Noncommutative Parameter Research Articles

Superradiance scattering of electromagnetic and gravitational fields and thin accretion disk around non-commutating Kerr black hole

We consider the non-commutative (NC) Kerr black hole where the mass of the central object is smeared over a region of linear size b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{b}$$\\end{document}, b is the strength of the NC character of spacetime. For the spacetime under consideration, we calculate the amplification factor for electromagnetic and gravitational fields and study various properties of a thin accretion disk. The expression for the amplification factor is obtained with the help of the asymptotic matching technique. The amplification factor is then plotted against frequency for various values of the spin a and the NC parameter b. Though the amplification factor increases with a but decreases with b, the cut-off frequency up to which we have amplification increases with a and b. We then study the effect of the spin and the NC nature of spacetime on the energy flux, temperature distribution, emission spectrum, energy conversion efficiency, and the radius of the innermost stable circular orbit of a thin accretion disk around the black hole with the help of the steady-state Novikov–Thorne model. Our study reveals that these quantities increase with the spin and the NC parameter. We also find that the disk around the NC Kerr black is hotter and more luminous than that around the Kerr black hole and the NC Schwarzschild black hole. We can conclusively infer from our investigation that the NC nature of spacetime has a significant impact on the superradiance phenomenon as well as on various properties of thin accretion disks.

Non-Commutativity and its Role in Constant-Roll Inflation Models with Non-Minimal Coupling Constrained by Swampland Conjectures

Abstract In this paper, using Hamiltonian formalism, we obtain solutions for constant-roll inflation according to the non-commutativity and the non-minimal coupling field of Lagrangian. We consider three different types of couplings: power-law, exponential, and logarithmic. Then, by plotting some figures, we study the effects of these coupling in constant-roll inflation with non-commutative parameters. We identify and specify the permissible regions of each case about swampland conjecture and determine the best model. We find that the exponential coupling, logarithmic coupling, and power-law coupling with $\theta>0$ agree with the dS swampland conjecture. These couplings give us similar results in both cases, some of which are compatible and some incompatible with the dS swampland conjectures. Moreover, $\theta>0$ is more compatible than $\theta<0$ and the consistency value in the second boundary condition is much higher than in the first. The order of better compatibility of couplings with the Swampland Conjecture is ranked as follows: exponential non-minimal coupling, logarithmic non-minimal coupling, and power-law non-minimal coupling. For each type of coupling, we calculate the values of the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ for two different potentials and compare them with the observational data from Planck 2018. We also determine the range of the free parameters $(a,b,q)$ of the further refining de Sitter swampland conjecture (FRDSSC) that make the model consistent with the conjecture. We find that the model satisfies the FRDSSC for all types of couplings and both potentials, with some constraints on the parameters.

Noncommutative of Klein–Gordon and Schrödinger equations in the background of the improved Hua plus modified Eckart potential model in 3D-(R/NR)NCQS symmetries: Spectrum and thermodynamic properties

The impact of deformation space on the physical characteristics of diverse physics systems has been thoroughly investigated in research papers. In this work, we study the deformed Klein–Gordon equation (DKGE) in the three-dimensional relativistic non-commutative quantum space (3D-RNCQS) regime by using the improved Hua plus modified Eckart potential (IHPMEP) model. For this consideration, the DKGE in the 3D-RNCQS regime is solved using the standard perturbation theory and the well-known Bopp’s shifts method with the Greene–Aldrich approximation to the centrifugal barrier. The new relativistic energy equation and eigenfunction for the IHPMEP in the presence of deformation space-space for the heterogeneous (CO, HF, and NO) and homogeneous (N2, H2, and Li2) diatomic molecules are obtained to be sensitive to the atomic quantum numbers ([Formula: see text] and [Formula: see text]), the mixed potential depths ([Formula: see text], and [Formula: see text]), the inverse of the screening parameter [Formula: see text], and non-commutativity parameters ([Formula: see text], [Formula: see text], and [Formula: see text]). Analysis is performed on the non-relativistic limit of new energy spectra. By appropriately adjusting the combined potential parameters, we analyze the obtained new bound state eigenvalues of the DKGE and deformed Schrödinger equation with the IHPMEP in 3D-NCQS symmetries and obtain the new modified Eckart potential, the modified Hua potential, the modified Morse potential, and the modified Pöschl–Teller potential. Within the framework of the 3D-NRNCQS regime, the homogeneous and heterogeneous composite systems under IHPMEP models are examined. A thorough investigation is carried out into the impact of space-space deformation on the thermal parameters of the IHPMEP, including the partition function, mean energy, free energy, specific heat, and entropy. This work is of a fundamental absorbability nature and pedagogical interest in atomic and molecular physics.

