Related papers: Supercritical holes for the doubling map

The extended thermodynamics of Reissner-Nordstr\"om charged black holes in D-dimensional anti-de Sitter spacetime has a phase structure in the (T,p) plane that includes a line of first order phase transitions ending in a second order…

Generic $U(1)^2$ 4-d black holes with unbroken $N=1$ supersymmetry are shown to tend to a Robinson-Bertotti type geometry with a linear dilaton and doubling of unbroken supersymmetries near the horizon. Purely magnetic dilatonic black…

The semiclassical geometry of charged black holes is studied in the context of a two-dimensional dilaton gravity model where effects due to pair-creation of charged particles can be included in a systematic way. The classical mass-inflation…

If S is a set of q+2 points in P^2(F_q) such that some point of S is not on any line containing two other points of S, then in suitable coordinates S has the form S_f:={(c:f(c):1) : c in F_q} U {(1:0:0),(0:1:0)} for some f(X) in F_q[X]. Let…

An important theorem of geometric measure theory (first proved by Besicovitch and Davies for Euclidean space) says that every analytic set of non-zero $s$-dimensional Hausdorff measure $\mathcal H^s$ contains a closed subset of non-zero…

We describe some properties of the hyperbolically symmetric black hole (hereafter referred to as the $HSBH$) proposed a few years ago. We start by explaining the main motivation behind such an idea, and we determine the main differences…

Supersymmetric black holes in five-dimensional gauged supergravity must necessarily be rotating, and so in order to study the passage to black holes away from supersymmetry, it is of great interest to obtain non-extremal black holes that…

For a Banach space $X$ by $Conv_H(X)$ we denote the space of non-empty closed convex subsets of $X$, endowed with the Hausdorff metric. We prove that for any closed convex set $C\subset X$ and its metric component $H_C=\{A\in…

We consider high-dimensional percolation at the critical threshold. We condition the origin to be disjointly connected to two points, $x$ and $x'$, and subsequently take the limit as $|x|$, $|x'|$ as well as $|x-x'|$ diverge to infinity.…

A discrete subset $S$ of a topological gyrogroup $G$ with the identity $0$ is said to be a {\it suitable set} for $G$ if it generates a dense subgyrogroup of $G$ and $S\cup \{0\}$ is closed in $G$. In this paper, it was proved that each…

A bicirculant is a regular graph that admits an automorphism having two vertex-orbits of the same size. A bicirculant can be described as follows. Given an integer $m \ge 1$ and sets $R, S, T \subseteq \mathbb Z_m$ such that $R=-R$, $T=-T$,…

We study supercritical $O(d)$-equivariant biharmonic maps with a focus on $d = 5$, where $d$ is the dimension of the domain. We give a characterisation of non-trivial equivariant biharmonic maps from $\mathbf{R}^5$ into $S^5$ as…

In this paper, we investigate holographic superconductors dual to asymptotically anti-de Sitter black holes in an Einstein-Maxwell-scalar model with a non-minimal coupling between the scalar and Maxwell fields. In the probe limit, it shows…

Five-dimensional stringy rotating black holes are embedded into N=2 supergravity interacting with one vector multiplet. The existence of an unbroken supersymmetry of the rotating solution is proved directly by solving the Killing spinor…

It is an interesting, maybe surprising, fact that different dense subspaces of even "nice" topological spaces can have different densities. So, our aim here is to investigate the set of densities of all dense subspaces of a topological…

The multicritical point at which both a 3-component and a 2-component order parameters order simultaneously in 3 dimensions is shown to have the critical behavior of the decoupled fixed point, with separate n=3 and n=2 behavior. This…

We demonstrate the existence of $P-V$ criticality of the topological Ho\v{r}ava-Lifshitz(HL) black holes with a spherical horizon $(k=1)$ in the extended phase space. With the electric charge, we find that the critical behaviors of the HL…

We prove discrete Helly-type theorems for pseudohalfplanes, which extend recent results of Jensen, Joshi and Ray about halfplanes. Among others we show that given a family of pseudohalfplanes $\cal H$ and a set of points $P$, if every…

Supermassive black holes (SMBHs) found in the centers of many galaxies have been recognized to play a fundamental active role in the cosmological structure formation process. In hierarchical formation scenarios, SMBHs are expected to form…

A multiplicative subset $S$ of a ring $R$ is called \textit{strongly multiplicative} if $(\bigcap_{i\in\Delta}s_iR)\cap S \neq \emptyset$ for each family $(s_i)_{i\in\Delta}$ of elements in $S$. In this paper, we investigate how these sets…