Related papers: Variations on Birkhoff's theorem
Although the Gauss-Bonnet term is a topological invariant for general relativity, it couples naturally to a quintessence scalar field, modifying gravity at solar system scales. We determine the solar system constraints due to this term by…
The paper extends Birkhoff's theorem on doubly stochastic matrices to some countable families of discrete probability spaces with nonempty intersections. We join every two elements lying in the same probability space by an edge and…
A class of 2-dimensional models including 2-d dilaton gravity, spherically symmetric reduction of d-dimensional Einstein gravity and other related theories are classically analyzed. The general analytic solutions in the absence of matter…
The discovery of the acceleration of the rate of expansion of the Universe fosters new explorations of the behavior of gravitation theories in the cosmological context. Either the GR framework is valid but a cosmic component with a negative…
Our standard model of the Universe predicts the distribution of dark matter to $1\%$ at the scales needed for upcoming experiments, yet our predictions for how the luminous matter -- which has interactions besides gravity -- is distributed…
The analysis of the validity of Birkhoff's theorem about the uniqueness of the spherically symmetric solution of the gravitational field equations is extended to the framework of the Poincar\'e gauge gravity theory. The class of models with…
We present bounds on mirror dark matter scenario derived by using the effect of mirror matter on the luminosity of the Sun. In the perturbative regime where the mirror matter concentration is small relative to the ordinary matter we…
It has been argued that a Universe governed by Eddington-Born-Infeld gravity can be compatible with current cosmological constraints. The extra fields introduced in this theory can behave both as dark matter and dark energy, unifying the…
A generalized scalar-tensor theory is investigated whose cosmological term depends on both a scalar field and its time derivative. A correspondence with solutions of five-dimensional Space-Time-Matter theory is noted. Analytic solutions are…
Quantum manifestations of the dynamics around resonant tori in perturbed Hamiltonian systems, dictated by the Poincar\'e--Birkhoff theorem, are shown to exist. They are embedded in the interactions involving states which differ in a number…
We present a new universal relation, satisfied by matter distributions at all observed scales, and show its amazingly good and detailed agreement with the predictions of the most up-to-date pure dark matter simulations of structure…
In Newtonian gravity (NG) it is known that the gravitational field anywhere inside a spherically symmetric distribution of mass is determined only by the enclosed mass. This is also widely believed to be true in general relativity (GR), and…
Does the Solar System and, more generally, a gravitationally bound system follow the cosmic expansion law ? Is there a cosmological influence on the dynamics or optics in such systems ? The general relativity theory provides an unique and…
The increasing rate of the Birkhoff sums in the infinite iterated function systems with polynomial decay of the derivative (for example the Gauss map) is studied. For different unbounded potential functions, the Hausdorff dimensions of the…
Recent results indicate the presence of a cosmological constant (or related dark energy) in the universe. It has been conjectured recently that the interaction parameters of physical theories may be dependant on the size parameter of the…
Recently, it was hypothesized that some supermassive black holes (SMBHs) may couple to the cosmic expansion. The mass of these SMBHs increase as the cubic power of the cosmic scale factor, leaving the energy density of the SMBHs unchanged…
An interaction between dark matter and dark energy is usually introduced by a phenomenological modification of the matter conservation equations, while the Einstein equations are left unchanged. Starting from some general and fundamental…
We provide a Kingman-like Theorem for arbitrary finite measures and a version of Birkhoff's Theorem for bounded observable. As an application, we show that Birkhoff's limit exists for some continuous observable, in an example of Bowen.
The source of the acceleration of the expansion of the Universe is still unknown. We examine some consequences of the possible scale invariance of the empty space at large scales. The central hypothesis of this work is that, at macroscopic…
Birkhoff's variety theorem, a fundamental theorem of universal algebra, asserts that a subclass of a given algebra is definable by equations if and only if it satisfies specific closure properties. In a generalized version of this theorem,…