Tajron Jurić

A bstract: 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 RF _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 a special choice 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 ⋆ F ^ab ).

A bstract: 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 ℓ → 0, and resolve the central singularity by introducing a smooth core controlled by the new length scale ℓ . 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 ℓ 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 ℓ 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.

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.

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.

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 the 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, the 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.