arXiv subjects

Andjelo Samsarov

Publications and source records attributed to Andjelo Samsarov.

At least 19 recordsLinked to original sources

arXiv2026

Noncommutative Regge-Wheeler potential: some nonperturbative results

We study the gravitational perturbation theory of black holes in noncommutative spacetimes with noncommutativity of the type $[t\stackrel{\star}{,} r] = i a αA(r)$ and $[φ\stackrel{\star}{,} r] = i a βA(r)$ for arbitrary $A(r)$, which includes several Moyal-type spaces and also the $κ$-Minkowski space. The main result of this paper is an analytical expression for the effective potential of the axial perturbation modes, valid to all orders in the noncommutativity parameter. This is achieved by evaluating the $\star$-products using translations in the radial direction, i.e., Bopp shift. We comment on various regimes, such as Planck-scale black holes, where the noncommutativity length scale is of the same order of magnitude as the black hole horizon.

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arXiv2025

Dirac Quasinormal Modes in Noncommutative Reissner-Nordström Black Holes

Noncommutative (NC) geometry provides a novel approach to probe quantum gravity effects in black hole spacetimes. This work explores Dirac quasinormal modes (QNMs) of a deformed Reissner-Nordström black hole, where noncommutativity induces an effective metric with an additional ($ r-φ$) component. Employing a semiclassical model equivalent to a NC gauge theory, we investigate the dynamics of massless Dirac fields and calculate their QNM frequencies using the continued fraction method, enhanced by Gauss elimination to address the six-term recurrence relations. Our results demonstrate notable shifts in oscillation frequencies and damping rates relative to the commutative Reissner-Nordström case, exhibiting a distinctive Zeeman-like splitting in the QNM spectrum driven by the NC parameter.

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arXiv2025

Dirac QNM spectrum from twisted semiclassical gauge theory of gravity

Twisted Abelian gauge theory coupled to a noncommutative (NC) Dirac field is studied in order to infer the quasinormal mode (QNM) spectrum of the fermion matter perturbations in the vicinity of the Reissner-Nordström (RN) black hole. The action functional of the theory is invariant under the truncated NC local $U(1)_{\star}$ gauge transformations that keep the gravitational background intact. The latter, being a classical gravitational background unaffected by the NC local gauge transformations, makes the theory semiclassical. The most prominent feature of the QNM spectrum is the splitting in the total angular momentum projection due to the noncommutativity induced $SO(3) \rightarrow U(1)$ symmetry breaking pattern.

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arXiv2025

Fermion quasinormal modes on modified RN background

Noncommutative (NC) geometry may open an alternative route to quantum gravity. We study the influence of the spacetime noncommutativity on the Dirac quasinormal modes in the modified Reissner-Nordström black hole spacetime. The framework for the latter study is provided by a certain effective model of gravity coupled to fermions which in itself encapsulates noncommutative deformation. This model describes a classical Dirac field coupled to a modified Reissner-Nordström geometry where the corresponding metric acquires an additional nonvanishing $r-φ$ component. As the earlier study shows, this model appears to be equivalent to a model of semiclassical NC gauge theory in which a NC gauge field is being coupled to a NC fermion field on the one side and the classical Reissner-Nordström background on the other. In comparison to the undeformed model where the Dirac field is coupled to the commutative Reissner-Nordström black hole, the numerical results show that the oscillation frequencies and magnitude of damping of the Dirac quasinormal modes change to an extent that cannot be neglected. In fact, the influence of spacetime noncommutativity is shown to produce features reminiscent of a Zeeman-like splitting in the effective potential and quasinormal-mode spectrum.

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arXiv2025

Noncommutative fields in Reissner-Nordström black hole background

In this short paper we discuss dynamics of noncommutative (NC) matter fields in the Reissner-Nordström (RN) black hole background. After reviewing the propagation of charged NC scalar and spinor fields, we derive the equation governing the propagation of NC electromagnetic (EM) perturbation in the RN background. The propagation of NC scalar and spinor perturbation have a dual description in terms of the propagation of commutative fields in the effective/dual metric. Finally, we turn to the gravitational perturbations. We present equations of motion for the NC gravitational field obtained in two different models: $SO(2,3)_\star$ NC gravity and braided NC gravity. Typically for NC gravity models, the first nontrivial corrections are quadratic in the NC parameter. The obtained NC gravity equations are the starting point to discuss the propagation of NC gravitational perturbations and the validity of the dual description in terms of the effective metric.

