Related papers: Birkhoff's Theorem in Lovelock Gravity for General…
We present a Born-Infeld gravity theory based on generalizations of Maxwell symmetries denoted as $\mathfrak{C}_{m}$. We analyze different configuration limits allowing to recover diverse Lovelock gravity actions in six dimensions. Further,…
We consider pure three-dimensional Maxwell-Chern-Simons electrodynamics in the static limit. We show that this theory can be mapped onto a two-dimensional gravitational model in the first-order formalism of Riemannian manifolds with…
The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…
The f(T) theory, a generally modified teleparallel gravity, has been proposed as an alternative gravity model to account for the dark energy phenomena. Following our previous work [Xin-he Meng and Ying-bin Wang, EPJC(2011),…
We generalize Brendle's geometric inequality considered in \cite{B} to static manifolds. The inequality bounds the integral of inverse mean curvature of an embedded mean-convex hypersurface by geometric data of the horizon. As a…
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…
We extend Birkhoff's theorem for almost LRS-II vacuum spacetimes to show that the rigidity of spherical vacuum solutions of Einstein's field equations continues even in the perturbed scenario.
Birkhoff's theorem is discussed in the frame of f(R) gravity by using its scalar-tensor representation. Modified gravity has become very popular at recent times as it is able to reproduce the unification of inflation and late-time…
f(T) gravity, a generally modified teleparallel gravity, has become very popular in recent times as it is able to reproduce the unification of inflation and late-time acceleration without the need of a dark energy component or an inflation…
It is known that the Jebsen-Birkhoff theorem is valid for vacuum solutions to Einstein's equation, as well as some of its generalizations. Using symmetry inheritance properties we investigate in detail the additional constraints that fields…
In this note we prove a Birkhoff type transitivity theorem for continuous maps acting on non-separable completely metrizable spaces and we give some applications for dynamics of bounded linear operators acting on complex Fr\'{e}chet spaces.…
It can be easily shown that bound orbits around a static source can exist only in 4 dimension and in none else for any long range force. This is so not only for Maxwell's electromagnetic and Newton's gravity but also for Einstein's…
In this paper, we introduce the counterterms that remove the non-logarithmic divergences of the action in third order Lovelock gravity for static spacetimes. We do this by defining the cosmological constant in such a way that the asymptotic…
We introduce a simple method for the investigation of the classical stability of static solutions with a horizon in Lovelock gravity. The method is applicable to the investigation of high angular momentum instabilities, similar to those…
We give an alternative proof of the stable manifold theorem as an application of the (right and left) inverse mapping theorem on a space of sequences. We investigate the diffeomorphism class of the global stable manifold, a problem which in…
We classify the existent Birkhoff-type theorems into four classes: First, in field theory, the theorem states the absence of helicity 0- and spin 0-parts of the gravitational field. Second, in relativistic astrophysics, it is the statement…
We consider extensions of the Einstein-Hilbert Lagrangian to a general functional of metric and Riemann curvature tensor. A given such Lagrangian describes two different theories depending on considering connection and metric (Palatini…
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 model aimed at understanding quantum gravity in terms of Birkhoff's approach is discussed. The geometry of this model is constructed by using a winding map of Minkowski space into a $\mathbb{R}^{3} \times S^{1}$-cylinder. The basic field…
In this note we classify a certain family of solutions of Lovelock gravity in the Chern-Simons (CS) case, in arbitrary (odd) dimension greater than four. The spacetime is characterized by admitting a metric that is a warped product of a…