Investigations on asymptotic safety of metric, tetrad and Einstein-Cartan gravity

Among the different approaches for a construction of a fundamental quantum theory of gravity the Asymptotic Safety scenario conjectures that quantum gravity can be defined within the framework of conventional quantum field theory, but only non-perturbatively. In this case its high energy behavior is controlled by a non-Gaussian fixed point of the renormalization group flow, such that its infinite cutoff limit can be taken in a well defined way. A theory of this kind is referred to as non-perturbatively renormalizable. In the last decade a considerable amount of evidence has been collected that in four dimensional metric gravity such a fixed point, suitable for the Asymptotic Safety construction, indeed exists. This thesis extends the Asymptotic Safety program of quantum gravity by three independent studies that differ in the fundamental field variables the investigated quantum theory is based on, but all exhibit a gauge group of equivalent semi-direct product structure. It allows for the first time for a direct comparison of three asymptotically safe theories of gravity constructed from different field variables. The first study investigates metric gravity coupled to SU(N) Yang-Mills theory. In particular the gravitational effects to the running of the gauge coupling are analyzed and its implications for QED and the Standard Model are discussed. The second analysis amounts to the first investigation on an asymptotically safe theory of gravity in a pure tetrad formulation. Its renormalization group flow is compared to the corresponding approximation of the metric theory and the influence of its enlarged gauge group on the UV behavior of the theory is analyzed. The third study explores Asymptotic Safety of gravity in the Einstein-Cartan setting. Here, besides the tetrad, the spin connection is considered a second fundamental field. The larger number of independent field components and the enlarged gauge group render any RG analysis of this system much more difficult than the analog metric analysis. In order to reduce the complexity of this task a novel functional renormalization group equation is proposed, that allows for an evaluation of the flow in a purely algebraic manner. As a first example of its suitability it is applied to a three dimensional truncation of the form of the Holst action, with the Newton constant, the cosmological constant and the Immirzi parameter as its running couplings. A detailed comparison of the resulting renormalization group flow to a previous study of the same system demonstrates the reliability of the new equation and suggests its use for future studies of extended truncations in this framework.

Bouncing black holes in loop quantum gravity

In questo lavoro viene presentato un recente modello di buco nero che implementa le proprietà quantistiche di quelle regioni dello spaziotempo dove non possono essere ignorate, pena l'implicazione di paradossi concettuali e fenomenologici. In suddetto modello, la regione di spaziotempo dominata da comportamenti quantistici si estende oltre l'orizzonte del buco nero e suscita un'inversione, o più precisamente un effetto tunnel, della traiettoria di collasso della stella in una traiettoria di espansione simmetrica nel tempo. L'inversione impiega un tempo molto lungo per chi assiste al fenomeno a grandi distanze, ma inferiore al tempo di evaporazione del buco nero tramite radiazione di Hawking, trascurata e considerata come un effetto dissipativo da studiarsi in un secondo tempo. Il resto dello spaziotempo, fuori dalla regione quantistica, soddisfa le equazioni di Einstein. Successivamente viene presentata la teoria della Gravità Quantistica a Loop (LQG) che permetterebbe di studiare la dinamica della regione quantistica senza far riferimento a una metrica classica, ma facendo leva sul contenuto relazionale del tessuto spaziotemporale. Il campo gravitazionale viene riformulato in termini di variabili hamiltoniane in uno spazio delle fasi vincolato e con simmetria di gauge, successivamente promosse a operatori su uno spazio di Hilbert legato a una vantaggiosa discretizzazione dello spaziotempo. La teoria permette la definizione di un'ampiezza di transizione fra stati quantistici di geometria spaziotemporale, applicabile allo studio della regione quantistica nel modello di buco nero proposto. Infine vengono poste le basi per un calcolo in LQG dell'ampiezza di transizione del fenomeno di rimbalzo quantistico all'interno del buco nero, e di conseguenza per un calcolo quantistico del tempo di rimbalzo nel riferimento di osservatori statici a grande distanza da esso, utile per trattare a posteriori un modello che tenga conto della radiazione di Hawking e, auspicatamente, fornisca una possibile risoluzione dei problemi legati alla sua esistenza.

Bianchi type II cosmology in Hořava–Lifshitz gravity

In this work a Bianchi type II space-time within the framework of projectable Horava Lifshitz gravity was investigated; the resulting field equations in the infrared limit λ = 1 were analyzed qualitatively. We have found the analytical solutions for a toy model in which only the higher curvature terms cubic in the spatial Ricci tensor are considered. The resulting behavior is still described by a transition among two Kasner epochs, but we have found a different transformation law of the Kasner exponents with respect to the one of Einstein's general relativity.

PS-GANS: A Patient-Specific, Gravity Assisted Navigation System for Acetabular Cup Placement

In this paper we propose a new system that allows reliable acetabular cup placement when the THA is operated in lateral approach. Conceptually it combines the accuracy of computer-generated patient-specific morphology information with an easy-to-use mechanical guide, which effectively uses natural gravity as the angular reference. The former is achieved by using a statistical shape model-based 2D-3D reconstruction technique that can generate a scaled, patient-specific 3D shape model of the pelvis from a single conventional anteroposterior (AP) pelvic X-ray radiograph. The reconstructed 3D shape model facilitates a reliable and accurate co-registration of the mechanical guide with the patient’s anatomy in the operating theater. We validated the accuracy of our system by conducting experiments on placing seven cups to four pelvises with different morphologies. Taking the measurements from an image-free navigation system as the ground truth, our system showed an average accuracy of 2.1 ±0.7 o for inclination and an average accuracy of 1.2 ±1.4 o for anteversion.