is not ruled out by the fσ8 data from the Redshift-space distortions measurements. The evolving curve of the growth rate has a distinct plummet at z≃0.39, which is a great difference with the DW model. The possible reason is that the DW-2019 model provides the strong nonlocal effect, which behaves as the anisotropic effect to influence the matter perturbation in the low-redshift range. Finally the qualitative analysis of the screening mechanism is discussed by considering the spacial dependence of the nonlocal modification in the small-scale range.

Cosmological Solutions of Some Nonlocal Gravity Models

Significant phenomenological success and nice theoretical properties of general relativity (GR) are well known. However, GR is not a complete theory of gravity. Hence, there are many attempts to modify GR. One of the current approaches to a more complete theory of gravity is a nonlocal modification of GR. The nonlocal gravity approach, which we consider here without matter, is based on the action $$S=(16 \pi G)^{-1} \int \sqrt{-g}(R-2 \Lambda+P(R) \mathcal{F}(\square) Q(R)) d^{4} x$$, where R is the scalar curvature, Γ is the cosmological constant, P(R) and Q(R) are some differentiable functions of R, and $$\mathcal{F}(\square)=\sum\nolimits_{n=1}^{+\infty} f_{n} \square^{n}$$ is an analytic function of the corresponding d’Alembert operator □. We present here a brief review of some general properties and cosmological solutions for some specific functions P(R) and Q(R).

Modified gravitational-wave propagation and standard sirens

Studies of dark energy at advanced gravitational-wave (GW) interferometers normally focus on the dark energy equation of state $w_{\rm DE}(z)$. However, modified gravity theories that predict a non-trivial dark energy equation of state generically also predict deviations from general relativity in the propagation of GWs across cosmological distances, even in theories where the speed of gravity is equal to $c$. We find that, in generic modified gravity models, the effect of modified GW propagation dominates over that of $w_{\rm DE}(z)$, making modified GW propagation a crucial observable for dark energy studies with standard sirens. We present a convenient parametrization of the effect in terms of two parameters $(\Xi_0,n)$, analogue to the $(w_0,w_a)$ parametrization of the dark energy equation of state, and we give a limit from the LIGO/Virgo measurement of $H_0$ with the neutron star binary GW170817. We then perform a Markov Chain Monte Carlo analysis to estimate the sensitivity of the Einstein Telescope (ET) to the cosmological parameters, including $(\Xi_0,n)$, both using only standard sirens, and combining them with other cosmological datasets. In particular, the Hubble parameter can be measured with an accuracy better than $1\%$ already using only standard sirens while, when combining ET with current CMB+BAO+SNe data, $\Xi_0$ can be measured to $0.8\%$ . We discuss the predictions for modified GW propagation of a specific nonlocal modification of gravity, recently developed by our group, and we show that they are within the reach of ET. Modified GW propagation also affects the GW transfer function, and therefore the tensor contribution to the ISW effect.

Gravitational-wave luminosity distance in modified gravity theories

In modified gravity the propagation of gravitational waves (GWs) is in general different from that in general relativity. As a result, the luminosity distance for GWs can differ from that for electromagnetic signals, and is affected both by the dark energy equation of state $w_{\rm DE}(z)$ and by a function $\delta(z)$ describing modified propagation. We show that the effect of modified propagation in general dominates over the effect of the dark energy equation of state, making it easier to distinguish a modified gravity model from $\Lambda$CDM. We illustrate this using a nonlocal modification of gravity, that has been shown to fit remarkably well CMB, SNe, BAO and structure formation data, and we discuss the prospects for distinguishing nonlocal gravity from $\Lambda$CDM with the Einstein Telescope. We find that, depending on the exact sensitivity, a few tens of standard sirens with measured redshift at $z\sim 0.4$, or a few hundreds at $1 < z < 2$, could suffice.

The 1.5 post-Newtonian radiative quadrupole moment in the context of a nonlocal field theory of gravity

We recently suggested a nonlocal modification of Einstein’s field equations in which Newton’s constant G was promoted to a covariant differential operator . The latter contains two independent contributions which operate respectively in the infrared (IR) and ultraviolet (UV) energy regimes. In the light of the recent direct gravitational radiation measurements we aim to determine the UV-modified 1.5 post-Newtonian radiative quadrupole moment of a generic n-body system. We eventually use these preliminary results in the context of a binary system and observe that in the limit vanishing UV parameters we precisely recover the corresponding general relativistic results. Moreover we notice that the leading order deviation of the UV-modified radiative quadrupole moment numerically coincides with findings obtained in the framework of calculations performed previously in the context of the perihelion precession of Mercury.

On nonlocally interacting metrics, and a simple proposal for cosmic acceleration

We propose a simple, nonlocal modification to general relativity (GR) on large scales, which provides a model of late-time cosmic acceleration in the absence of the cosmological constant and with the same number of free parameters as in standard cosmology. The model is motivated by adding to the gravity sector an extra spin-2 field interacting nonlocally with the physical metric coupled to matter. The form of the nonlocal interaction is inspired by the simplest form of the Deser-Woodard (DW) model, α R1/□R, with one of the Ricci scalars being replaced by a constant m2, and gravity is therefore modified in the infrared by adding a simple term of the form m21/□R to the Einstein-Hilbert term. We study cosmic expansion histories, and demonstrate that the new model can provide background expansions consistent with observations if m is of the order of the Hubble expansion rate today, in contrast to the simple DW model with no viable cosmology. The model is best fit by w0∼−1.075 and wa∼0.045. We also compare the cosmology of the model to that of Maggiore and Mancarella (MM), m2R1/□2R, and demonstrate that the viable cosmic histories follow the standard-model evolution more closely compared to the MM model. We further demonstrate that the proposed model possesses the same number of physical degrees of freedom as in GR. Finally, we discuss the appearance of ghosts in the local formulation of the model, and argue that they are unphysical and harmless to the theory, keeping the physical degrees of freedom healthy.

Transmission of information in nonlocal field theories

The signaling between two observers in 3+1 dimensional flat spacetime coupled locally to a non-local field is considered. We show that in the case where two observers are purely timelike related -- so that an exchange of on-shell massless quanta cannot occur -- signaling is still possible because of a violation of Huygens' principle. In particular, we show that the signaling is exponentially suppressed by the non-locality scale. Furthermore, we consider the case in which the two observers are light-like related and show that the non-local modification to the local result is polynomially suppressed in the non-locality scale. This may have implications for phenomenological tests of non-local theories.