Related papers: Addendum: Observables for General Relativity relat…
This article provides a simple geometric interpretation of the quadratic formula. The geometry helps to demystify the formula's complex appearance and casts it into a much simpler existence, thus potentially benefits early algebra students.
The orbital Lense-Thirring precession is considered in the context of constraints for weak-field General Relativity involving the cosmological constant $\Lambda$. It is shown that according to the current accuracy of satellite measurements…
In this work, we discuss the conditions that allow the establishment of an equivalence between $f(R,T)=R+\lambda h(T)$ gravity models and General Relativity (GR) coupled to a modified matter sector. We do so by considering a $D$-dimensional…
Consider a finite-dimensional, complex Lie algebra G and a semi-simple automorphism {\alpha}. This note aims to give a short and simple proof for explicit upper bounds for the derived length of the radical R and the rank of a Levi…
We study the field equations of modified theories of gravity in which the lagrangian is a general function of the Ricci scalar and Ricci-squared terms in Palatini formalism. We show that the independent connection can be expressed as the…
We prove that the C*-algebra of a second-countable, \'etale, amenable groupoid is simple if and only if the groupoid is topologically principal and minimal. We also show that if G has totally disconnected unit space, then the associated…
We show that some primary special relativity effects, which are believed to be hardly detectable in everyday life, such as time dilation, relativistic Doppler effect, and length contraction, should tangibly and spectacularly show up here on…
Let $V_{L}$ be the vertex algebra associated to a non-degenerate even lattice $L$, $\theta$ the automorphism of $V_{L}$ induced from the $-1$-isometry of $L$, and $V_{L}^{+}$ the fixed point subalgebra of $V_{L}$ under the action of…
We calculate the deflection angle, as well as the positions and magnifications of the lensed images, in the case of covariant $f(T)$ gravity. We first extract the spherically symmetric solutions for both the pure-tetrad and the covariant…
An action principle is described which unifies general relativity and topological field theory. An additional degree of freedom is introduced and depending on the value it takes the theory has solutions that reduce it to 1) general…
The exploration of the notion of observability exhibits transparently the rich interplay between algebraic and geometric ideas in \emph{geometric invariant theory}. The concept of \emph{observable subgroup} was introduced in the early 1960s…
By changing to an orthogonal basis, we give a short proof that the subfactor of the graded algebra of a planar algebra reproduces the planar algebra.
We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.
We present a framework that reformulates gravitational lensing as an optical phenomenon governed by an effective refractive index, enabling exploration of modified gravity theories using undergraduate-level mathematics and optics. After…
If the Universe satisfies a perturbed Friedmann-Lema\^{\i}tre model, then the bright matter (e.g. radio-loud active galactic nuclei, RLAGNs) may be topologically lensed by global geometry. The generation of candidate topological lensing…
In this work we will consider the concepts of partial and complete observables for canonical general relativity. These concepts provide a method to calculate Dirac observables. The central result of this work is that one can compute Dirac…
Firstly, we present a reformulation of the standard canonical approach to spherically symmetric systems in which the radial gauge is imposed. This is done via the gauge unfixing technique, which serves as the exposition in the context of…
Cosmic acceleration may be due to modifications of cosmic gravity and to test this we need robust connections between theory and observations. However, in a model independent approach like effective field theory or a broad class like…
The purpose of this erratum and addendum is to correct the errors in [1]. It consists of five components: 1. Lemma 7.1 and Proposition 7.2 are wrong and discarded; 2. A new proof of existence $\lambda(\xi)$ in (7.1) without Proposition 7.2;…
We consider some natural generalizations to the class of all GLP-algebras of the so-called reduction property for reflection algebras in arithmetic. An analogue of this property is established for the free GLP-algebras and for some…