It was discovered by the French mathematician Elie Cartan that the geometry of a surface could be revealed by rolling a ball on it. Remarkably, the mathematical description of this rolling process involve ingredients familiar from modern gauge theories. Cartan-geometrical descriptions of General Relativity and teleparallel gravity are presented and it is argued that typically Cartan-geometric...
We investigate a Schwarzschild metric exhibiting a signature
change across the event horizon, which gives rise to what we term a
Lorentzian-Euclidean black hole. The resulting geometry is regularized
by employing the Hadamard partie finie technique, which allows us to
prove that the metric represents a solution of vacuum Einstein
equations. In this framework, we introduce the concept of...
In this talk, I will review our new approach to constructing gravitational instantons in teleparallel gravity, based on the observation that the teleparallel action can be written as a product of torsion and excitation forms. This naturally leads to the idea of considering solutions in which these two forms are equal—solutions we call self-excited, in analogy with self-dual solutions in...
In the study of cosmology in teleparallel gravity, one can find a number of models whose dynamics turn out to have certain homogeneity properties, which allows finding a system of coordinates which separates the dynamics of "angular" and "radial" coordinates. In this split, one finds that the angular coordinates form a compact phase space, and that the qualitative dynamics in this part of the...
Palatini $F(R,X)$ gravity, with $X$ the inflaton kinetic term, proved to be a powerful framework for generating asymptotically flat inflaton potentials. Here we show that a quadratic Palatini $F(R,X)$ restores compatibility with data of the Peebles-Vilenkin quintessential model. Moreover, the same can be achieved with an exponential version of the Peebles-Vilenkin potential if embedded in a...
Distinct formulations of nonminimal models have been a leading motivating factor for the development of alternative theories of gravity. The metric and Palatini formulations, understood to be equivalent in minimally coupled models, can lead to physically distinct theories when a nonminimal coupling is introduced. The choice of formulation, made before the action is written down, is a discrete...
In the phase space perspective, scalar field slow roll inflation is described by a heteroclinic orbit from a saddle type fixed point to a final attractive point. In many models the saddle point resides in the scalar field asymptotics, and thus for a comprehensive view of the dynamics a global phase portrait is necessary. For this task, in the literature one mostly encounters dynamical...
The work addresses the calculation of the Kerr spacetime energy within the framework of the general teleparallel equivalent of general relativity. As an alternative to general relativity, teleparallel geometry is used instead of classical Riemannian geometry, where curvature is zero while torsion and non-metricity play an important role. Unlike the Schwarzschild metric, the Kerr metric allows...
We investigate non-metricity-based gravity models through a model-independent framework, confronting them with recent observational data. Employing Bayesian statistical methods, we analyze late time background evolution using DESI-BAO and Supernovae data, and probe linear perturbations via the modified gravity functions, effective gravitational coupling and damping in the gravitational wave...
Spacetime configurations corresponding to warp drives allow observers to traverse distances faster than the speed of light without violating the postulates of special relativity. Although appealing for space travel, it has been shown that warp drives in general relativity require exotic matter that violates energy conditions. Cosmological observations bring out the shortcomings of general...
We propose a new class of inflationary attractors in metric-affine gravity. Such class features a non-minimal coupling $\tilde\xi \, \Omega(\phi)$ with the Holst invariant $\tilde {\cal R}$ and an inflaton potential proportional to $\Omega(\phi)^2$. The attractor behaviour of the class takes place with two combined strong coupling limits. The first limit is realized at large $\tilde\xi$, which...
I will show how the Belinfante-Rosenfeld improvement terms, that render the energy-momentum tensor symmetric, emerge by coupling the matter to the affine-connection. In this sense the improvement terms correspond to the hypermomentum of matter. I will show how this is realized in two standard examples, the Maxwell field and the Dirac field. I will also show how the connection-matter couplings...
General theory of relativity, which is currently the widely accepted theory of gravity, directly predicts the existence of gravitational waves. This phenomenon was directly measured only in 2015 and in 2017 observational data confirmed the prediction that gravitational waves propagate at the speed of light. However, there are phenomena that general relativity cannot satisfactorily explain...
