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The light rings (LRs) topological charge (TC) of a spacetime measures the number of stable LRs minus the number of unstable LRs. It is invariant under smooth spacetime deformations obeying fixed boundary conditions. Asymptotically flat equilibrium black holes (BHs) have, generically, TC=−1. In Einstein-Maxwell theory, however, the Schwarzschild-Melvin BH -describing a neutral BH immersed in a strong magnetic field -has TC= 0. This allows the existence of BHs without LRs and produces remarkable phenomenological features, like panoramic shadows. Here we investigate the generalised Schwarzschild-Melvin solution in Einstein-Maxwell-dilaton theory, scanning the effect of the dilaton coupling a. We find that the TC changes discontinuously from TC= 0 to TC= −1 precisely at the Kaluza-Klein value a = √ 3, when the (empty) Melvin solution corresponds to a twisted Kaluza-Klein reduction of five-dimensional flat spacetime, i.e. the dilaton coupling a induces a topological transition in the TC. We relate this qualitative change to the Melvin asymptotics for different a. We also study the shadows and lensing of the generalised Schwarzschild-Melvin solution for different values of a, relating them to the TC.

We analyze the quasinormal modes (QNMs) of a recently obtained solution of a Schwarzschild black hole (BH) with corrections motivated by Loop Quantum Gravity (LQG). This spacetime is regular everywhere and presents the global structure of a wormhole, with a minimal surface whose radius depends on a LQG parameter. We focus on the investigation of massless scalar field perturbations over the spacetime. We compute the QNMs with the WKB approximation, as well as the continued fraction method. The QNM frequency orbits, for 𝑙 = 0 and 𝑛 > 0, where 𝑙 and 𝑛 are the multipole and overtone numbers, respectively, are self-intersecting, spiraling curves in the complex plane. These orbits accumulate to a fixed complex value corresponding to the QNMs of the extremal case. We obtain that, for small values of the LQG parameter, the overall damping decreases as we increase the LQG parameter. Moreover the spectrum of the quantum corrected black hole exhibits an oscillatory pattern, which might imply in the existence of QNMs with vanishing real part. This pattern suggests that the limit 𝑛 → ∞ for the real part of the QNMs is not well-defined, what differs from Schwarzschild's case. We also analyze the time-domain profiles for the scalar perturbations, showing that the LQG correction does not alter the Schwarzschild power-law tail. We compute the fundamental mode from the time profile by means of the Prony method, obtaining excellent agreement with the two previously mentioned methods.

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