arXiv subjects

Tajron Jurić

Publications and source records attributed to Tajron Jurić.

At least 19 recordsLinked to original sources

arXiv2026

Geodesic equation in noncommutative space: a field theory perspective

We derive the geodesic equation for point particles propagating in Moyal-type noncommutative spacetimes using a field-theoretic approach based on the quasi-classical limit of the noncommutative Klein-Gordon equation. Starting from a twisted-geometric construction of the covariant Laplace-Beltrami operator, we obtain the noncommutative Hamilton-Jacobi equation and show that all noncommutative effects are absorbed into an effective, position-dependent mass function $M(x)$ appearing in an otherwise standard relativistic dispersion relation. The corresponding particle dynamics then acquires an additional term in the geodesic equation that takes the form of a fixed external force $F_{\text{NC}}^μ= -\frac{1}{2} g^{μν}\partial_νM^2(x)$, sourced entirely by the quantum nature of spacetime. We compute this effective mass perturbatively up to fourth order in the noncommutativity parameter for a general metric, proving that all odd-order corrections vanish identically. For the specific case of an $(r-θ)$ twist applied to spherically symmetric backgrounds, we obtain explicit expressions demonstrating that the leading correction to geodesic motion appears at $Θ^2$ order and is proportional to the probe particle's mass, while massless particles remain unaffected.

hep-th↗

arXiv2026

Spectral Bifurcations in Quasinormal Modes of Regular BTZ Black Holes

We study the quasinormal spectrum of massless scalar fields propagating on a family of regular BTZ black holes arising from an infinite tower of dimensionally regularized Lovelock corrections. These geometries are asymptotically AdS, reduce to the standard BTZ solution in the limit $\ell \to 0$, and resolve the central singularity by introducing a smooth core controlled by the new length scale $\ell$. The scalar quasinormal modes are computed using both Leaver's continued-fraction method and the Horowitz-Hubeny power-series method; the two approaches agree to high accuracy across the parameter space. We find that the regularization preserves linear stability ($ω_I < 0$) while qualitatively reshaping the spectrum: as $\ell$ increases, BTZ-like complex branches collide with the imaginary axis and undergo a hierarchy of bifurcations into multiple purely imaginary branches, leading to mode switching and a nontrivial reordering of overtones as functions of $\ell$ and the harmonic index $m$. Our results place regular BTZ black holes within the emerging family of bifurcating quasinormal spectra known from nearly extremal and asymptotically AdS black holes, and highlight these $(2+1)$-dimensional geometries as a controlled arena for exploring geometric mechanisms behind spectral branching and late-time ringdown in regular black hole spacetimes.

gr-qc↗

arXiv2026

Constraints on regular black holes with nonminimally coupled electromagnetic fields

Construction of physically realistic theories admitting regular black hole solutions remains an important open problem in gravitational physics. While theories with electromagnetic fields minimally coupled to gravity have been extensively studied over the past two decades, theories with nonminimal couplings remain comparatively unexplored. We investigate theories containing the interaction terms $R F_{ab}F^{ab}$, $R_{ab} F^a_{\ \, c} \, F^{bc}$ and $R_{abcd} F^{ab} F^{cd}$, which generically arise in low-energy effective Lagrangians. We prove that magnetically charged regular black holes are excluded, except possibly for finely tuned choices of coupling constants, and argue that a similar conclusion applies to electrically charged regular black holes. We further show that similar conclusions hold for Lagrangian terms of the form $f(R,F_{ab}{\star F}^{ab})$.

gr-qc↗

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.

gr-qc↗

arXiv2026

Conundrum of regular black holes with nonlinear electromagnetic fields

The search for regular black holes with nonlinear electromagnetic fields has sprouted numerous candidates, each exhibiting certain virtues but often accompanied by significant drawbacks. We demonstrate that Komar mass, electric charge and magnetic charge are mutually dependent in regular black holes with nonlinear electromagnetic fields, defined by a Lagrangian which is a function of both electromagnetic invariants, $F_{ab} F^{ab}$ and $F_{ab}{\star F}^{ab}$, regardless of the specific weak field limit of the theory. Also, we generalize one of the key no-go theorems by showing that static, spherically symmetric, electrically charged black holes in a theory respecting the relaxed Maxwellian weak field limit do not admit a bounded Kretschmann scalar. Finally, we address one of the long-standing niche questions, whether regular black hole solutions can exist when both electric and magnetic charges are present, by constructing an exotic family of regular dyonic black holes with nonlinear electromagnetic fields in theories respecting the Maxwellian weak field limit. Mounting evidence suggests that regularizing black holes through simplistic nonlinear extensions of Maxwell's electromagnetism entails a high cost in the form of unorthodox theoretical assumptions.

