In this paper, we use a suitable conformal rescaling to construct static and rotating regular black holes in conformal massive gravity. The new metric is characterized by the mass M, the "scalar charge" Q, the angular momentum parameter a, the "hair parameter" λ, and the conformal scale factor encoded in the parameter L. We explore the shadow images and the deflection angles of relativistic massive particles in the spacetime geometry of a rotating regular black hole. For λ = 0 and Q > 0, the shadow is larger than the shadow of a Kerr black hole. In particular, if λ < 0, the shadow radius increases considerably. For λ = 0 and Q < 0, the shadow is smaller than the shadow of a Kerr black hole. Additionally we put observational constraints on the parameter Q using the latest Event Horizon Telescope (EHT) observation of the supermassive black hole M87*. Lastly, using the Gauss-Bonnet theorem, we show that the deflection angle of massive particles is strongly affected by the parameter L. The deflection angle might be used to distinguish rotating regular black holes from rotating singular black holes.

We present a dynamical toy model for an expanding universe inside a black hole. The model is built by matching a spherically symmetric collapsing matter cloud to an expanding Friedmann–Robertson–Walker universe through a phase transition that occurs in the quantum-gravity dominated region, here modeled with semi-classical corrections at high density. The matching is performed on a space-like hyper-surface identified by the co-moving time at which quantum–gravity induced effects halt collapse. The purpose of the model is to suggest a possible reconciliation between the observation that black holes are well described by the classical solutions and the fact that the theoretical resolution of space–time singularities leads to a bounce for the collapsing matter.

The Janis-Newman-Winicour metric is a solution of Einstein's gravity minimally coupled to a real massless scalar field. The γ-metric is instead a vacuum solution of Einstein's gravity. Both spacetimes have no horizon and possess a naked singularity at a finite value of the radial coordinate, where curvature invariants diverge and the spacetimes are geodetically incomplete. In this paper, we reconsider these solutions in the framework of conformal gravity and we show that it is possible to solve the spacetime singularities with a suitable choice of the conformal factor. Now curvature invariants remain finite over the whole spacetime. Massive particles never reach the previous singular surface and massless particles can never do it with a finite value of their affine parameter. Our results support the conjecture according to which conformal gravity can fix the singularity problem that plagues Einstein's gravity.

We study scalar perturbations and quasinormal modes of a nonlinear magnetic charged black hole surrounded by quintessence. Time evolution of scalar perturbations is studied for different parameters associated with the black hole solution. We also study the reflection and transmission coefficients along with absorption cross-section for the considered black hole spacetime. It was shown that the real part of quasinormal frequency increases with increase in nonlinear magnetic charge while the module of the imaginary part of the frequency decreases. The analysis of the perturbations with changing quintessential parameter c showed that perturbations with high values of c become unstable.

We study weak gravitational lensing around a compact object with arbitrary quadrupole moment in the presence of plasma. The studied compact objects are considered to be spherically symmetric. The additional parameter regulating the quadrupole moment in the metric alters the deflection angle of light rays along with the plasma parameters. In the vacuum, the number of images due to the presence of the parameter increases and causes the increase of the magnification of the image source. The effects of uniform and nonuniform plasma on gravitational lensing around the compact object are also studied.