We discuss quantum black holes in asymptotically safe quantum gravity with a scale identification based on the Kretschmann scalar. After comparing this scenario with other scale identifications, we investigate in detail the Kerr-(A)dS and Schwarzschild-(A)dS space-times. The global structure of these geometries is studied as well as the central curvature singularity and test particle trajectories. The existence of a Planck-sized, extremal, zero temperature black hole remnant guarantees a stable endpoint of the evaporation process via Hawking radiation.

This work studies the Hawking energy in a cosmological context. The past lightcone of a point in spacetime is the natural geometric structure closely linked to cosmological observations. By slicing the past lightcone into a one-parameter family of spacelike two-surfaces, the evolution of the Hawking energy down the lightcone is studied. Strong gravitational fields may generate lightcone self-intersections and wave front singularities. We show that in the presence of swallow-tail type singularities, the Hawking energy and its variation along the null generators of the lightcone remains well-defined and subsequently discuss its positivity and monotonicity.

We reconstruct the radial profile of the projected gravitational potential of the galaxy cluster MACS J1206 from 592 spectroscopic measurements of velocities of cluster members. To accomplish this, we use a method we have developed recently based on the Richardson-Lucy deprojection algorithm and an inversion of the spherically-symmetric Jeans equation. We find that, within the uncertainties, our reconstruction agrees very well with a potential reconstruction from weak and strong gravitational lensing as well as with a potential obtained from X-ray measurements. In addition, our reconstruction is in good agreement with several common analytic profiles of the lensing potential. Varying the anisotropy parameter in the Jeans equation, we find that isotropy parameters, which are either small, β < ∼ 0.2, or decrease with radius, yield potential profiles that strongly disagree with that obtained from gravitational lensing. We achieve the best agreement between our potential profile and the profile from gravitational lensing if the anisotropy parameter rises steeply to β ≈ 0.6 within ≈0.5 Mpc and stays constant further out.

The past lightcone of an observer in a cosmological spacetime is the unique geometric structure directly linked to observations. After general properties of the Hawking energy along slices of the past lightcone have previously been studied, the present work continues along this path by providing explicit cosmological applications of the Hawking energy associated with a lightcone. Firstly, it is shown that amongst all two-dimensional non-trapped spheres with equal area and average matter density, a shear-free matter distribution maximizes the Hawking energy for sufficiently high densities. Secondly, a Robertson–Walker reference slice is constructed for every lightcone slice based on area and energy. Thirdly, after a few pedagogical examples in concrete FLRW spacetimes, the implications of monotonicity of the energy down the lightcone are explored, arriving at two new bounds on the cosmic fluid’s density and equation-of-state parameter.