In this study, we investigate electromagnetic and Dirac test field perturbations of a charged regular black hole arising from quantum gravity effects, commonly referred to as the Frolov black hole, a regular (nonsingular) black hole solution. We derive the master wave equations for massless electromagnetic and Dirac perturbations and solve them using the standard Wentzel-Kramers-Brillouin (WKB) method along with Pade Averaging. From these solutions, we extract the dominant and overtone quasinormal mode (QNM) frequencies along with the associated grey-body factors, highlighting the deviations introduced by quantum gravity corrections compared to the classical case of Reissner-Nordstrom black hole. Furthermore, we analyze the Unruh-Verlinde temperature of this spacetime, providing quantitative estimates of how quantumgravity effects influence both quasinormal ringing and particle emission in nonsingular black hole models.

We discuss static, spherically symmetric solutions to the 5D Einstein- Maxwell equations (belonging to wide classes of multidimensional solutions known at least from the 1990s) and select among them those which must observationally look like local objects whose surface reflects back particles or signals getting there, the so-called mirror stars (also called “topological stars” by some authors). Their significant parameters are the Schwarzschild mass m and the magnetic charge q, such that q² > 3m², while the radius of their mirror surface is r_b = 2q² /(3m) > 2m. We also discuss their black hole counterparts for which q² ≤ 3m². For both these objects, we study spherically symmetric time-dependent perturbations and determine the stability regions in their parameter spaces. Thus, mirror stars turn out to be stable only at r_b < r ≈ 4.004m, while the black holes prove to be stable in the whole range of their parameters. We calculate the fundamental frequencies and decay rates of black hole perturbations using the WKB and time domain methods. Our stability results disagree with some of those previously announced in the literature.

Using an expansion beyond the eikonal regime, we derive relatively compact and accurate analytic expressions for the gravitational quasinormal modes of an asymptotically flat black hole supported by a Dehnen-type dark-matter halo. The spacetime admits a simple analytic metric describing a supermassive black hole embedded in a galactic environment, with the lapse function $ f(r)=1-\frac{2 M r^{2}}{(r+a)^{3}}.$ The parameter 𝑎 sets the characteristic scale of the surrounding halo and controls the regularization of the central region. The axial gravitational sector splits into two distinct channels, referred to as the “up” and “down” perturbations, which are not isospectral.

We investigate particle motion in regular and asymptotically flat black hole spacetimes supported by Dehnen-type dark-matter halos. Two analytic models are analyzed, allowing a systematic study of circular geodesics, photon-sphere properties, shadow radius, Lyapunov exponent, ISCO frequency, binding energy, and Hawking temperature. The corrected numerical results show that the halo scale parameter can significantly modify strong-field observables. In both models, for moderate density slopes, increasing the halo parameter reduces characteristic radii while enhancing orbital instability and accretion efficiency. For steeper density falloff, however, deviations from the Schwarzschild case remain small. These results demonstrate that halo-induced modifications of optical and dynamical black hole signatures are strongly controlled by the density profile parameters.

The higher-order WKB Mathematica^® code for computing quasinormal modes, whose accuracy was significantly enhanced through extensions to higher orders and, in particular, through the use of Pad´e resummation, has been widely employed in numerous studies over the past several years. In this work, we present an updated and optimized version of the code. The main improvement consists in expanding the effective potential in a Taylor series around its maximum, rather than evaluating the full analytic expression of the WKB formula for each specific potential. This modification leads to a substantial reduction in computation time. In cases where the effective potential is complicated and involves non-rational functions, the speed gain can reach several orders of magnitude, while preserving the accuracy of the method.

It was recently demonstrated that imposing the condition 𝑃𝑟 = −𝜌 on the radial pressure of a galactic halo can lead to regular black-hole solutions for certain density profiles, such as the Dehnen and Einasto models. In the present work, we show that some of the most commonly used halo profiles, including the Hernquist model, do not yield regular geometries under the same condition, but instead support black-hole solutions that retain a central singularity.

We study grey-body factors for a massless scalar field in the spacetime of regular black holes arising in four-dimensional non-polynomial quasi-topological gravity. We consider two representative metrics that capture the typical features of regular geometries. Using the WKB method, we compute the transmission probabilities and analyze their dependence on the regularization parameter. The grey-body factors are found to deviate only slightly from the Schwarzschild case, indicating that the scattering properties are largely insensitive to near-horizon regularization of the geometry. The correspondence between quasinormal modes and grey-body factors is shown to be sufficiently accurate for higher multipole numbers.