We reassess foundational aspects of Metric-Affine Gravity (MAG) in light of the Dressing Field Method, a tool allowing to systematically build gauge-invariant field variables. To get MAG started, one has to deal with the problem of "gauge translations". We first recall that Cartan geometry is the proper mathematical foundation for gauge theories of gravity, and that this problem never arises in that framework, which still allows to clarify the geometric status of gauge translations. Then, we show how the MAG kinematics is obtained via dressing in a technically streamlined way, which highlights that it reduces to a Cartan-geometric kinematics. less

We explore the possibility that part of what we call dark matter may be the mark of a preferred frame, revealing a breakdown of diffeomorphism invariance. In the non-relativistic limit this appears as a deviant matter source capable of attracting normal matter, but not feeling the attraction from other forms of matter or from itself. While this implies a violation of momentum conservation, no logical inconsistencies arise in this deviant ``Newtonian'' limit. In contrast, due to Bianchi identities, the relativistic theory must undergo core change, and we discuss a modification of Einstein's gravity capable of coupling a non-conserved source to gravity. It results from fixing some of the spatial components of the metric, thereby constraining the possible diffeomorphisms and clipping some of the equations. Bianchi identities can always be used to refill the equations, but the effective Stueckelberg stresses are so outlandish that this defines symmetry breakdown and violations of local energy-momentum conservation. We work out spherically symmetric solutions with static halos and flat rotation curves, with and without a central black hole. The model has the drawback that it can evade experimental constraints simply by setting to zero the local density of deviant matter (which is a non-dynamic input). Its presence, in contrast, would leave inimitable signatures. We briefly discuss the Hamiltonian formulation of these models, where such dark matter appears as a central charge in the Poisson bracket of the Hamiltonian and the momentum. less

This paper develops a renormalized perturbation theory framework for nonlinear structure formation in a broad class of modified gravity models that exhibit Vainshtein screening, with a focus on a viable subclass of Horndeski theories. We extend earlier perturbative methods, originally applied to DGP model, to construct a self-consistent treatment that captures both the linear modifications to gravity at large scales and the nonlinear screening effects at small scales. In the framework, the response of the gravitational potential to matter density fluctuations is characterized by renormalized propagators, leading to the definition of a nonlinear (or renormalized) effective gravitational constant. The paper details several numerical strategies to compute this renormalized gravitational constant. Numerical examples illustrate how the effective gravitational constant evolves with scale and redshift. These results are key to accurately predicting cosmological observables such as the matter power spectrum and bispectrum in modified gravity scenarios. less

Regular and spherically symmetric black holes that solve the singularity problems of the Schwarzschild solution are phenomenologically viable at large distance but usually suffer from the Cauchy horizon instability. To overcome this drawback, we extended the analysis to include hyperbolic and toroidal horizon topologies within the framework of static, topologically maximally symmetric spacetimes. We show that both hyperbolic and toroidal black holes can be constructed without Cauchy horizons and without curvature singularities, thereby avoiding the mass inflation instability. These solutions exhibit asymptotic flatness in a generalized quasi-Minkowskian sense. The phenomenological aspects of these solutions are also studied by examining their thermodynamical properties, the photon sphere, and the effective potentials, ensuring consistency with observable properties such as black hole shadows. Lastly, we investigate a reconstruction technique within a scalar-tensor gravity framework, illustrating how the discussed metrics can arise from well-defined scalar field dynamics. Our investigation presents a viable pathway for constructing physically realistic, regular black holes in both General Relativity and modified gravity, broadening the landscape of singularity-free spacetimes and offering models that may better reflect the nature of strong gravitational fields in astrophysical and cosmological settings. less

Black hole quasinormal modes (QNMs) can exhibit resonant excitations associated with avoided crossings in their complex frequency spectrum. Such resonance phenomena can serve as novel signatures for probing new physics, where additional degrees of freedom are commonly introduced. Motivated by this possibility, we investigate QNMs in systems where multiple degrees of freedom are coupled with each other, and introduce a definition of excitation factors suitable for such systems. To demonstrate our formulation, we apply it to a black hole in the Einstein-Maxwell-axion theory, where we find that avoided crossings can appear even between longest-lived modes originating from the fundamental modes of different degrees of freedom, in contrast to the Kerr case in General Relativity. We show that the excitation factors are indeed amplified as a manifestation of resonance at parameter values corresponding to the avoided crossings. less

Spinfoam theories propose a well-defined path-integral formulation for quantum gravity and are hoped to provide the dynamics of loop quantum gravity. However, it is computationally hard to calculate spinfoam amplitudes. The well-studied Euclidean Barrett-Crane model provides an excellent setting for testing analytical and numerical tools to probe spinfoam models. We explore a data-driven approach to accelerating spinfoam computations by showing that the vertex amplitude is an object that can be learned from data using deep learning. We divide the learning process into a classification and a regression task: Two networks are independently engineered to decide whether the amplitude is zero or not and to predict the precise numerical value, respectively. The trained networks are tested with several accuracy measures. The classifier in particular demonstrates robust generalisation far outside the training domain, while the regressor demonstrates high predictive accuracy in the domain it is trained on. We discuss limitations, possible improvements, and implications for future work. less

In this proof-of-principle study, we demonstrate the capability of the numerical-relativity code BAM to simulate fully relativistic black-hole binary-single and binary-binary encounters that result in flybys, delayed or accelerated eccentric mergers, exchanges, and other more complex dynamical interactions of initially non-spinning, equal-mass black holes. Our results show that we are able to simulate the time evolution of $N$ black holes in relativistic scattering scenarios, which exhibit interesting dynamics and gravitational-wave signals. The dynamics of these systems show noticeable differences compared to analogous systems in post-Newtonian approximations up to 2.5PN. A key result is that the gravitational waveforms exhibit remarkable features that could potentially make them distinguishable from regular binary mergers. less

Brane observers executing appropriate motion through a partially compactified Lorentz invariant bulk spacetime, such as M4xS1, can send signals along the brane that are instantaneous or even travel backward in time. Nevertheless, causality in the braneworld remains intact. We establish these results, which follow from superluminal signal propagation reported in arXiv:2206.13590, through classical analysis and then extend our reasoning by examining quantum mechanical microcausality. One implication is the capacity for real time communication across arbitrarily large distances. less

In this paper we will detail an approach to generate metrics and matter models on end-periodic manifolds, which are used extensively in the study of the exotic smooth structures of $\mathbb{R}^4$. We will present three distinct examples, discuss their associated matter models by solving the Einstein equations, and determine their physical viability by examining the energy conditions. We will also compare one of the models directly with existing models of matter distributions in extragalactic systems, to highlight the viability of utilizing exotic smooth structures to understand the existence and distribution of dark matter. less

In this paper we calculate the effect of the inclusion of exotic smooth structures on typical observables in Euclidean quantum gravity. We do this in the semiclassical regime for several gravitational free-field actions and find that the results are similar, independent of the particular action that is chosen. These are the first results of their kind in dimension four, which we extend to include one-loop contributions as well. We find these topological features can have physically significant results without the need for additional exotic physics. less