Related papers: Birkhoff for Lovelock Redux
A general analytic spherically symmetric solution of the Bogomol'nyi equations is found. It depends on two constants and one arbitrary function on radius and contains the Bogomol'nyi-Prasad-Sommerfield and Singleton solutions as particular…
Three dimensional space is said to be spherically symmetric if it admits SO(3) as the group of isometries. Under this symmetry condition, the Einsteins Field equations for vacuum, yields the Schwarzschild Metric as the unique solution,…
An algorithm recently presented by Lake to obtain all static spherically symmetric perfect fluid solutions, is extended to the case of locally anisotropic fluids (principal stresses unequal). As expected, the new formalism requires the…
The classic Birkhoff- von Neumann theorem states that the set of doubly stochastic matrices is the convex hull of the permutation matrices. In this paper, we study a generalisation of this theorem in the type $II_1$ setting. Namely, we…
It was shown recently that Birkhoff's theorem for doubly stochastic matrices can be extended to unitary matrices with equal line sums whenever the dimension of the matrices is prime. We prove a generalization of the Birkhoff theorem for…
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…
The hierarchies of both Lovelock gravity and power-Yang-Mills field are combined through gravity in a single theory. In static, spherically symmetric ansatz exact particular integrals are obtained in all higher dimensions. The advantage of…
The possibility of spherically symmetric solutions in bi-metric theory of gravity is examined. It is shown that two possible black hole type solutions exists in the model. Spherically symmetric solution of general theory of relativity is…
We give a simple proof of the Birkhoff theorem about existence of a faithful representation for any finite-dimensional nilpotent Lie algebra of characteristic zero.
We prove an abstract Birkhoff normal form theorem for Hamiltonian partial differential equations on torus. The normal form is complete up to arbitrary finite order. The proof is based on a valid non-resonant condition and a suitable norm of…
We derive the general $\Sigma_2\times S$ solution of topologically massive gravity in vacuum and in presence of a cosmological constant. The field equations reduce to three-dimensional Einstein equations and the solution has constant Ricci…
We develop a new covariant formalism to treat spherically symmetric spacetimes in metric} f(R) theories of gravity. Using this formalism we derive the general equations for a static and spherically symmetric metric in a general…
We consider the Lovelock theory of gravity that assumes a nonlinearity of the field equations in the second-order derivatives of the metric. We prove the opportunity of obtaining cosmological solutions without isotropization in the presence…
We consider spherically symmetric space-times in GR under the unconventional assumptions that the spherical radius $r$ is either a constant or has a null gradient in the $(t,x)$ subspace orthogonal to the symmetry spheres (i.e., $(\partial…
We derive electrically charged black hole solutions of the Einstein-Gauss-Bonnet equations with a nonlinear electrodynamics source in $n (\ge 5)$ dimensions. The spacetimes are given as a warped product $M^2 \times K^{n-2}$, where $K^{n-2}$…
We consider linearly stable elliptic fixed points for a symplectic vector field and prove generic results of super-exponential stability for nearby solutions. Morbidelli and Giorgilli have proved a theorem of stability over…
A nonsymmetric gravitational theory (NGT) is presented which is free of ghost poles, tachyons and higher-order poles and there are no problems with asymptotic boundary conditions. An extended Birkhoff theorem is shown to hold for the…
We give a complete classification of all static, spherically symmetric solutions of the SU(2) Einstein-Yang-Mills theory with a positive cosmological constant. Our classification proceeds in two steps. We first extend solutions of the…
We consider static spherically symmetric solutions of the Einstein equations with cosmological constant coupled to the SU(2) Yang Mills equations. We prove that most solutions can be continued back to the origin of spherical symmetry and…
It is well known that vacuum equation of arbitrary Lovelock order for static spacetime ultimately reduces to a single algebraic equation, we show that the same continues to hold true for pure Lovelock gravity of arbitrary order $N$ for…