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arXiv2025

Noncommutative quasinormal modes of Schwarzschild black hole

We study gravitational perturbations of the Schwarzschild metric in the context of noncommutative gravity. $r-φ$ and $r-t$ noncommutativity are introduced through a Moyal twist of the Hopf algebra of diffeomorphisms. Differential geometric structures such as curvature tensors are also twisted. Noncommutative equations of motion are derived from the recently proposed NC vacuum Einstein equation. Here, in addition to previously calculated axial NC potential, we present the polar solution which generalizes the work done by Zerilli. Quasinormal mode frequencies of the two potentials are calculated using three methods: WKB, Pöschl-Teller and Rosen-Morse. Notably, we apply the WKB method up to the 13th order and determine the optimal order for each noncommutative parameter value individually. Additionally, we provide comprehensive error estimations for the higher-order WKB calculations, offering insights into the accuracy of our results. By comparing the spectra, we conclude that the classical isospectrality of axial and polar modes is broken upon spacetime quantization. Isospectrality is restored in the eikonal limit.

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arXiv2025

Noncommutative Quasinormal Modes and the Violation of Isospectrality

We explore quasinormal modes (QNMs) of the Schwarzschild black hole under a noncommutative (NC) deformation of spacetime, constructed via a Drinfeld twist formalism. In this approach, the usual Regge--Wheeler (axial) and Zerilli (polar) equations acquire additional contributions that depend on the NC parameter. Employing semi-analytical approximations (high-order WKB, Pöschl--Teller and Rosen--Morse), we calculate the corresponding QNM spectra. Our results show that whereas the commutative case preserves the isospectrality of axial and polar modes, noncommutativity systematically violates this degeneracy. The discrepancy grows with the strength of the NC parameter, becoming evident through distinct real and imaginary parts in the ringdown frequencies. These findings highlight the potential of black hole QNMs to serve as probes of quantum-spacetime corrections in strong-field regimes.

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arXiv2025

Noncommutative Reissner-Nordström black hole from noncommutative charged scalar field

Within the framework of noncommutative (NC) deformation of gauge field theory by the angular twist, we first rederive the NC scalar and gauge field model from our previous papers and then generalize it to the second order in the Seiberg-Witten (SW) map. It turns out that SW expansion is finite and that it ceases at the second order in the deformation parameter, ultimately giving rise to the equation of motion for the scalar field in Reissner--Nordström (RN) metric that is nonperturbative and exact at the same order. As a further step, we show that the effective metric put forth and constructed in our previous work satisfies the equations of Einstein-Maxwell gravity, but only within the first order of deformation and when the gauge field is fixed by the Coulomb potential of the charged black hole. Thus obtained NC deformation of the Reissner--Nordström (RN) metric appears to have an additional off-diagonal element which scales linearly with a deformation parameter. We analyze various properties of this metric.

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arXiv2024

Near-horizon aspects of black holes in quantum spacetime

We give a short introduction to the formalism of noncommutative (twisted) differential geometry that is used to derive the equations of motion for the gravitational perturbation of the Schwarzschild black hole in quantized spacetime. Special attention is given to quantum spacetime arising from $r - φ$ noncommutativity. Tortoise coordinate and near-horizon regions of the effective potentials are analyzed for both polar and axial modes. By carefully examining the associated Schrödinger-type equations, we provide the asymptotic solutions at the horizon and illustrate some differences between the polar and axial modes. These findings give further insight into the polar-axial isospectrality violation in the presence of the quantum structure of spacetime.

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arXiv2024

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.

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arXiv2024

Gravitational probe of quantum 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.

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arXiv2023

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.

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arXiv2023

Noncommutative scalar field theory in a curved background: duality between noncommutative and effective commutative description

We study a noncommutative (NC) deformation of a charged scalar field, minimally coupled to a classical (commutative) Reissner Nordstrom like background. The deformation is performed via a particularly chosen Killing twist to ensure that the geometry remains undeformed (commutative). An action describing a NC scalar field minimally coupled to the RN geometry is manifestly invariant under the deformed U(1) gauge symmetry. We find the equation of motion and conclude that the same equation is obtained from the commutative theory in a modified geometrical background described by an effective metric. This correspondence we call duality between formal and effective approach. We also show that a NC deformation via semi Killing twist operator cannot be rewriten in terms of an effective metric. There is a dual description for those particular deformations.

