No abstract

Quadratic gravity constitutes a prototypical example of a perturbatively renormalizable quantum theory of the gravitational interactions. In this work, we construct the associated phase space of static, spherically symmetric, and asymptotically flat spacetimes. It is found that the Schwarzschild geometry is embedded in a rich solution space comprising horizonless, naked singularities and wormhole solutions. Characteristically, the deformed solutions follow the Schwarzschild solution up outside of the photon sphere while they differ substantially close to the center of gravity. We then carry out an analytic analysis of observable signatures accessible to the Event Horizon Telescope, comprising the size of the black hole shadow as well as the radiation emitted by infalling matter. On this basis, we argue that it is the brightness within the shadow region which constrains the phase space of solutions. Our work constitutes the first step towards bounding the phase space of black hole type solutions with a clear quantum gravity interpretation based on observational data.

We set up a consistent background field formalism for studying the renormalization group (RG) flow of gravity coupled to Nf Dirac fermions on maximally symmetric backgrounds. Based on Wetterich’s equation, we perform a detailed study of the resulting fixed point structure in a projection including the Einstein–Hilbert action, the fermion anomalous dimension, and a specific coupling of the fermion bilinears to the spacetime curvature. The latter constitutes a mass-type term that breaks chiral symmetry explicitly. Our analysis identified two infinite families of interacting RG fixed points, which are viable candidates to provide a high-energy completion through the asymptotic safety mechanism. The fixed points exist for all values of Nf outside of a small window situated at low values Nf and become weakly coupled in the large Nf-limit. Symmetry-wise, they correspond to “quasi-chiral” and “non-chiral” fixed points. The former come with enhanced predictive power, fixing one of the couplings via the asymptotic safety condition. Moreover, the interplay of the fixed points allows for cross-overs from the non-chiral to the chiral fixed point, giving a dynamical mechanism for restoring the symmetry approximately at intermediate scales. Our discussion of chiral symmetry breaking effects provides strong indications that the topology of spacetime plays a crucial role when analyzing whether quantum gravity admits light chiral fermions.

Black holes constitute some of the most fascinating objects in our universe. According to Einstein’s theory of general relativity, they are also deceivingly simple: Schwarzschild black holes are completely determined by their mass. Moreover, the singularity theorems by Penrose and Hawking indicate that they host a curvature singularity within their event horizon. The presence of the latter invites the question whether these dead-end points of spacetime can be made regular by considering (quantum) corrections to the classical field equations. In this light, we use the Frobenius method to investigate the phase space of asymptotically flat, static, and spherically symmetric black hole solutions in quadratic gravity. We argue that the only asymptotically flat black hole solution visible in this approach is the Schwarzschild solution.

We set up a consistent background field formalism for studying the renormalization group (RG) flow of gravity coupled to N f Dirac fermions on maximally symmetric backgrounds. Based on Wetterich's equation we perform a detailed study of the resulting fixed point structure in a projection including the Einstein-Hilbert action, the fermion anomalous dimension, and a specific coupling of the fermion bilinears to the spacetime curvature. The latter constitutes a mass-type term which breaks chiral symmetry explicitly. Our analysis identifies two infinite families of interacting RG fixed points which are viable candidates to provide a high-energy completion through the asymptotic safety mechanism. The fixed points exist for all values of N f outside of a small window situated at low values N f and become weakly coupled in the large N f -limit. Symmetry-wise, they correspond to "quasi-chiral" and "non-chiral" fixed points. The former come with enhanced predictive power, fixing one of the couplings via the asymptotic safety condition. Moreover, the interplay of the fixed points allows for cross-overs from the non-chiral to the chiral fixed point, giving a dynamical mechanism for restoring the symmetry approximately at intermediate scales. Our discussion of chiral symmetry breaking effects provides strong indications that the topology of spacetime plays a crucial role when analyzing whether quantum gravity admits light chiral fermions.