We study the quantum gravitational effects in spherically symmetric black hole spacetimes. The effective quantum spacetime felt by a point-like test mass is constructed by "renormalization group improving" the Schwarzschild metric. The key ingredient is the running Newton constant which is obtained from the exact evolution equation for the effective average action. The conformal structure of the quantum spacetime depends on its ADM-mass M and it is similar to that of the classical Reissner-Nordström black hole. For M larger * abo@sunct.ct.astro.it † reuter@thep.physik.uni-mainz.de 1 than, equal to, and smaller than a certain critical mass M cr the spacetime has two, one and no horizon(s), respectively. Its Hawking temperature, specific heat capacity and entropy are computed as a function of M . It is argued that the black hole evaporation stops when M approaches M cr which is of the order of the Planck mass. In this manner a "cold" soliton-like remnant with the near-horizon geometry of AdS 2 × S 2 is formed. As a consequence of the quantum effects, the classical singularity at r = 0 is either removed completely or it is at least much milder than classically; in the first case the quantum spacetime has a smooth de Sitter core which would be in accord with the cosmic censorship hypothesis even if M < M cr .

Homogeneous and isotropic cosmologies of the Planck era before the classical Einstein equations become valid are studied taking quantum gravitational effects into account. The cosmological evolution equations are renormalization group improved by including the scale dependence of Newton's constant and of the cosmological constant as it is given by the flow equation of the effective average action for gravity. It is argued that the Planck regime can be treated reliably in this framework because gravity is found to become asymptotically free at short distances. The epoch immediately after the initial singularity of the Universe is described by an attractor solution of the improved equations which is a direct manifestation of an ultraviolet attractive renormalization group fixed point. It is shown that quantum gravity effects in the very early Universe might provide a resolution to the horizon and flatness problems of standard cosmology, and could generate a scale-free spectrum of primordial density fluctuations.

Mass‐loss of red giant branch (RGB) stars is still poorly determined, despite its crucial role in the chemical enrichment of galaxies. Thanks to the recent detection of solar‐like oscillations in G–K giants in open clusters with Kepler, we can now directly determine stellar masses for a statistically significant sample of stars in the old open clusters NGC 6791 and 6819. The aim of this work is to constrain the integrated RGB mass‐loss by comparing the average mass of stars in the red clump (RC) with that of stars in the low‐luminosity portion of the RGB [i.e. stars with L≲L(RC)]. Stellar masses were determined by combining the available seismic parameters νmax and Δν with additional photometric constraints and with independent distance estimates. We measured the masses of 40 stars on the RGB and 19 in the RC of the old metal‐rich cluster NGC 6791. We find that the difference between the average mass of RGB and RC stars is small, but significant [ (random) ±0.04 (systematic) M⊙]. Interestingly, such a small does not support scenarios of an extreme mass‐loss for this metal‐rich cluster. If we describe the mass‐loss rate with Reimers prescription, a first comparison with isochrones suggests that the observed is compatible with a mass‐loss efficiency parameter in the range 0.1 ≲η≲ 0.3. Less stringent constraints on the RGB mass‐loss rate are set by the analysis of the ∼2 Gyr old NGC 6819, largely due to the lower mass‐loss expected for this cluster, and to the lack of an independent and accurate distance determination. In the near future, additional constraints from frequencies of individual pulsation modes and spectroscopic effective temperatures will allow further stringent tests of the Δν and νmax scaling relations, which provide a novel, and potentially very accurate, means of determining stellar radii and masses.