Quantization of length in spaces with position-dependent noncommutativity

In this paper, we present a novel approach to quantizing the length in noncommutative spaces with positional-dependent noncommutativity. The method involves constructing ladder operators that change the length not only along a plane but also along the third direction due to a noncommutative parameter that is a combination of canonical/Weyl–Moyal-type and Lie algebraic-type. The primary quantization of length in canonical-type noncommutative space takes place only on a plane, while in the present case, it happens in all three directions. We establish an operator algebra that allows for the raising or lowering of eigenvalues of the operator corresponding to the square of the length. We also attempt to determine how the obtained ladder operators act on different states and work out the eigenvalues of the square of the length operator in terms of eigenvalues corresponding to the ladder operators. We conclude by discussing the results obtained.

Dirac Theory in Noncommutative Phase Spaces

Based on the position and momentum of noncommutative relations with a noncanonical map, we study the Dirac equation and analyze its parity and time reversal symmetries in a noncommutative phase space. Noncommutative parameters can be endowed with the Planck length and cosmological constant such that the noncommutative effect can be interpreted as an effective gauge potential or a (0,2)-type curvature associated with the Plank constant and cosmological constant. This provides a natural coupling between dynamics and spacetime geometry. We find that a free Dirac particle carries an intrinsic velocity and force induced by the noncommutative algebra. These properties provide a novel insight into the Zitterbewegung oscillation and the physical scenario of dark energy. Using perturbation theory, we derive the perturbed and nonrelativistic solutions of the Dirac equation. The asymmetric vacuum gaps of particles and antiparticles reveal the particle–antiparticle symmetry breaking in the noncommutative phase space, which provides a clue to understanding the physical mechanisms of particle–antiparticle asymmetry and quantum decoherence through quantum spacetime fluctuation.

Supersymmetric Quantum Mechanics on a noncommutative plane through the lens of deformation quantization

A gauge invariant mathematical formalism based on deformation quantization is outlined to model an N=2 supersymmetric system of a spin 1/2 charged particle placed in a nocommutative plane under the influence of a vertical uniform magnetic field. The noncommutative involutive algebra (C∞(R2)[[ϑ]],∗r) of formal power series in ϑ with coefficients in the commutative ring C∞(R2) was employed to construct the relevant observables, viz., SUSY Hamiltonian H, supercharge operator Q and its adjoint Q† all belonging to the 2 × 2 matrix algebra M2(C∞(R2)[[ϑ]],∗r) with the help of a family of gauge-equivalent star products ∗r. The energy eigenvalues of the SUSY Hamiltonian all turned out to be independent of not only the gauge parameter r but also the noncommutativity parameter ϑ. The nontrivial Fermionic ground state was subsequently computed associated with the zero energy which indicates that supersymmetry remains unbroken in all orders of ϑ. The Witten index for the noncommutative SUSY Landau problem turns out to be −1 corroborating the fact that there is no broken supersymmetry for the model we are considering.

Metric perturbations in noncommutative gravity

We use the framework of Hopf algebra and noncommutative differential geometry to build a noncommutative (NC) theory of gravity in a bottom-up approach. Noncommutativity is introduced via deformed Hopf algebra of diffeomorphisms by means of a Drinfeld twist. The final result of the construction is a general formalism for obtaining NC corrections to the classical theory of gravity for a wide class of deformations and a general background. This also includes a novel proposal for noncommutative Einstein manifold. Moreover, the general construction is applied to the case of a linearized gravitational perturbation theory to describe a NC deformation of the metric perturbations. We specifically present an example for the Schwarzschild background and axial perturbations, which gives rise to a generalization of the work by Regge and Wheeler. All calculations are performed up to first order in perturbation of the metric and noncommutativity parameter. The main result is the noncommutative Regge-Wheeler potential. Finally, we comment on some differences in properties between the Regge-Wheeler potential and its noncommutative counterpart.