In metric-affine gravity, both the gravitational and matter actions depend not just on the metric, but also on the independent affine connection. Thus, matter can be modeled as a hyperfluid, characterized by both the energy-momentum and hypermomentum tensors. The latter is defined as the variation of the matter action with respect to the connection, and it encodes extra (micro)properties of...
We investigate the regularization of the Euclidean gravitational action in the teleparallel equivalent of general relativity (TEGR), where the action is dynamically equivalent to that of GR but depends on both the tetrad and an undetermined spin connection. We evaluate the action using both bulk and quasi-local surface integrals across three frames: proper, canonical, and a newly introduced...
Due to GR's age as a theory, many coordinate systems have been developed for it, each of which is specialized for some particular application. However, extensions of GR often lack these coordinate systems, as the GR ones are not trivially generalizable. In this thesis, we seek to develop such coordinate systems for New General Relativity (NGR), specifically in the context of black hole...
We analyze which internal affine gauge transformations can be attributed to the torsion, focussing on those that tensor give rise to Lie algebras. We find two such non-trivial structures, in which the gauge parameters are a two form and a scalar. In the first case gauge invariant variables are singled out, and a higher derivative power-counting renormalizable invariant action is derived. The...
Finsler spacetime geometry offers a natural generalization of Lorentzian one, based on a most general notion of arc length. In this talk, I will discuss:
- The physical motivations for adopting a Finslerian model of spacetime, with emphasis on its potential to describe scenarios beyond the reach of Riemannian geometry.
- The overlap between Finsler gravity and metric-affine gravity -- and...
Observations of energy-dependent photon time delays from distant flaring sources provide significant constraints on Lorentz Invariance Violation (LIV). Such effects originate from modified vacuum dispersion relations, causing differences in propagation times for photons emitted simultaneously from gamma-ray bursts, active galactic nuclei, or pulsars. These modifications are often parametrized...
We study the weak equivalence principle in the context of modified dispersion relations, a prevalent approach to quantum gravity phenomenology. We find that generic modified dispersion relations violate the weak equivalence principle. The acceleration in general depends on the mass of the test body, unless the Hamiltonian is either 2-homogeneous in the test particles’ 4-momenta or the...
We discuss the problem of describing the effective quantum spacetime probed by a high energetic particle by Finsler Geometry. We highlight the main theoretical gains and challenges of this approach in quantum gravity.
We also discuss the use of present and future experiments and observations to constrain Finslerian departures of Riemannian Geomety at the Planck scale and the prospects for...
In BF-theory terms, apart from the structure group itself, gravity and Yang-Mills theory or electromagnetism are distinguished in the constitutive law, or the simplicity constraints. This is suggestive of a unified topological phase, which is broken into separate internal and external gauge theory, with clear, almost canonical preferences for the excitation B-field for either part. But what if...
In alternative theories of gravity, particles may follow either Riemannian geodesics or non-Riemannian autoparallels, depending on the presence of a geometry-matter coupling via hypermomentum. Typically, autoparallels associated with connections that have nonmetricity are not derived from a variational principle. In this talk, we take the first steps toward finding a Finslerian variational...
Lorentz gauge theory of gravity with a symmetry breaking "Cartan khronon" field demonstrates its successful explanation for the $\Lambda$CDM model, with an emergent integration 3-form behaving as ideal dust. Within the chiral scheme of this theory, only the right-handed regime recovers the general relativity. A natural question that arises is what happens with the left-handed gravity? When...
Modified dispersion relations gives an effective way to incorporate Planck-scale effects into particle kinematics and quantum gravity phenomenology. These effects can be encoded in Hamilton functions and it goes beyond the standard quadratic dependence on the four-momentum. This leads to nontrivial modifications in the geodesic equations for point particles. In this talk, I explore the...
We review the current state of the numerical relativity formalism for teleparallel theories of gravity and assess the hyperbolicity of the 3+1 decomposition of the equations of motion in the Hamiltonian formulation. For this, we analyse a simplified version of the analog to the ADM equations in the teleparallel equivalent of general relativity. We consider linear perturbations around a flat...
