Related papers: Birkhoff rigidity from a covariant optical seed
In this paper we prove the birational superrigidity of Fano-Mori fibre spaces $\pi\colon V\to S$, every fibre of which is a complete intersection of type $d_1\cdot d_2$ in the projective space ${\mathbb P}^{d_1+d_2}$, satisfying certain…
We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open…
We study static, spherically symmetric vacuum solutions to Quadratic Gravity, extending considerably our previous Rapid Communication [Phys. Rev. D 98, 021502(R) (2018)] on this topic. Using a conformal-to-Kundt metric ansatz, we arrive at…
All three-dimensional matter-free spacetimes with negative cosmological constant, compatible with cyclic symmetry are identified. The only cyclic solutions are the 2+1 (BTZ) black hole with SO(2) x R isometry, and the self-dual…
A modified theory of gravity with the function $F(R) = (1-\sqrt{1-2\lambda R})/\lambda$ is suggested and analyzed. At small value of the parameter $\lambda$ introduced the action is converted into Einstein$-$Hilbert action. The theory is…
We study the evolution of vortex sheets according to the Birkhoff-Rott equation, which describe the motion of sharp shear interfaces governed by the incompressible Euler equation in two dimensions. In a recent work, the authors demonstrated…
We study the nilpotent part $N'$ of a pseudo-periodic automorphism $h$ of a real oriented surface with boundary $\Sigma$. We associate a quadratic form $Q$ defined on the first homology group (relative to the boundary) of the surface…
The Kerr solution is generated from the Schwarzschild solution by a simple combination of real global coordinate transformations and of invariance transformations acting on the space of stationary solutions of the Einstein-Maxwell…
We derive the linearly perturbed matching conditions between a Schwarzschild spacetime region with stationary and axially symmetric perturbations and a FLRW spacetime with arbitrary perturbations. The matching hypersurface is also perturbed…
We give a thorough description of the shape of rotating axisymmetric stable black-hole (apparent) horizons applicable in dynamical or stationary regimes. It is found that rotation manifests in the widening of their central regions…
The generic null geodesic of the Schwarzschild--Kruskal--Szekeres geometry has a natural complexification, an elliptic curve with a cusp at the singularity. To realize that complexification as a Riemann surface without a cusp, and also to…
We study spherically symmetric static empty space solutions in $R+\varepsilon/R$ model of $f(R)$ gravity. We show that the Schwarzschild metric is an exact solution of the resulted field equations and consequently there are general…
We generalize Birkhoff's Theorem in the following fashion. We find necessary and sufficient conditions for any spherically symmetric space-time to be static in terms of the eigenvalues of the stress-energy tensor. In particular, we…
In this paper we extend our previously discovered exact solution for an SU(2) gauge theory coupled to a massless, non-interacting scalar field, to the general group SU(N+1). Using the first-order formalism of Bogomolny, an exact,…
We consider rotating black hole configurations of self-gravitating maps from spacetime into arbitrary Riemannian manifolds. We first establish the integrability conditions for the Killing fields generating the stationary and the…
The Chern-Simons modification to general relativity in four dimensions consists of adding to the Einstein-Hilbert term a scalar field that couples to the first class Pontryagin density. In this theory, which has attracted considerable…
We present a closed-form surrogate for the equivalent diameter of the Kerr black-hole shadow, defined as the diameter of the circle with the same area as the shadow's critical curve. The construction enforces the exact face-on (polar) limit…
In this paper, we identify two fractals if and only if they are biLipschitz equivalent. Fix ratio $r,$ for dust-like graph-directed sets with ratio $r$ and integer characteristics, we show that they are rigid in the sense that they are…
We perform the stability analysis of the Kerr black hole in the Einstein-Chern-Simons-Scalar theory with quadratic scalar coupling. For positive coupling parameter ($\alpha>0$), we introduce the (2+1)-dimensional hyperboloidal foliation…
Kerr-Schild solutions to the vacuum Einstein equations are considered from the viewpoint of integral equations. We show that, for a class of Kerr-Schild fields, the stress-energy tensor can be regarded as a total divergence in Minkowski…