gr-qc↗

arXiv2025

Entropy of black holes, charged probes and noncommutative generalization

The brick wall model is a semi-classical approach to understanding the microscopic origin of black hole entropy. We outline the formalism for the brick wall model in arbitrary number of dimensions and generalize it to include both charged spacetimes and charged probes in order to systematically show how to calculate the entropy for any black hole, in higher orders of the WKB approximation. We calculate the entropy for the Reissner-Nordström and charged BTZ black holes, and by looking at the chargeless limits we recover the entropy of the Schwarzschild and neutral BTZ black holes. We also study noncommutative corrections to the black hole entropy by using a Drinfeld twist to deform spacetime symmetries. Using the noncommutative action for a charged scalar field, we derive the noncommutative Klein-Gordon equation and the radial equation in arbitrary dimension on which we generalize the brick wall method. We study case by case the noncommutative Reissner-Nordström and noncommutative charged BTZ black holes, the entropy of which we calculate using the generalized brick wall method. Corrections due to higher order in the WKB approximation arise, and they are given by the logarithms of the black hole area. The corrections in the lowest order of WKB due to noncommutativity are also given by the logarithms of the black hole area.

hep-th↗

arXiv2025

Constructing noncommutative black holes

We present a self-contained and consistent formulation of noncommutative (NC) gauge theory of gravity, focusing on spherically symmetric black hole geometries. Our construction starts from the gauge-theoretic viewpoint of Poincaré (or de Sitter) gravity and introduces noncommutativity through the Moyal star product and the Seiberg-Witten map, retaining NC gauge invariance at each order in the deformation parameter $Θ$. Working systematically to second order in $Θ$, we obtain explicit NC corrections to the spin connection, the vierbein, and various geometric objects such as the metric and curvature scalars. Using these results, we compute NC modifications of four-dimensional Schwarzschild and Reissner-Nordström solutions, including scenarios with a cosmological constant, as well as three-dimensional BTZ-type black holes (both uncharged and charged). For each black hole solution, we explore various possible Moyal twists, each of which generally breaks some symmetries and modifies the horizon structure, surface gravity, and curvature invariants. In particular, we show that while the radial location of horizons in Schwarzschild-like solutions remains unchanged for some twists, other twists introduce important but finite deformations in curvature scalars and can decouple the Killing horizon from the causal horizon. Similar patterns arise in the charged and lower-dimensional cases. Beyond constructing explicit examples, our approach provides a blueprint for systematically incorporating short-distance quantum corrections through noncommutativity in gravitational settings. The methods and expansions we present can be extended to more general geometries including rotating black holes and additional matter fields, offering a broad framework for future studies of NC effects in classical solutions of general relativity.

hep-th↗

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.

gr-qc↗

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.

gr-qc↗

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.

hep-th↗

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.

gr-qc↗

arXiv2024

Hexadecapole at the heart of nonlinear electromagnetic fields

In classical Maxwell's electromagnetism, monopole term of the electric field is proportional to $r^{-2}$, while higher order multipole terms, sourced by anisotropic sources, fall-off faster. However, in nonlinear electromagnetism even a spherically symmetric field has multipole-like contributions. We prove that the leading subdominant term of the electric field, defined by nonlinear electromagnetic Lagrangian obeying Maxwellian weak field limit, in a static, spherically symmetric, asymptotically flat spacetime, is of the order $O(r^{-6})$ as $r \to \infty$. Moreover, using Lagrange inversion theorem and Faà di Bruno's formula, we derive the series expansion of the electric field from the Taylor series of an analytic electromagnetic Lagrangian.

gr-qc↗

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.

hep-th↗

arXiv2024

Lagrangian reverse engineering for regular black holes

Nonlinear extensions of classical Maxwell's electromagnetism are among the prominent candidates for theories admitting regular black hole solutions. A quest for such examples has been fruitful, but mostly unsystematic and littered by the introduction of physically unrealistic Lagrangians. We provide a procedure which admits the reconstruction of a nonlinear electromagnetic Lagrangian, consistent with the Euler--Heisenberg Lagrangian in the weak-field limit, from a given metric representing a regular, magnetically charged black hole.

gr-qc↗

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.

gr-qc↗

arXiv2024

Arrival time from Hamiltonian with non-hermitian boundary term

We develop a new method for finding the quantum probability density of arrival at the detector. The evolution of the quantum state restricted to the region outside of the detector is described by a restricted Hamiltonian that contains a non-hermitian boundary term. The non-hermitian term is shown to be proportional to the flux of the probability current operator through the boundary, which implies that the arrival probability density is equal to the flux of the probability current.

quant-ph↗

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.

hep-th↗

arXiv2023

Passive quantum measurement: Arrival time, quantum Zeno effect and gambler's fallacy

Classical measurements are passive, in the sense that they do not affect the physical properties of the measured system. Normally, quantum measurements are not passive in that sense. In the infinite dimensional Hilbert space, however, we find that quantum projective measurement can be passive in a way which is impossible in finite dimensional Hilbert spaces. Specifically, we find that expectation value of a hermitian Hamiltonian can have an imaginary part in the infinite dimensional Hilbert space and that such an imaginary part implies a possibility to avoid quantum Zeno effect, which can physically be realized in quantum arrival experiments. The avoidance of quantum Zeno effect can also be understood as avoidance of a quantum version of gambler's fallacy, leading to the notion of passive quantum measurement that updates information about the physical system without affecting its physical properties. The arrival time probability distribution of a particle is found to be given by the flux of the probability current. Possible negative fluxes correspond to regimes at which there is no arrival at all, physically understood as regimes at which the particle departs rather than arrives.

quant-ph↗