Exploring non-commutativity as a perturbation in the Schwarzschild black hole: quasinormal modes, scattering, and shadows

In this work, by a novel approach to studying the scattering of a Schwarzschild black hole, the non-commutativity is introduced as perturbation. We begin by reformulating the Klein–Gordon equation for the scalar field in a new form that takes into account the deformed non-commutative spacetime. Using this formulation, an effective potential for the scattering process is derived. To calculate the quasinormal modes, we employ the WKB method and also utilize fitting techniques to investigate the impact of non-commutativity on the scalar quasinormal modes. We thoroughly analyze the results obtained from these different methods. Moreover, the greybody factor and absorption cross section are investigated. Additionally, we explore the behavior of null geodesics in the presence of non-commutativity. Specifically, we examine the photonic, and shadow radius as well as the light trajectories for different non-commutative parameters. Therefore, by addressing these various aspects, we aim to provide a comprehensive understanding of the influence of non-commutativity on the scattering of a Schwarzschild-like black hole and its implications for the behavior of scalar fields and light trajectories.

A noncommutative Bianchi I model with radiation

In this work, we study the dynamical evolution of a homogeneous and anisotropic, noncommutative (NC) Bianchi I (BI) model coupled to a radiation perfect fluid. Our first motivation is determining if the present model tends to a homogeneous and isotropic NC Friedmann–Robertson–Walker (FRW) model, during its evolution. In order to simplify our task, we use the Misner parametrization of the BI metric. In terms of that parametrization the BI metric has three metric functions: the scale factor [Formula: see text] and the two parameters [Formula: see text], which measure the spatial anisotropy of the model. Our second motivation is trying to describe the present accelerated expansion of the universe using noncommutativity (NCTY). The NCTY is introduced by two nontrivial Poisson brackets between some geometrical as well as matter variables of the model. We recover the description in terms of commutative variables by introducing some variables transformations that depend on the NC parameter. Using those variables’ transformations, we rewrite the total NC Hamiltonian of the model in terms of commutative variables. From the resulting Hamiltonian, we obtain the dynamical equations for a generic perfect fluid. In order to solve these equations, we restrict our attention to a model in which the perfect fluid is radiation. We solve, numerically, these equations and compare the NC solutions to the corresponding commutative ones. The comparison shows that the NC model may be considered as a possible candidate for describing the accelerated expansion of the universe. Finally, we obtain estimates for the NC parameter and compare the main results of the NC BI model coupled to radiation with the same NC BI model coupled to other perfect fluids. As our main result, we show that the solutions, after some time, produce an isotropic universe. Based on that result, we can speculate that the solutions may represent an initial anisotropic stage of our Universe, that later, due to the expansion, became isotropic.

Gravitational probe of ꝗuantum spacetime

A quest for phenomenological footprints of quantum gravity is among the central scientific tasks in the rising era of gravitational wave astronomy. We study gravitational wave dynamics within the noncommutative geometry framework, based on a Drinfeld twist and newly proposed noncommutative Einstein equation, and obtain the leading quantum correction to Regge-Wheeler potential up to first order in the noncommutativity parameter. By calculating the quasinormal mode frequencies we show that the noncommutative Schwarzschild black hole remains stable under axial gravitational perturbations.

Quasinormal modes in noncommutative Schwarzschild black holes

We investigate the quasinormal modes of a massless scalar field in a Schwarzschild black hole, which is deformed due to noncommutative corrections. We introduce the deformed Schwarzschild black hole solution, which depends on the noncommutative parameter Θ. We then extract the master equation as a Schrödinger-like equation, giving the explicit expression of the effective potential which is modified due to the noncommutative corrections. After that, we solve the master equation numerically. The significance of these results is twofold. Firstly, our results can be related to the detection of gravitational waves by the near future gravitational wave detectors, such as LISA, which will have a significantly increased accuracy. In particular, these observed gravitational waves produced by binary strong gravitational systems have oscillating modes which can provide valuable information. Secondly, our results can serve as an additional tool to test the predictions of GR, as well as to examine the possible detection of this kind of gravitational corrections.

