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Regular black hole spacetimes are obtained from an effective Lagrangian for quantum Einstein gravity. The interior matter is modeled as a dust fluid, which interacts with the geometry through a multiplicative coupling function denoted as χ. The specific functional form of χ is deduced from asymptotically safe gravity, under the key assumption that the Reuter fixed point remains minimally affected by the presence of matter. As a consequence the gravitational coupling vanishes at high energies. The static exterior geometry of the black hole is entirely determined by the junction conditions at the boundary surface. Consequently, the resulting global spacetime geometry remains devoid of singularities at all times. This outcome offers a new perspective on how regular black holes are formed through gravitational collapse.

Superflares are large explosive events on stellar surfaces one to six orders-of-magnitude larger than the largest flares observed on the Sun throughout the space age. Due to the huge amount of energy released in these superflares, it has been speculated if the underlying mechanism is the same as for solar flares, which are caused by magnetic reconnection in the solar corona. Here, we analyse observations made with the LAMOST telescope of 5,648 solar-like stars, including 48 superflare stars. These observations show that superflare stars are generally characterized by larger chromospheric emissions than other stars, including the Sun. However, superflare stars with activity levels lower than, or comparable to, the Sun do exist, suggesting that solar flares and superflares most likely share the same origin. The very large ensemble of solar-like stars included in this study enables detailed and robust estimates of the relation between chromospheric activity and the occurrence of superflares.

We study spontaneous breakdown of chiral symmetry during the nonlinear evolution of the Tayler instability. We start with an initial steady state of zero helicity. Within linearized perturbation calculations, helical perturbations of this initial state have the same growth rate for either sign of helicity. Direct numerical simulations (DNS) of the fully nonlinear equations, however, show that an infinitesimal excess of one sign of helicity in the initial perturbation gives rise to a saturated helical state. We further show that this symmetry breaking can be described by weakly nonlinear finite-amplitude equations with undetermined coefficients which can be deduced solely from symmetry consideration. By fitting solutions of the amplitude equations to data from DNS, we further determine the coefficients of the amplitude equations.

We review the evidence for and against the possibility that a strong enough poloidal field stabilizes an axisymmetric magnetostatic field configuration. We show that there does exist a class of resonant magnetohydrodynamic (MHD) waves which produce instability for any value of the ratio of poloidal and toroidal field strength. We argue that recent investigations of the stability of mixed poloidal and toroidal field configurations based on three-dimensional numerical simulations can miss this instability because of the very large azimuthal wave numbers involved and its resonant character.

We study the stability of a compressible magnetic plane Couette flow and show that compressibility profoundly alters the stability properties if the magnetic field has a component perpendicular to the direction of flow. The necessary condition of an instability can be satisfied in a wide variety of flows in laboratory and astrophysical conditions. The instability can operate even in a very strong magnetic field which entirely suppresses other magnetohydrodynamics (MHD) instabilities. The growth time of this instability can be rather short and reach approximately 10 shear time scales.