Related papers: Kerr stability for small angular momentum
In this paper, we introduce and explore the properties of a new gauge choice for the vacuum Einstein equation inspired by the ingoing and outgoing radiation gauges (IRG, ORG) for the linearized vacuum Einstein equation introduced by…
We study the eigenvalues of the MOTS stability operator for the Kerr black hole with angular momentum per unit mass $|a| \ll M$. We prove that each eigenvalue depends analytically on $a$ (in a neighbourhood of $a=0$), and compute its first…
The ring wormhole is the zero-mass limit of the Kerr metric. Its geometry is locally flat, but the topology is nontrivial, with a throat connecting two asymptotic regions and a distributional curvature singularity on the ring encircling the…
We study the stability of static, spherically symmetric solutions to the Einstein equations with a scalar field as the source. We describe a general methodology of studying small radial perturbations of scalar-vacuum configurations with…
We prove the existence of a class of orbitally stable bound state solutions to nonlinear Schr\"odinger equations with super-quadratic confinement in two and three spatial dimensions. These solutions are given by time-dependent rotations of…
We investigate the existence and properties of traveling waves for the Euler-Korteweg system with general capillarity and pressure. Our main result is the existence in dimension two of waves with arbitrarily small energy. They are obtained…
This paper investigates the stability of traveling wave solutions to the free boundary Euler equations with a submerged point vortex. We prove that sufficiently small-amplitude waves with small enough vortex strength are conditionally…
A new class of exact spacetimes in Einstein's gravity, which are Kerr black holes immersed in an external magnetic (or electric) field that is asymptotically uniform and oriented along the rotational axis, is presented. These are…
We study the Klein--Gordon equation $\Box_{g_{a,M,l}}\psi-\mu^2_{\textit{KG}}\psi=0$ on subextremal Kerr--de Sitter black hole backgrounds with parameters $(a,M,l)$, where $l^2=\frac{3}{\Lambda}$. We prove boundedness and Morawetz estimates…
For a general spherically four--dimensional metric the notion of "circularity" of a family of equatorial geodesic trajectories is defined in geometrical terms. The main object turns out to be the angular--momentum function $J$ obeying a…
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…
For $1/3<K<1$, we consider the stability of two distinct families of spatially homogeneous solutions to the relativistic Euler equations with a linear equation of state $p=K\rho$ on exponentially expanding FLRW spacetimes. The two families…
The Kerr solution is defined by a null congruence which is geodesic and shear free and has a singular line contained in a bounded region of space. A generalization of the Kerr congruence for nonstationary case is obtained. We find a…
We consider the one-dimensional nonlinear Schr\"odinger equation with an attractive delta potential and mass-supercritical nonlinearity. This equation admits a one-parameter family of solitary wave solutions in both the focusing and…
We prove linear semi-stability for a large class of Einstein metrics of non-positive scalar curvature. More precisely, we show that any Einstein $n$-manifold with non-positive scalar curvature carrying a parallel twisted pure spin$^r$…
A compactness theorem is proved for a family of K\"{a}hler surfaces with constant scalar curvature and volume bounded from below, diameter bounded from above, Ricci curvature bounded and the signature bounded from below. Furthermore, a…
We consider the stability of the toroidal AdS-Schwarzshild black holes as solutions of the Einstein--Klein-Gordon system, with Dirichlet or Neumann boundary conditions for the scalar field. Restricting to perturbations that respect the…
We prove the asymptotic stability of the moving kinks for the nonlinear relativistic wave equations in one space dimension with a Ginzburg-Landau potential: starting in a small neighborhood of the kink, the solution, asymptotically in time,…
We develop a small-data Maxwell--Higgs theory on Schwarzschild and slowly rotating Kerr black-hole exteriors for gauge-invariant nonnegative self-interactions near the trivial vacuum. The Schwarzschild part gives a complete global,…
We show that the angular momentum - area inequality 8\pi |J| =< A for weakly stable minimal surfaces would apply to (I^+)-regular many-Kerr solutions, if any existed. Hence we remove the undesirable hypothesis in the Hennig-Neugebauer proof…