Related papers: Non-Relativistic Gravity and its Coupling to Matte…
The intriguing choice to treat alternative theories of gravity by means of the Palatini approach, namely elevating the affine connection to the role of independent variable, contains the seed of some interesting (usually under-explored)…
This thesis studies modified theories of gravity from a geometric viewpoint. We review the motivations for considering alternatives to General Relativity and cover the mathematical foundations of gravitational theories in Riemannian and…
We study the small speed of light expansion of general relativity, utilizing the modern perspective on non-Lorentzian geometry. This is an expansion around the ultra-local Carroll limit, in which light cones close up. To this end, we first…
We study scalar, fermionic and gauge fields coupled nonminimally to gravity in the Einstein-Cartan formulation. We construct a wide class of models with nondynamical torsion whose gravitational spectra comprise only the massless graviton.…
The coupling between matter and gravity in General Relativity is given by a proportionality relation between the stress tensor and the geometry. This is an oriented assumption driven by the fact that both the stress tensor and the Einstein…
Einstein's equations in matter are gravitational analogues of Maxwell's equations in matter, providing an effective classical description of gravitational fields. We derive Einstein's equations in matter for relativistic fluids, and use…
The role of space-time torsion in general relativity is reviewed in accordance with some recent results on the subject. It is shown that, according to the connection compatibility condition, the usual Riemannian volume element is not…
Cartan's spacetime reformulation of the Newtonian theory of gravity is a generally-covariant Galilean-relativistic limit-form of Einstein's theory of gravity known as the Newton-Cartan theory. According to this theory, space is flat, time…
We study gravity coupled to scalar and fermion fields in the Einstein-Cartan framework. We discuss the most general form of the action that contains terms of mass dimension not bigger than four, leaving out only contributions quadratic in…
In this paper, starting from the common foundation of Connes' noncommutative geometry (NCG) [1,2,3,4], various possible alternatives in the formulation of a theory of gravity in noncommutative spacetime are discussed in detail. The…
The non-relativistic versions of the generalized Poincar\'{e} algebras and generalized $AdS$-Lorentz algebras are obtained. This non-relativistic algebras are called, generalized Galilean algebras type I and type II and denoted by…
We discuss a particular non-relativistic limit of NS-NS gravity that can be taken at the level of the action and equations of motion, without imposing any geometric constraints by hand. This relies on the fact that terms that diverge in the…
A new asymptotic expansion method is developed to separate the Wheeler-DeWitt equation into the time-dependent Schr\"{o}dinger equation for a matter field and the Einstein-Hamilton-Jacobi equation for the gravitational field including the…
We offer a perspective on some recent results obtained in the context of the group field theory approach to quantum gravity, on top of reviewing them briefly. These concern a natural mechanism for the emergence of non-commutative field…
In particular cases of stationary and stationary axially symmetric space-time passage to non-relativistic limit of Einstein equation is completed. For this end the notions of absolute space and absolute time are introduced due to…
This paper investigates the polytropic matter shell collapse in the non-commutative Reissner-Nordstr$\ddot{o}$m geometry. Using the Israel criteria, equation of motion for the polytropic matter shell is derived. In order to explore the…
We develop a covariant variational framework for relativistic electromagnetic continua (fluids and solid) based on Hamilton's principle formulated directly in the material description. The approach extends the geometric theory of…
Following the formalism of enveloping algebras and star product calculus we formulate and analyze a model of gauge gravity on noncommutative spaces and examine the conditions of its equivalence to general relativity. The corresponding…
We present a novel theory of gravity by considering an extension of symmetric teleparallel gravity. This is done by introducing, in the framework of the metric-affine formalism, a new class of theories where the nonmetricity $Q$ is…
We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain…