Related papers: Generalized derivations and general relativity
We study the behavior of a general gravitational action, including quadratic terms in the curvature, supplemented by a compact scalar field in 4+1 dimensions. The generalized Einstein equation for this system admits solutions which are…
We give a derivation of general relativity and the gauge principle that is novel in presupposing neither spacetime nor the relativity principle. We consider a class of actions defined on superspace with two key properties. The first is…
J. C. Maxwell, B. Riemann and H. Poincar$\acute{e}$ have proposed the idea that all microscopic particles are sink flows in a fluidic aether. Following this research program, a previous theory of gravitation based on a mechanical model of…
We introduce the generalized Heisenberg algebra appropriate for realizations of the $\mathfrak{gl}(n)$ algebra. Linear realizations of the $\mathfrak{gl}(n)$ algebra are presented and the corresponding star product, coproduct of momenta and…
In this paper we imitate the traditional method which is used customarily in the General Relativity and some mathematical literatures to derive the Gauss-Codazzi-Ricci equations for dimensional reduction. It would be more distinct…
The generalized harmonic representation of Einstein's equation is manifestly hyperbolic for a large class of gauge conditions. Unfortunately most of the useful gauges developed over the past several decades by the numerical relativity…
We develop a generic spacetime model in General Relativity which can be used to build any gravitational model within General Relativity. The generic model uses two types of assumptions: (a) Geometric assumptions additional to the inherent…
After the 1916 success of General relativity that explained gravity by adding time as a fourth dimension, physicists have been trying to explain other physical fields by adding extra dimensions. In 1921, Kaluza and Klein has shown that…
A generalized geometric method is developed for constructing exact solutions of gravitational field equations in Einstein theory and generalizations. First, we apply the formalism of nonholonomic frame deformations (formally considered for…
We define a generalized form of $L_\infty$-algebras called $E_2L_\infty$-algebras. As we show, these provide the natural algebraic framework for generalized geometry and the symmetries of double field theory as well as the gauge algebras…
In this paper, we aim to present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella hypergeometric functions, by using the extended Bessel function due to Boudjelkha [4].…
The Hamiltonian system of general relativity and its quantization without any matter or gauge fields are discussed on the basis of the symplectic geometrical theory. A symplectic geometry of classical general relativity is constructed using…
We study a model of the generalized Brans-Dicke gravity presented in both the Jordan and in the Einstein frames, which are conformally related. We show that the scalar field equations in the Einstein frame are reduced to the geodesics…
Einstein's general relativity can emerge from pregeometry, with the metric composed of more fundamental fields. We formulate euclidean pregeometry as a $SO(4)$ - Yang-Mills theory. In addition to the gauge fields we include a vector field…
This article shows that the approach to generalised curvature and torsion pioneered by Polacek and Siegel [1] is a generalisation of Cartan Geometry -- rendering latter natural from the point of view of O(d,d)-generalised geometry. We…
We investigate Lie symmetries of Einstein's vacuum equations in N dimensions, with a cosmological term. For this purpose, we first write down the second prolongation of the symmetry generating vector fields, and compute its action on…
General Relativity in dimension $n = p + q$ can be formulated as a gauge theory for the conformal group $SO(p+1,q+1)$, along with an additional field reducing the structure group down to the Poincar\'e group $ISO(p,q)$. In this paper, we…
Recently it was demonstrated that by adding to the Einstein-Hilbert action a series in powers of the curvature invariants with specially chosen coefficients one can obtain a theory of gravity which has spherically symmetric solutions…
The brane-worlds model was inspired partly by Kaluza-Klein's theory, where the gravitation and the gauge fields are obtained of a geometry of higher dimension (bulk). Such a model has been showing positive in the sense of we find…
We obtain the complete theory of Newton-Cartan gravity in a curved spacetime by considering the large $c$ limit of the vielbein formulation of General Relativity. Milne boosts originate from local Lorentzian transformations, and the special…