Related papers: Boundary dynamics in competing critical black hole…
The objective of this work is to establish a systematic study of boundary value problems within the framework of differential forms and variable exponent spaces. Specifically, we investigate the Hodge Laplacian and related first order…
An accelerated boundary correspondence (i.e. a flat spacetime accelerating mirror trajectory) is derived for the Kerr spacetime, with a general formula that ranges from the Schwarzschild limit (zero angular momentum) to the extreme maximal…
Combining several results from the previous works of the author, three main subtleties will be clarified here. First, similar to the rotating BTZ black holes, we show how for the warped BTZ black holes, the consideration of the effective…
In hyperbolic dynamics, a well-known result is: every hyperbolic Lyapunov stable set, is attracting; it's natural to wonder if this result is maintained in the sectional-hyperbolic dynamics. This question is still open, although some…
We study the gravity dual of a Lifshitz field theory in the context of a RSII brane-world scenario, taking into account the effects of the extra dimension through the contribution of the electric part of the Weyl tensor. We study the…
We consider the critical behavior at the threshold of black hole formation for the five dimensional vacuum Einstein equations satisfying the cohomogeneity-two triaxial Bianchi IX ansatz. Exploiting a discrete symmetry present in this model…
In this paper we consider a doubly critical nonlinear elliptic problem with Neumann boundary conditions. The existence of blow-up solutions for this problem is related to the blow-up analysis of the classical geometric problem of…
We solve dynamical equations of motion to determine the conditions under which an over-dense region in the early universe will lead to collapse to a black hole, starting from horizon crossing of the over-dense region to the point of…
The stellar ejection rate and the rates of change of the binary semimajor axis and eccentricity are derived from scattering experiments for the restricted three-body problem. They are used to study the evolution of binaries in simple models…
We consider initial-boundary-value problems for a class of nonlinear third order equations having non-autonomous forcing terms and get new asymptotic stability results by means of the Liapunov second method. The class includes equations…
Fractal basin boundaries provide an important means of characterizing chaotic systems. We apply these ideas to general relativity, where other properties such as Lyapunov exponents are difficult to define in an observer independent manner.…
In this paper, we deal with the boundary value problem $-\Delta u= |u|^{4/(n-2)}u/[\ln (e+|u|)]^\varepsilon$ in a bounded smooth domain $\Omega$ in $\mathbb{R}^n$, $n\geq 3$ with homogenous Dirichlet boundary condition. Here…
By using different continuation methods, we unveil a wide region in the parameter space of the discrete cubic-quintic complex Ginzburg-Landau equation, where several families of stable vortex solitons coexist. All these stationary solutions…
The gravitational collapse of a complex scalar field in the harmonic map is modeled in spherical symmetry. Previous work has shown that a change of stability of the attracting critical solution occurs in parameter space from the discretely…
We investigate the thermodynamic phase structure of four-dimensional \textit{R}-charged black holes--characterized by four independent $U(1)$ charges--through the lens of Lyapunov exponents associated with unstable circular orbits of both…
The critical solution in Choptuik scaling is shown to be closely related to the critical solution in the black-string black-hole transition (the merger), through double analytic continuation, and a change of a boundary condition. The…
We present the first study of the dynamical evolution of an isolated star cluster that combines a significant population of primordial binaries with the presence of a central black hole. We use equal-mass direct N-body simulations, with N…
We present the most general class of charged black hole solutions in third-order Lovelock gravity within even-dimensional spacetimes in the presence of an electromagnetic field. These solutions feature nonconstant-curvature horizons that…
We study the indivisibility of a quantum-corrected AdS black hole involving two kinds of global monopoles, regular or phantom ones to declare the effects from the quantum fluctuation, monopole factors and the negative cosmological constant…
By employing Duan's topological method, we classify critical points by their topological charge Q = +/-1 or 0. Previous work (Wei et al., Phys. Rev. D 105, 104003, 2022) investigated two typical anti-de Sitter (AdS) black holes: the…