Related papers: Supercritical holes for the doubling map

We discuss a sequence of numerically constructed geometries describing binary black hole event horizons -- providing the necessary input for characteristic evolution of the exterior spacetime. Our sequence approaches a single Schwarzschild…

We introduce a class of infinitely renormalizable, unicritical diffeomorphisms of the disk (with a non-degenerate "critical point"). In this class of dynamical systems, we show that under renormalization, maps eventually become…

We construct certain non-degenerate maps and sets, mainly in the complex-analytic category. For example, we show that for every countable subset S in an irreducible complex space X there exists a holomorphic map from the unit disk to X such…

The profile of a critical hole in an undercooled wetting layer is determined by the saddle-point equation of a standard interface Hamiltonian supported by convenient boundary conditions. It is shown that this saddle-point equation can be…

We prove that the characterization of the critical locus for complex H\'enon maps that are small perturbations of quadratic polynomials with disconnected Julia sets given by Firsova holds in a much larger HOV-like region from the complex…

We discuss in detail the dynamics of maps $z\mapsto ae^z+be^{-z}$ for which both critical orbits are strictly preperiodic. The points which converge to $\infty$ under iteration contain a set $R$ consisting of uncountably many curves called…

We consider hybrid systems consisting of a hole-doped semiconductor coupled to electronic states of finite-size superconductors, where the opposite sign of the masses in the two subsystems give rise to insulating gaps at subband…

Three-dimensional equi-potential surfaces of a galactic system with supermassive binary black holes are discussed herein. The conditions of topological transitions for the important surfaces, i.e. Roche Lobes and Jiang-Yeh Lobe, are studied…

Let $X$ be a (real or complex) rearrangement-in\-va\-riant function space on $\Om$ (where $\Om = [0,1]$ or $\Om \subseteq \bbN$) whose norm is not proportional to the $L_2$-norm. Let $H$ be a separable Hilbert space. We characterize…

The existence and uniqueness of equilibrium points, including Lagrange Points and Jiang-Yeh Points, of a galactic system with supermassive binary black holes embedded in a centrally cuspy galactic halo are investigated herein. Differing…

In this note we show that for any hyperbolic surface S, the number of geodesics of length bounded above by L in the mapping class group orbit of a fixed closed geodesic with a single double point is asymptotic to L raised to the dimension…

Recently, observational hints for supermassive black holes have been accumulating, which has inspired ones to wonder: Can primordial black holes (PBHs) be supermassive, in particular with the mass $M\gtrsim 10^{9}M_\odot$? A supercritical…

Let $\mathcal{H}$ be a complex, separable Hilbert space, and set $\mathfrak{c}($NIL$_2)=\{ MN - NM : N, M \in \mathcal{B}(\mathcal{H}), M^2 = 0 = N^2 \}$. When $\dim\, \mathcal{H}$ is finite, we characterise the set $\mathfrak{c}($NIL$_2)$…

We consider the restriction of twice differentiable functionals on a Hilbert space to families of subspaces that vary continuously with respect to the gap metric. We study bifurcation of branches of critical points along these families, and…

We investigate the supercritical crossovers for black hole thermodynamics in the supercritical regime beyond the critical point, where small and large black holes are indistinguishable from the conventional viewpoint. We establish a refined…

Quadratic gravity illustrates how a replacement for black holes can emerge from a UV completion of gravity. 2-2-holes are extremely compact horizonless objects with an entropy $S_{22}$ due to trapped normal matter, and in this way they are…

Gravitationally bound supermassive black hole binaries (SBHBs) are thought to be a natural product of galactic mergers and growth of the large scale structure in the universe. They however remain observationally elusive, thus raising a…

A separable metric space X is an H-null set if any uniformly continuous image of X has Hausdorff dimension zero. upper H-null, directed P-null and P-null sets are defined likewise, with other fractal dimensions in place of Hausdorff…

Let $X$ and $Y$ be compact connected complex manifolds of the same dimension with $b_2(X)= b_2(Y)$. We prove that any surjective holomorphic map of degree one from $X$ to $Y$ is a biholomorphism. A version of this was established by the…

The dynamics of galactic systems with central binary black holes is studied. The model is a modification from the restricted three body problem, in which a galactic potential is added as an external potential. Considering the case with an…