Tuning the separability in noncommutative space

With the help of the generalized Peres–Horodecki separability criterion (Simon’s condition) for a bipartite Gaussian state, we have studied the separability of the noncommutative (NC) space coordinate degrees of freedom. Non-symplectic nature of the transformation between the usual commutative space and NC space restricts the straightforward use of Simon’s condition in NCS. We have transformed the NCS system to an equivalent Hamiltonian in commutative space through the Bopp shift, which enables the utilization of the separability criterion. To make our study fairly general and to analyze the effect of parameters on the separability of bipartite state in NC-space, we have considered a bilinear Hamiltonian with time-dependent (TD) parameters, along with a TD external interaction, which is linear in field modes. The system is transformed (Sp(4,R)) into canonical form keeping the intrinsic symplectic structure intact. The solution of the TD-Schrödinger equation is obtained with the help of the Lewis–Riesenfeld invariant method (LRIM). Expectation values of the observables (thus the covariance matrix) are constructed from the states obtained from LRIM. It turns out that the existence of the NC parameters in the oscillator determines the separability of the states. In particular, for isotropic oscillators, the separability condition for the bipartite Gaussian states depends on specific values of NC parameters. Moreover, particular anisotropic parameter values for the oscillator may cease the separability. In other words, both the deformation parameters (θ, η) and parameter values of the oscillator (mass, frequency) are important characteristics for the separability of bipartite Gaussian states. Thus tuning the parameter values, one can destroy or recreate the separability of states. With the help of a toy model, we have demonstrated how the tuning of a TD-NC space parameter affects the separability.

Non-Commutative Classical and Quantum Fractionary Cosmology: FRW Case

In this work, we will explore the effects of non-commutativity in fractional classical and quantum schemes using the flat Friedmann–Robertson–Walker (FRW) cosmological model coupled to a scalar field in the K-essence formalism. In previous work, we have obtained the commutative solutions in both regimes in the fractional framework. Here, we introduce non-commutative variables, considering that all minisuperspace variables qnci do not commute, so the symplectic structure was modified. In the quantum regime, the probability density presents a new structure in the scalar field corresponding to the value of the non-commutative parameter, in the sense that this probability density undergoes a shift back to the direction of the scale factor, causing classical evolution to arise earlier than in the commutative world.

The optical features of noncommutative charged 4D-AdS-Einstein–Gauss–Bonnet black hole: shadow and deflection angle

In this paper, we have explored the optical characteristics, namely the shadow and the deflection angle, inherent to the solution of a 4D-AdS-Einstein–Gauss–Bonnet black hole. This solution, which finds its inspiration in noncommutative geometry, had previously been established in our previous work. The radius of the shadow was determined using the Hamilton-Jacobi method and the Carter separation. Our results revealed that the presence of noncommutativity in the background of spacetime impacts the variation of the shadow radius. More specifically, we have demonstrated that an increase in the parameter θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta $$\\end{document} induces a decrease in the radius of the shadow. In a similar way, analogous observations have been made by studying the variation of the electric charge Q. The noncommutative parameter θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta $$\\end{document} and the electric charge Q have been constrained regarding the EHT observation data of the M87* and Sgr A* black holes. Furthermore, the angle of deflection, which is the outcome of lensing by the black hole, has been derived following the Ishihara et al. approach for a receiver and source positioned at finite distances from the black hole in an asymptotically non-flat spacetime. The impact of the noncommutative parameter θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta $$\\end{document} and the charge Q of the black hole are hence analyzed, and our results depict that these parameters have a significant influence on the angle at which light is deflected by the gravitational field of the black hole.

Thin-shell gravastar in a noncommutative BTZ geometry

In this paper, we build a thin-shell gravastar model within a noncommutative BTZ geometry. For this, we consider a noncommutative BTZ metric in the inner region and a geometry associated with a BTZ solution in the outer region, joined by the generalized join technique. After investigating the inner spacetime, surface and outer spacetime, we observe that there is a surface energy density and surface pressure, such as to make gravastar stable. This effect persists even when the cosmological constant is zero. Besides, we found a bound for the noncommutativity parameter. In addition, we examine the thermodynamics of the noncommutative BTZ black hole in Schwarzschild-type form in three-dimensional spacetime. We also check the stability condition by calculating the specific heat capacity, as well as for the formation of black hole remnants.

New spin and p-spin symmetries of the deformed Dirac equation for the IMRQHPs including the improved YLT interaction in three-dimensional extended relativistic quantum mechanics symmetries

