arXiv subjects

Ivica Smolić

Publications and source records attributed to Ivica Smolić.

At least 19 recordsLinked to original sources

arXiv2026

A converse to generalized Runcorn's theorem

We study an inverse problem for generalized Runcorn's theorem motivated by an apparent paradox of lunar magnetism. In mathematical terms, we characterize square-integrable complex functions $f$ such that $$ \int_{\{ x\in\mathbb{R}^n : a \leq |x| \leq b \}} f(x) \nabla u(x)\cdot\nabla v(x)\,\mathrm{d}\mathrm{V}(x) = 0 $$ for every complex harmonic function $u$ in the inner ball $|x| r_-$ that vanishes at infinity. The solution space depends on whether the radii $a$ and $b$ such that $r_-<a<b<r_+$ are regarded as varying or fixed. The solutions are described through the expansion of $f$ into spherical harmonics, and explicit representations are provided.

math-ph↗

arXiv2026

Partial Orderings of Curvature Invariants

We establish a new set of pointwise inequalities that order curvature invariants across various Petrov and Segre types of spacetimes. In arbitrary spacetime dimension, we systematically analyze inequalities among contractions of the Ricci tensor. We further explore the conditions under which all Zakhary--McIntosh invariants in $(1+3)$-dimensional spacetimes are bounded above (up to appropriate powers) by the Kretschmann scalar. These results establish a practical hierarchy among curvature scalars and clarify the extent to which higher-order invariants are algebraically controlled by lower-order ones or vice versa.

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

Weighing the curvature invariants

We prove several inequalities between the curvature invariants, which impose constraints on curvature singularities. Some of the inequalities hold for a family of spacetimes which include static, Friedmann--Lemaître--Robertson--Walker, and Bianchi type I metrics, independently of whether they are solutions of some particular field equations. In contrast, others hold for solutions of Einstein's gravitational field equation and a family of energy-momentum tensors (featuring ideal fluids, scalar fields and nonlinear electromagnetic fields), independently of the specific form of the spacetime metric. We illustrate different behaviour of the basic curvature invariants with numerous examples and discuss the consequences and limitations of the proven results.

gr-qc↗

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

Generalized Runcorn's theorem and crustal magnetism

During the era of NASA's Apollo missions, Keith S. Runcorn proposed an explanation of discrepancy between the Moon's negligible global magnetic field and magnetized samples of lunar regolith, based on identical vanishing of external magnetic field of a spherical shell, magnetized by an internal source which is no longer present. We revisit and generalize the Runcorn's result, showing that it is a consequence of a (weighted) orthogonality of gradients of harmonic functions on a spherical shell in arbitrary number of dimensions. Furthermore, we explore bounds on external magnetic field in the case when the idealized spherical shell is replaced with a more realistic geometric shape and when the thermoremanent magnetization susceptibility deviates from the spherical symmetry. Finally, we analyse a model of thermoremanent magnetization acquired by crustal inward cooling of a spherical astrophysical body and put some general bounds on the associated magnetic field.

physics.geo-ph↗

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

Lorentz contraction of electric field lines for a point charge in uniform motion

We examine a logical foundation of depicting a Lorentz contraction of a Coulomb field (an electric field of a point charge in uniform motion) by means of the 'Lorentz contracted' field lines. Two existing arguments for a contraction of field lines sound appealing and lead to very simple calculations yielding the correct results. However, one of them is a victim to subtle logical weaknesses, as it relies on ascribing a degree of physical reality to the electric field lines. The other one correctly proves what it sets out to prove. But it does not provide a proof, or even a suggestion, of an additional result that can be obtained by a new poof that we present here. Though our idea is very simple, the calculations used to prove it - based on a little known, half a century old result by Tsien - are somewhat more involved than those from past arguments.

physics.gen-ph↗

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

Generalizations and challenges for the spacetime block-diagonalization

Discovery that gravitational field equations may coerce the spacetime metric with isometries to attain a block-diagonal form compatible with these isometries, was one of the gems built into the corpus of black hole uniqueness theorems. We revisit the geometric background of a block-diagonal metric with isometries, foliation defined by Killing vector fields and the corresponding Godbillon-Vey characteristic class. Furthermore, we analyse sufficient conditions for various matter sources, including scalar, nonlinear electromagnetic and Proca fields, that imply the isometry-compatible block-diagonal form of the metric. Finally, we generalize the theorem on the absence of null electromagnetic fields in static spacetimes to an arbitrary number of spacetime dimensions, wide class of gravitational field equations and nonlinear electromagnetic fields.

gr-qc↗

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↗