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arXiv2023

Propagation of spinors on a noncommutative spacetime: equivalence of the formal and the effective approach

Some noncommutative (NC) theories posses a certain type of dualities that are implicitly built within their structure. In this paper we establish still another example of this kind. More precisely, we show that the noncommutative U(1) gauge theory coupled to a NC scalar field and to a classical geometry of the Reissner Nordstrom (RN) type is completely equivalent at the level of equations of motion to the commutative U(1) gauge theory coupled to a commutative scalar field and to a classical geometry background, different from the starting RN background. The new (effective) metric is obtained from the RN metric by switching on an additional nonvanishing r-phi component. Using this duality between two theories and physical systems they describe, we formulate an effective approach to studying a dynamics of spin 1/2 fields on the curved background of RN type with an abiding noncommutative structure. As opposed to that, we also study the dynamics of spin 1/2 fields in a more formal way, by studying the semiclassical theory which describes the NC U(1) gauge field coupled with NC spin 1/2 field and also with gravity which is however treated classically. Upon utilising the Seiberg Witten map in order to write the NC spinor and NC gauge fields in terms of their corresponding commutative degrees of freedom, we find that the equation of motion for the fermion field obtained within the formal approach exactly coincides with the equation of motion obtained within the effective approach that utilises noncommutative duality. We then use these results to analyze the problem of stability of solutions of the equations of motion and the associated issue of superradiance, as related to fermions in RN spacetime with an allpervasive noncommutative structure.

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arXiv2019

Search for footprints of quantum spacetime in black hole QNM spectrum

Black hole (BH) perturbation is followed by a ringdown phase which is dominated by quasinormal modes (QNM). These modes may provide key signature of the gravitational waves. The presence of a deformed spacetime structure may distort this signal. In order to account for such effects, we consider a toy model consisting of a noncommutative charged scalar field propagating in a realistic black hole background. We then analyse the corresponding field dynamics by applying the methods of the Hopf algebra deformation by Drinfeld twist. The latter framework is well suited for incorporating deformed symmetries into a study of this kind. As a result, we obtain the BH QNM spectrum that, besides containing the intrinsic information about a black hole that is being analysed, also carry the information about the underlying structure of spacetime.

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arXiv2019

Noncommutativity and the Weak Cosmic Censorship

We show that a noncommutative massless scalar probe can dress a naked singularity in $AdS_3$ spacetime, consistent with the weak cosmic censorship. The dressing occurs at high energies, which is typical at the Planck scale. Using a noncommutative duality, we show that the dressed singularity has the geometry of a rotating BTZ black hole which satisfies all the laws of black hole thermodynamics. We calculate the entropy and the quasi-normal modes of the dressed singularity and show that the corresponding spacetime can be quantum mechanically complete. The noncommutative duality also gives rise to a light scalar, which can be relevant for early universe cosmology.

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arXiv2019

Noncommutative scalar field in the non-extremal Reissner-Nordström background: QNM spectrum

In our previous work [18] we constructed a model of a noncommutative, charged and massive scalar field based on the angular twist. Then we used this model to analyze the motion of the scalar field in the Reissner-Nordström black hole background. In particular, we determined the QNM spectrum analytically in the near-extremal limit. To broaden our analysis, in this paper we apply a well defined numerical method, the continued fraction method and calculate the QNM spectrum for a non-extremal Reissner-Nordström black hole. To check the validity of our analytic calculations, we compare results of the continued fraction method in the near extremal limit with the analytic results obtained in the previous paper. We find that the results are in good agreement. For completeness, we also study the QNM spectrum in the WKB approximation.

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arXiv2018

Noncommutative Scalar Quasinormal Modes of the Reissner Nordström Black Hole

Aiming to search for a signal of space-time noncommutativity, we study a quasinormal mode spectrum of the Reissner Nordström black hole in the presence of a deformed space-time structure. In this context we study a noncommutative (NC) deformation of a scalar field, minimally coupled to a classical Reissner Nordström background. Our model is thus semiclassical from the beginning and scalar field is in addition minimally coupled to U(1) gauge field. The deformation is performed via particularly chosen Killing twist to yield a geometrical form of the action, which maintains the diffeomorphism invariance manifest, as well as the invariance under a deformed gauge symmetry group. We find the quasinormal mode solutions of the equations of motion governing the matter content of the model in some particular range of system parameters which corresponds to a near extremal limit. In addition, we obtain a well defined analytical condition which allows for a detailed numerical analysis. Moreover, there exists a parameter range, rather restrictive though, which allows for obtaining a QNM spectrum in a closed analytic form. We also argue within a semiclassical approach that NC deformation does not affect the Hawking temperature of thermal radiation.

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