In this paper, the modified Dirac equation (MDE) has been solved approximately for improved Manning–Rosen plus quasi-Hellman potentials (IMRQHPs), including the improved Yukawa tensor interaction under new spin symmetry and pseudospin symmetry for arbitrary spin–orbit number [Formula: see text], an appropriate approximation employed on the centrifugal terms in the symmetries of three-dimensional extended relativistic quantum mechanics (3D-ERQM). This potential is a superposition of Manning–Rosen plus quasi-Hellman potentials and some other exponential terms. Through the application of both new approximations to deal with the centrifugal term, Bopp’s shift method and the independent-time perturbation theory method, the recent modified approximate energy corrections under IMRQHPs are obtained for nuclei [Formula: see text]O and [Formula: see text]F and (O2, I2, N2, H2, LiH, CO and NO) diatomic molecules in 3D-ERQM and three-dimensional extended non-relativistic quantum mechanics (3D-ENRQM) symmetries. The recent values that we get appear sensitive to [Formula: see text], which are known as the discrete atomic quantum numbers, the mixed potential depths ([Formula: see text], [Formula: see text]) and [Formula: see text], the range of the potential [Formula: see text] and non-commutativity parameters [Formula: see text]. In both 3D-ERQM and 3D-ENRQM symmetries, we show that the recent corrections obtained on the new bound states under IMRQHPs are infinitesimal to the principal part of energy in the ordinary cases of 3D-RQM and 3D-NRQM symmetries. In the new symmetries of 3D-ERQM symmetries, it is not possible to get the exact analytical solutions [Formula: see text] and [Formula: see text], only the approximate solutions are possible. In addition, we discussed in detail the non-relativistic study of the studied mixed potentials. Four special cases, i.e. we investigated some special cases in the context of modified Schrödinger theories. In the framework of known relativistic quantum mechanics, we have clearly demonstrated that the modified Schrödinger equation can be represented as the Dirac equation under the influence of IMRQHPs.

Towards gravitational QNM spectrum from quantum spacetime

The effective potential for the axial mode of gravitational wave on noncommutative Schwarzschild background is presented. Noncommutativity is introduced via deformed Hopf algebra of diffeomorphisms by means of a semi-Killing Drinfeld twist. The analysis is performed up to the first order in perturbation of the metric and noncommutativity parameter. This results in a modified Regge-Wheeler potential with the strongest differences in comparison to the classical Regge-Wheeler potential being near the horizon.

Study of He–Mckellar–Wilkens Effect in Noncommutative Space

The He–McKellar–Wilkens (HMW) effect in noncommutative space has been explored through two distinct methodologies. One approach treats the neutral particle, which harbors a permanent electric dipole moment, as an unstructured entity, while the other approach considers the neutral particle as a composite system consisting of a pair of oppositely charged particles. To preserve gauge symmetry, we apply the Seiberg–Witten map. Surprisingly, both of these approaches converge on the same result. They independently confirm that, up to the first order of the noncommutative parameter (NCP), no corrections are observed in the phase of the HMW effect. Remarkably, these two approaches, although founded on fundamentally different mechanisms, yield identical conclusions.

Casimir Wormholes driven by non-commutative geometries in higher dimensional Einstein Gauss–Bonnet gravity

This manuscript investigates the construction of a new class of wormhole solutions motivated by non-commutative geometry in fusion with Casimir wormholes in Einstein Gauss–Bonnet (EGB) gravity . It is not likely to ensure that the violation at small scales is significant enough to produce a macroscopic wormhole by depending merely on the Casimir effect. In our strategy, we solely utilised modifications to the energy–momentum tensor (EMT) in the non-commutative background, coupled with the impact of Casimir phenomena. On the other hand, the Einstein tensor remains unchanged in the Einstein field equations. In this regard, we have assumed four cases of non-commutative effects combined with the Casimir wormholes. We have investigated the non-commutative effects using Gaussian and Lorentzian distributions. Also, we incorporated the Casimir and Generalised Uncertainty Principle (GUP) corrected Casimir wormholes to study the basic features of wormhole solutions. The dynamics of a theory that relates the Gauss–Bonnet (GB) parameters (μ) and non-commutative parameter (β) have been addressed graphically, with a particular focus on analysing null energy conditions (NEC) through contour plots to identify the presence of exotic matter. Furthermore, embedding diagrams have been used to investigate the geometry of newly produced asymptotically flat wormholes. Additionally, the active gravitational mass has been calculated and plotted up to the radius r in the area around the wormhole throat. We have discussed equilibrium conditions to analyse the stability of obtained wormhole solutions. Finally, to understand the complexity of wormhole solutions, we have examined the complexity factor graphically.

Is a loopy and noncommutative early Universe viable?

We conduct a (pre-)inflationary dynamics study of the chaotic quadratic potential within the framework of a simple noncommutative extension of effective loop quantum cosmology put forward recently. It is concluded that, for typically small values of the noncommutativity parameter, the resulting (pre-)inflationary scenario is essentially indistinguishable from the one corresponding to standard loop quantum cosmology.