We study the quantum gravitational effects in spherically symmetric black hole spacetimes. The effective quantum spacetime felt by a pointlike 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 than, equal to, and smaller than a certain critical mass $M_{\mathrm{cr}}$ the spacetime has two, one, and no horizon(s), respectively. Its Hawking temperature, specific heat capacity, and entropy are computed as a function of $M.\mathrm{}$ It is argued that the black hole evaporation stops when $M$ approaches $M_{\mathrm{cr}}$ which is of the order of the Planck mass. In this manner a “cold” soliton-like remnant with the near-horizon geometry of ${\mathrm{AdS}}_2\times {\mathrm{S}}^2$ is formed. As a consequence of the quantum effects, the classical singularity at $r=0\mathrm{}$ 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 $M<\mathrm{}{M}_{\mathrm{cr}}.$

We use asteroseismic data obtained by the NASA Kepler mission to estimate the fundamental properties of more than 500 main-sequence and sub-giant stars. Data obtained during the first 10 months of Kepler science operations were used for this work, when these solar-type targets were observed for one month each in survey mode. Stellar properties have been estimated using two global asteroseismic parameters and complementary photometric and spectroscopic data. Homogeneous sets of effective temperatures, T eff, were available for the entire ensemble from complementary photometry; spectroscopic estimates of T eff and [Fe/H] were available from a homogeneous analysis of ground-based data on a subset of 87 stars. We adopt a grid-based analysis, coupling six pipeline codes to 11 stellar evolutionary grids. Through use of these different grid-pipeline combinations we allow implicitly for the impact on the results of stellar model dependencies from commonly used grids, and differences in adopted pipeline methodologies. By using just two global parameters as the seismic inputs we are able to perform a homogenous analysis of all solar-type stars in the asteroseismic cohort, including many targets for which it would not be possible to provide robust estimates of individual oscillation frequencies (due to a combination of low signal-to-noise ratio and short dataset lengths). The median final quoted uncertainties from consolidation of the grid-based analyses are for the full ensemble (spectroscopic subset) approximately 10.8% (5.4%) in mass, 4.4% (2.2%) in radius, 0.017 dex (0.010 dex) in log g, and 4.3% (2.8%) in mean density. Around 36% (57%) of the stars have final age uncertainties smaller than 1 Gyr. These ages will be useful for ensemble studies, but should be treated carefully on a star-by-star basis. Future analyses using individual oscillation frequencies will offer significant improvements on up to 150 stars, in particular for estimates of the ages, where having the individual frequency data is most important.

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.

The impact of the leading quantum gravity effects on the dynamics of the Hawking evaporation process of a black hole is investigated. Its spacetime structure is described by a renormalization group improved Vaidya metric. Its event horizon, apparent horizon, and timelike limit surface are obtained by taking the scale dependence of Newton’s constant into account. The emergence of a quantum ergosphere is discussed. The final state of the evaporation process is a cold, Planck size remnant.