Abstract: The imaging by the Event Horizon Telescope (EHT) of the supermassive central objects at the heart of the M87 and Milky Way (Sgr A*) galaxies, has marked the first step into peering at the photon rings and central brightness depression that characterize the optical appearance of black holes surrounded by an accretion disk. Recently, Vagnozzi et al. [arXiv:2205.07787] used the claim by the EHT that the size of the shadow of Sgr A* can be inferred by calibrated measurements of the bright ring enclosing it, to constrain a large number of spherically symmetric space-time geometries. In this work we use this result to study some features of the first and second photon rings of a restricted pool of such geometries in thin accretion disk settings. The emission profile of the latter is described by calling upon three analytic samples belonging to the family introduced by Gralla, Lupsasca, and Marrone, in order to characterize such photon rings using the Lyapunov exponent of nearly bound orbits and discuss its correlation with the luminosity extinction rate between the first and second photon rings. We finally elaborate on the chances of using such photon rings as observational discriminators of alternative black hole geometries using very long baseline interferometry.

Abstract: In loop quantum cosmology (LQC) the big bang singularity is generically resolved by a big bounce. This feature holds even when modified quantization prescriptions of the Hamiltonian constraint are used such as in mLQC-I and mLQC-II. While the later describes an effective description qualitatively similar to that of standard LQC, the former describes an asymmetric evolution with an emergent Planckian de-Sitter pre-bounce phase even in the absence of a potential. We consider the potential relation of these canonically quantized non-singular models with effective actions based on a geometric description. We find a 3-parameter family of metric-affine f (R) theories which accurately approximate the effective dynamics of LQC and mLQC-II in all regimes and mLQC-I in the post-bounce phase. Two of the parameters are fixed by enforcing equivalence at the bounce, and the background evolution of the relevant observables can be fitted with only one free parameter. It is seen that the non-perturbative effects of these loop cosmologies are universally encoded by a logarithmic correction that only depends on the bounce curvature of the model. In addition, we find that the best fit value of the free parameter can be very approximately written in terms of fundamental parameters of the underlying quantum description for the three models. The values of the best fits can be written in terms of the bounce density in a simple manner, and the values for each model are related to one another by a proportionality relation involving only the Barbero-Immirzi parameter.

Abstract: We consider the metric-affine formulation of bumblebee gravity, derive the field equations, and show that the connection can be written as Levi-Civita of a disformally related metric in which the bumblebee field determines the disformal part. As a consequence, the bumblebee field gets coupled to all the other matter fields present in the theory, potentially leading to nontrivial phenomenological effects. To explore this issue we compute the post-Minkowskian, weak-field limit and study the resulting effective theory. In this scenario, we couple scalar and spinorial matter to the effective metric, and then we explore the physical properties of the VEV of the bumblebee field, focusing mainly on the dispersion relations and the stability of the resulting effective theory.

Abstract: The metric-affine bumblebee model in the presence of fermionic matter minimally coupled to the connection is studied. We show that the model admits an Einstein frame representation in which the matter sector is described by a non-minimal Dirac action without any analogy in the literature. Such non-minimal terms involve unconventional couplings between the bumblebee and the fermion field. We then rewrite the quadratic fermion action in the Einstein frame in the basis of 16 Dirac matrices in order to identify the coefficients for Lorentz/CPT violation in all orders of the non-minimal coupling xi. The exact result for the fermionic determinant in the Einstein frame, including all orders in xi, is also provided. We demonstrate that the axial contributions are at least of second order in the perturbative expansion of xi. Furthermore, we compute the one-loop effective potential within the weak field approximation.

Abstract: A Weyl structure is usually defined by an equivalence class of pairs (g, omega) related by Weyl transformations, which preserve the relation del g = omega circle times g, where g and omega denote the metric tensor and a 1-form field. An equivalent way of defining such a structure is as an equivalence class of conformally related metrics with a unique affine connection Gamma((omega)), which is invariant under Weyl transformations. In a standard Weyl structure, this unique connection is assumed to be torsion-free and have vectorial non-metricity. This second view allows us to present two different generalizations of standard Weyl structures. The first one relies on conformal symmetry while allowing for a general non-metricity tensor, and the other comes from extending the symmetry to arbitrary (disformal) transformations of the metric.