Related papers: Structural stability of spherical horizons
Geometries with horizons offer insights into relationships between general relativity and quantum physics. For static spherically symmetric space-times, the event horizon is coincident with a coordinate anomaly that introduces complications…
We obtain the static spherically symmetric solutions of a class of gravitational models whose additions to the General Relativity (GR) action forbid Ricci-flat, in particular, Schwarzschild geometries. These theories are selected to…
Using techniques from harmonic analysis, we derive several sharp stability estimates for the second order Heisenberg Uncertainty Principle. We also present the explicit lower and upper bounds for the sharp stability constants and compute…
Secondary homological stability is a recently discovered stability pattern for the homology of a sequence of spaces exhibiting homological stability in a range where homological stability does not hold. We prove secondary homological…
Stability results for the Helmholtz equations in both deterministic and random periodic structures are proved in this paper. Under the assumption of excluding resonances, by a variational method and Fourier analysis in the energy space, the…
We consider the nonlinear Schr{\"o}dinger equation with a harmonic potential in the presence of two combined energy-subcritical power nonlinearities. We assume that the larger power is defocusing, and the smaller power is focusing. Such a…
The subject of this paper are spherically symmetric thin shells made of barotropic ideal fluid and moving under the influence of their own gravitational field as well as that of a central black hole; the cosmological constant is assumed to…
We study static spherically symmetric solutions of high derivative gravity theories, with 4, 6, 8 and even 10 derivatives. Except for isolated points in the space of theories with more than 4 derivatives, only solutions that are nonsingular…
We prove the global in time existence of spherically symmetric solutions to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear,…
The origin of equilibrium gravitational configurations is sought in terms of the stability of their trajectories, as described by the curvature of their Lagrangian configuration manifold. We focus on the case of spherical systems, which are…
We consider the cubic-quintic nonlinear Schr{\"o}dinger equation in space dimension up to three. The cubic nonlinearity is thereby focusing while the quintic one is defocusing, ensuring global well-posedness of the Cauchy problem in the…
There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…
We study the stability of static, spherically symmetric solutions of Rastall's theory in the presence of a scalar field with respect to spherically symmetric perturbations. It is shown that the stability analysis is inconsistent in the…
In this paper we analyse the stability of black hole Cauchy horizons arising in a class of 2d dilaton gravity models. It is shown that due to the characteristic asymptotic Rindler form of the metric of these models, time dependent…
The super-horizon second-order density perturbations corresponding to cosmological random fluctuations are considered, their non-vanishing spatial average is shown to be useful in solving the serious problem on the cosmological tension…
This paper is the second part of a trilogy dedicated to the following problem: given spherically symmetric characteristic initial data for the Einstein-Maxwell-scalar field system with a cosmological constant $\Lambda$, with the data on the…
Higher-order theories of gravity have received much attention from several areas including quantum gravity, string theory and cosmology. This paper proposes a higher-order gravity whose action includes all curvature scalar terms up to the…
The gravitational force harbours a fundamental instability against collapse. In standard General Relativity without Quantum Mechanics, this implies the existence of black holes as natural, stable solutions of Einstein's equations. If one…
We discuss spherically symmetric solutions for point-like sources in Lorentz-breaking massive gravity theories. This analysis is valid for St\"uckelberg's effective field theory formulation, for Lorentz Breaking Massive Bigravity and…
We review recent developments in structural stability as applied to key topics in general relativity. For a nonlinear dynamical system arising from the Einstein equations by a symmetry reduction, bifurcation theory fully characterizes the…