Renormalization group improved black hole spacetimes

Abstract

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 .

Proper Time Flow Equation for Gravity

“…Recently a lot of work went into the exploration of the Wilsonian renormalization group (RG) flow of Quantum Einstein Gravity [1,2,3,4,5,6,7,8,9] and its possible impact on black holes and cosmology [10,11,12,13,14,15,16]. By definition, Quantum Einstein Gravity (QEG) is the conjectured quantum field theory of the spacetime metric whose bare action is (infinitesimally close to) an ultraviolet (UV) attractive non-Gaussian fixed point of the RG flow.…”

Astrophysical implications of the Asymptotic Safety Scenario in Quantum Gravity

“…In the case of Robertson-Walker spaces it will be shown that due to the very high degree of symmetry of the spacetime, the time-scale defined by "Hubble parameter" behaves essentially like the characteristic time scale associated to the relevant curvature invariants [38][39][40]. In the case of spherically symmetric spacetimes [30,31,41,42], near the singularity the proper distance of a radially free falling observer behaves essentially as 1/ √ Ψ 2 , being Ψ 2 the "Coulombian" component of the Weyl tensor.…”

“…In [30], a "RG-improvement" of the Schwarzschild metric has been performed and the properties of the corresponding "quantum black hole" have been explored. The improvement was based upon the scale dependent ("running") Newton constant G(k) obtained from the exact RG equation…”

“…In the RG improvement scheme of [30] the information about the k-dependence of G is exploited in the following way. The starting point is the classical Schwarzschild metric…”

“…The first one amounts to choose a fiducial metric which is a solution of the Einstein equations and RG-improve it by substituting the Newton constant G with the running G(k) together with a cutoff identification of the type (1.4). The limitation of this approach lies in the fact that in general the improved metric may not be a solution of Einstein equation, but one can imagine that this is a sort of "Thomas-Fermi" approximation where only the leading quantum corrections are taken into account [30,31]. The improved g µν (k) metric represents then a sort of "emergent" spacetime description of the effective geometry [32][33][34] according to the scale dependence of the Newton constant.…”