Related papers: POINTLESS SPACES IN GENERAL RELATIVITY
A simple general relativity theory for objects moving in gravitational fields is developed based on studying the behavior of an atom in a gravitational field. The theory is applied to calculate the satellite time dilation, light deflection…
A modified Mimetic gravity (MMG) is proposed as a generalization of general relativity. The model contain a physical metric which is function of an auxiliary (unphysical) metric and a Lyra's metric. We construct different kinds of…
In general relativity (GR), spacetime geometry is no longer just a background arena but a physical and dynamical entity with its own degrees of freedom. We present an overview of approaches to quantum gravity in which this central feature…
We have examined a modified dilaton gravity whose action is separable into the kinetic and the cosmological terms for the sake of the quantization. The black hole solutions survive even in the quantized theory, but the ADM mass of the…
The classifying space of inertial reference frames in special relativity is naturally hyperbolic. There is a remarkable interplay between central elements of hyperbolic geometry and those of special relativity -- which, to a certain extent,…
In this paper we apply the symmetry principle in order to search for an alternative unified explanation of several cosmological puzzles such as the present stage of accelerated expansion of the Universe and the Hubble tension issue, among…
Group field theory is a background-independent approach to quantum gravity whose starting point is the definition of a quantum field theory on an auxiliary group manifold (not interpreted as spacetime, but rather as the finite-dimensional…
We survey foundational principles of Grothendieck's generalized spaces, including a critical glossary of the various, and often conflicting, terminological usages. Known results using generalized points support a fully pointwise notation…
In the framework of the theory of scale relativity, we suggest a solution to the cosmological problem of the formation and evolution of gravitational structures on many scales. This approach is based on the giving up of the hypothesis of…
We briefly review ideas about ``noncommutativity of space-time'' and approaches toward a corresponding theory of gravity.
We present a novel derivation of the spacetime metric generated by matter, without invoking Einstein's field equations. For static sources, the metric arises from a relativistic formulation of D'Alembert's principle, where the inertial…
A free system, considered to be a comparison system, allows for the notion of objective existence and inertial frame. Transformations connecting inertial frames are shown to be either Lorentz or generalized Galilei.
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
We construct invariant differential operators acting on sections of vector bundles of densities over a smooth manifold without using a Riemannian metric. The spectral invariants of such operators are invariant under both the diffeomorphisms…
Two-dimensional matterless dilaton gravity is a topological theory and can be classically reduced to a (0+1)-dimensional theory with a finite number of degrees of freedom. If quantization is performed, a simple gauge invariant quantum…
We present an innovative approach to dimensional analysis, based on a general representation theorem for complete quantity functions admitting a covariant scalar representation; this theorem is in turn grounded in a purely algebraic theory…
An obvious criterion to classify theories of modified gravity is to identify their gravitational degrees of freedom and their coupling to the metric and the matter sector. Using this simple idea, we show that any theory which depends on the…
It is well known that the geometrical framework of Riemannian geometry that underlies general relativity and its torsionful extension to Riemann-Cartan geometry can be obtained from a procedure known as gauging the Poincare algebra.…
A number of recent proposals for a quantum theory of gravity are based on the idea that spacetime geometry and gravity are derivative concepts and only apply at an approximate level. There are two fundamental challenges to any such…
Following the approach of Grignani and Nardelli [1], we show how to cast the two-dimensional model $L \sim curv^2 + torsion^2 + cosm.const$ -- and in fact any theory of gravity -- into the form of a Poincare gauge theory. By means of the…