We present the full algebraic classification of the gravitational field in four-dimensional general metric-affine geometries. As an immediate application, we determine the algebraic types of the broadest family of static and spherically symmetric black hole solutions with spin, dilation and shear charges in Metric-Affine Gravity.
Disformal transformations are specific deformations of the metric, involving other fields and their derivatives. They have been used to relate different modified gravity models. For instance, mimetic and teleparallel gravities.
We will put forward a geometric formulation of disformal transformations, thereby elucidating the role of the non-metric fields therein. We will also identify key...
Since General Relativity is a classical gauge gravitational theory of diffeomorphisms, a natural question arises: does the same hold for TEGR?
In this talk, we explore the gauge structure of TEGR from the perspective of principal bundles. We also focus on the popular claim that TEGR can be viewed as a gauge theory of translations. It is explained that the standard way of approaching this...
Galilei geometry, which may be obtained as a degenerate limit of Lorentzian geometry, allows for a coordinate-free formulation of Newtonian gravity, called Newton–Cartan gravity. This enables a geometric understanding of the Newtonian $c\to\infty$ limit of standard general relativity (GR). Recently, analogous geometric descriptions of the Newtonian limits of the (metric) teleparallel...
This work serves as a sequel to our previous study, where, by assuming the existence of the canonical Killing tensor forms and applying a general null tetrad transformation, we obtained a variety of solutions (Petrov types D, III, N) in vacuum with cosmological constant $\Lambda$. Among those, there is a unique Petrov type D solution with a shear-free, diverging and non-geodesic null...
Scalar-tensor theories with derivative interactions form backgrounds which spontaneously break Lorentz invariance (cosmology during inflation or the dark energy era is the archetype). I will discuss how to think about the dynamics of free scalar perturbations, phonons, on general anisotropic backgrounds, showing that phonons move on null geodesics of an acoustic spacetime described by its own...
The Maldacena-Shenker-Stanford (MSS) conjecture establishes the existence of an upper bound to the Lyapunov exponent of a thermal quantum system with a large number of degrees of freedom.
Holographic calculations of out-of-time order correlation functions (OTOCs), which are conveniently employed as indicators of the magnitude of quantum chaos, motivate such a statement, leading to the...
We will explore the nature of gravity and the modern physics tools that enhance our understanding of this fundamental force. By studying remarkable objects such as neutron stars and white dwarfs, we gain access to natural laboratories where gravitational theories can be tested under extreme conditions, revealing the interplay of fundamental interactions. In addition, we will examine other...
In geometric-optics limits, there exists a mapping between black hole images and eikonal black hole quasinormal modes (QNMs). More explicitly, the real part and imaginary part of the QNM frequencies correspond to the ring size and the detailed ring structure of the image, respectively. The explicit identification of such eikonal correspondence, however, relies a lot on the symmetry of the...
In spite of their unequivocal potential and the increasing number of counterexamples, ghost-ridden theories remain eminently disregarded as necessarily unphysical. In this talk, we will being by providing a lightning review of the problematic, and troubleshooting proposals in the literature. Then, we will present our own recent constructive method to avoid catastrophe in the face of a ghost*....
We present the theoretical and phenomenological basis of the imaging of astrophysical objects compact enough to hold a photon sphere, namely, an unstable bound light orbit. We discuss the features of the two most salient features of such an imaging (the photon rings and the shadow) for black holes and horizonless compact objects alike and comment on the possibilities and difficulties within...
In this work we analyze the propagation properties of gravitational waves in the hybrid metric-Palatini gravity theory. We introduce the scalar-tensor representation of the theory to make explicit the scalar degrees of freedom of the theory and obtain their equations of motion in a form decoupled from the metric tensor. Then, we introduce linear perturbations for the metric tensor and for the...
I will describe a formalism, originally envisaged in the 1960s and 1970s, that reformulates four-dimensional General Relativity in terms of a triple of 2-forms rather than a metric. In this approach, the field equations are expressed using the exterior derivative acting on differential forms, bringing the theory structurally closer to electromagnetism than in the conventional metric...
Although Newton published a theory of gravitation in his Principia (1687), the birth of modern science of space and time might be traced to Kant's insight in the 18th century - rooted in what we could nowadays call spontaneous breaking of chiral symmetry - that led him to realise Euclidean space and time as categories of intuition.
In the 19th century, Riemann and Clifford reimagined...
Effects of ultraviolet completions of gravity can be captured in low-energy regimes by local higher curvature corrections. Such description, however, is limited to yield strictly perturbative corrections, due to unphysical Ostrogradsky instabilities induced by higher derivatives in the correction terms. I will present a procedure for expunging spurious degrees of freedom from effective...
Earlier studies investigating the allowed fraction of dark matter as primordial black holes (PBHs) tend to completely rule out PBHs with masses smaller than ~10⁻¹⁵ solar masses. This is due to the lack of evidence for Hawking radiation coming from the final evaporation stages of such small PBHs. These limits, however, make the key assumption that these PBHs can be modelled as uncharged,...
In this talk, we explore the quasinormal modes (QNMs) and absorption cross sections of the $(3+1)$-dimensional Bardeen black hole spacetime surrounded by perfect fluid dark matter. While the case of massless scalar field perturbations has been previously addressed, our analysis focuses on two less explored scenarios: massive scalar field perturbations and massless Dirac field...
We analyze solutions of Chamseddine's topological gravity in four space-time dimensions and discover various black hole solutions with(out) torsion as well as those that describe naked singularities. Because all of the solutions belong to the sector with vanishing scalar fields, they share peculiar trait that all conserved charges are vanishing.
The [Cadabra symbolic computer algebra system][1] is an open source tool designed specifically for problems in field theory. It has extensive functionality for tensor computer algebra, tensor polynomial simplification including multi-term symmetries, fermions and anti-commuting variables, Clifford algebras and Fierz transformations, component computations, implicit coordinate dependence,...
We propose a scenario according to which the ultraviolet completion of General Relativity is realized through a stochastic gradient flow towards a topological BF theory. Specifically, we consider the stochastic gradient flow of a pre-geometric theory proposed by Wilczek. Its infrared limit exists, and corresponds to a fixed point where stochastic fluctuations vanish. Diffeomorphism symmetries...
Extended metric-Palatini gravity, quadratic in the antisymmetric part of the affine curvature, is known to lead to the general relativity plus a geometric Proca field. The geometric Proca, equivalent of the non-metricity vector in the torsion-free affine connection, qualifies to be a distinctive signature of the affine curvature. In this talk, we explore how shadow and photon motion near black...
Like general relativity, we would expect metric-affine gravity to be a non-renormalisable and perturbative quantum theory. In such cases, effective field theories are crucial for deriving universal low-energy predictions, and have enjoyed huge success. They must, however, must be constructed according to certain rules, and in particular they demand symmetry. We perform an exhaustive and...
Perturbative nonrenormalizability of gravity based on Hilbert-Einstein or Palatini actions prompted vast research in higher-derivative theories. The actions that are at least quadratic in curvature lead to a renormalizable theory, but they bring along the issue of possible unitarity violation from ghost and tachyonic degrees of freedom. Whether ghosts can or cannot be quantized consistently,...
Scalar-tensor theories have shown great potential in inducing tailored modifications compared to cosmic evolution in the ΛCDM model. We reconsider quintessence models in this work in the context of three driving potentials. We center the action of these models in the late Universe which leaves early ΛCDM cosmology unchanged. The effects show the potential of producing a faster expanding...
We consider a Schwarzschild-like BH immersed in both a Dehnen-type DM halo and a surrounding quintessence field. We derive the composite spacetime metric and analyze its geometric features, including horizon structure, curvature invariants, and the classical energy conditions. We then investigate geodesic dynamics, focusing on effective potentials, circular orbits, and ISCOs. Additionally, we...
