Related papers: Birkhoff for Lovelock Redux
We present a symmetry result to solutions of equations involving the fractional Laplacian in a domain with at least two perpendicular symmetries. We show that if the solution is continuous, bounded, and odd in one direction such that it has…
We attempt to answer whether Birkhoff's theorem (BT) is valid in the Einstein-Aether (EA) theory. The BT states that any spherically symmetric solution of the vacuum field equations must be static, unique, and asymptotically flat. For a…
Static, spherically symmetric solutions of the field equations for a particular dimensional continuation of general relativity with negative cosmological constant are found. In even dimensions the solution has many similarities with the…
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…
The static black hole solutions to the Einstein-Maxwell equations are all spherically symmetric, as are many of the recently discovered black hole solutions in theories of gravity coupled to other forms of matter. However, counterexamples…
Spherically symmetric static empty space solutions are studied in f(R) theories of gravity. We reduce the set of modified Einstein's equations to a single equation and show how one can construct exact solutions in different f(R) models. In…
We introduce discrete equational theories where operations are induced by those having discrete arities. We characterize the corresponding monads as monads preserving surjections. Using it, we prove Birkhoff type theorems for categories of…
We provide a simple, unified proof of Birkhoff's theorem for the vacuum and cosmological constant case, emphasizing its local nature. We discuss its implications for the maximal analytic extensions of Schwarzschild, Schwarzschild(-anti)-de…
We consider the Dirac equations in static spherically-symmetric space-times, and we present a type of spinor field whose structure allows the separation of elevation angle and radial coordinate in very general situations. We demonstrate…
Generalizing a result of Roe \cite{Roe} Strichartz proved in \cite{Str} that if a doubly-infinite sequence $\{f_k\}$ of functions on $\R^n$ satisfies $f_{k+1}=\Delta f_k$ and $|f_{k}(x)|\leq M$ for all $k=0,\pm 1,\pm 2,...$ and $x\in \R^n$,…
There is undetermined potential function $V(\phi)$ in the action of mimetic gravity which should be resolved through physical means. In general relativity(GR), the static spherically symmetric(SSS) solution to the Einstein equation is a…
We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in the whole space or in any cylindrical smooth domain with smooth boundary data one can find an…
We prove metric rigidity for complete manifolds supporting solutions of certain second order differential systems, thus extending classical works on a characterization of space-forms. In the route, we also discover new characterizations of…
This work reveals a fundamental link between general covariance and Birkhoff's theorem. We extend Birkhoff's theorem from general relativity to a broad class of generally covariant gravity theories formulated in the Hamiltonian framework.…
In this paper, we establish the second Bogolyubov theorem and global averaging principle for stochastic partial differential equations (in short, SPDEs) with monotone coefficients. Firstly, we prove that there exists a unique…
Spherically symmetric, asymptotically flat solutions of Shape Dynamics were previously studied assuming standard falloff conditions for the metric and the momenta. These ensure that the spacetime is asymptotically Minkowski, and that the…
We show that any analytically integrable Hamiltonian system near an equilibrium point admits a convergent Birkhoff normalization. The proof is based on a new, geometric approach to the problem.
Generalization of a known theorem to generate static, spherically symmetric black-hole solutions in higher dimensional Lovelock gravity is presented. Particular limits, such as Gauss-Bonnet (GB) and/or Einstein-Hilbert (EH) in any dimension…
The Schwarzschild solution is a complete solution of Einstein's field equations for a static spherically symmetric field. The Einstein's field equations solutions appear in the literature, but in different ways corresponding to different…
We construct analytic symplectomorphisms of the cylinder or the sphere with zero or exactly two periodic points and which are not conjugated to a rotation. In the case of the cylinder, we show that these symplectomorphisms can be chosen…