Related papers: On Newton-Cartan Cosmology
We perform a covariant 1+3 split of the Newton-Cartan equations. The resulting 3-dimensional system of equations, called \textit{the 1+3-Newton-Cartan equations}, is structurally equivalent to the 1+3-Einstein equations. In particular it…
The ``Newtonian'' theory of spatially unbounded, self--gravitating, pressureless continua in Lagrangian form is reconsidered. Following a review of the pertinent kinematics, we present alternative formulations of the Lagrangian evolution…
We provide a formal definition of p-brane Newton--Cartan (pNC) geometry and establish some foundational results. Our approach is the same followed in the literature for foundations of Newton--Cartan Gravity. Our results provide control of…
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…
We study a five-dimensional non-relativistic gravity theory whose action is composed of a gravitational sector and a sector of matter where the gravitational sector is given by the so called Newton--Chern--Simons gravity and where the…
We consider the homothetic motion group. We construct a homothetic covariant Newtonian gravitation theory which unifies inertial homothetic forces and gravitational fields. This is achieved through an equivalence principle based on a local…
We present a pedagogical discussion of the Coriolis field, emphasizing its not-so-well-understood aspects. We show that this field satisfies the field equations of the so-called Newton-Cartan theory, a generalization of Newtonian gravity…
Inflation in the framework of Einstein-Cartan theory is revisited. Einstein-Cartan theory is a natural extension of the General Relativity, with non-vanishing torsion. The connection on Riemann-Cartan spacetime is only compatible with the…
Constructing an extension of Newton's theory which is defined on a non-Euclidean topology (in the sense of Thurston's decomposition), called a non-Euclidean Newtonian theory, corresponding to the zeroth order of a non-relativistic limit of…
Assuming that the relativistic universe is homogeneous and isotropic, we can unambiguously determine its model and physical properties, which correspond with the Einstein general theory of relativity (and with its two special partial…
This article deals with a nonrelativistic cosmological model based on Galilean covariance, formulated within a five-dimensional Galilean manifold. Within this framework, we construct an isotropic and homogeneous metric analogous to the…
Cosmology is built on a relativistic understanding of gravity, where the geometry of the Universe is dynamically determined by matter and energy. In the cosmological concordance model, gravity is described by General Relativity, and it is…
The geometric content of the MacDowell-Mansouri formulation of general relativity is best understood in terms of Cartan geometry. In particular, Cartan geometry gives clear geometric meaning to the MacDowell-Mansouri trick of combining the…
Within the framework of the minimum quadratic Poincare gauge theory of gravity in the Riemann-Cartan spacetime we study the influence of gravitational vacuum energy density (a cosmological constant) on the dynamics of various gravitating…
In this work we consider gravitational theories in which the effect of coupling characteristic classes, appropriately introduced as operators in the Einstein-Hilbert action, has been taken into account. As it is well known, this approach…
In this work we introduce a cosmological constant in the extended Newtonian gravity theory. To this end, we extend the exotic Newton-Hooke algebra by introducing new generators and central charges. The new algebra obtained here has been…
Einstein's celebrated theory of gravitation can be presented in three forms: general relativity, teleparallel gravity, and the rarely considered before symmetric teleparallel gravity. Extending the latter, we introduce a new class of…
Geometrical structure of homogeneous isotropic models in the frame of the metric-affine gauge theory of gravity (MAGT) is analyzed. By using general form of gravitational Lagrangian including both a scalar curvature and various invariants…
We review how the large $c$ expansion of General Relativity leads to an effective theory in the form of Twistless Torsional Newton-Cartan gravity. We show how this is a strong field expansion around the static sector of General Relativity…
The geometric trinity of gravity comprises three distinct formulations of general relativity: (i) the standard formulation describing gravity in terms of spacetime curvature, (ii) the teleparallel equivalent of general relativity describing…