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We are interested in the development of spherically symmetric geometries in $F(T)$ teleparallel gravity which are of physical importance. We first express the general forms for the spherically symmetric frame and the zero curvature, metric…
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
The resolution of the problem of cosmological singularity in the framework of gauge theories of gravitation is discussed. Generalized cosmological Friedmann equations for homogeneous isotropic models filled by interacting scalar fields and…
We present a detailed study of rotational asymmetry in galaxies for both morphological and physical diagnostic purposes. An unambiguous method for computing asymmetry is developed, robust for both distant and nearby galaxies. By degrading…
We present a class of general prolate and oblate spheroidal spacetimes for the description of cosmic structures in the Universe. They are exact geometries which represent, in an appropriated way, the imbedding of spheroidal matter-energy…
The universal character of the gravitational interaction provided by the equivalence principle motivates a geometrical description of gravity. The standard formulation of General Relativity \`a la Einstein attributes gravity to the…
Gravity theories with non-minimally coupled scalar fields are used as characteristic examples in order to demonstrate the challenges, pitfalls and future perspectives of considering alternatives to general relativity. These lecture notes…
In this work we analyze the viability of use a particular models of scalar fields in the context of the galactic dark matter problem. These models are based on a single scalar field, minimally coupled to the gravity in a asymptotically flat…
We provide a brief overview into recent tests of gravity, focusing on its foundational spacetime symmetries. In particular, we work with an agnostic, effective field-theory framework, named the Standard-Model Extension, that allows for…
The aim of this paper is to give, using some contiguous relations, the asymptotic behaviour of some linear combination of two symmetric contiguous hypergeometric functions, under some conditions of their parameters.
This article presents the lattice-smeared gravity phase space reduction defined by the cosmological gauge-fixing conditions. These conditions are specified to reduce the SU(2) symmetry and the spatial diffeomorphism invariance of the loop…
We present an elementary account of mathematical cosmology through a series of important unsolved problems. We introduce the fundamental notion of `a cosmology' and focus on the issue of singularities as a theme unifying many current,…
These are lecture notes from my talks at the "Current Developments in Mathematics" conference (Harvard, 2006). They cover a variety of topics involving symplectic cohomology. In particular, a discussion of (algorithmic) classification…
In this introductory talk we will establish connections between the statistical analysis of galaxy clustering in cosmology and recent work in mainstream spatial statistics. The lecture will review the methods of spatial statistics used by…
We propose novel asymptotically locally flat boundary conditions for Einstein Gravity without cosmological constant in four dimensions that are consistent with the variational principle. They allow for complex solutions that are…
The recently unveiled deep-field images from the James Webb Space Telescope have renewed interest in what we can and cannot see of the universe. Answering these questions requires understanding the so-called "cosmological horizons" and the…
Because the gravitational Hamiltonian is a pure boundary term on-shell, asymptotic gravitational fields store information in a manner not possible in local field theories. This fact has consequences for both perturbative and…
Inflationary homogeneous isotropic cosmological models filled by scalar fields and ultrarelativistic matter are examined in the framework of gauge theories of gravitation. By using quadratic scalar field potential numerical analysis of…
We investigate the large gauge transformations of a two-form gauge field in four-dimensional Minkowski space. Our goal is to establish a connection between these asymptotic symmetries and the scalar soft theorems described by Campiglia,…
To understand the underlying degrees of freedom, near horizon symmetry analysis of a black has gain significant interest in the recent past. In this paper we generalized those analysis first by taking into account a generic null surface…