Related papers: Random complex zeroes, III. Decay of the hole prob…
Investigating the rigidly rotating disc of dust with constant specific charge, we find that it leads to an extreme Kerr-Newman black hole in the ultra-relativistic limit. A necessary and sufficient condition for a black hole limit is, that…
The probability of finding a spherical cavity or "hole" of arbitrarily large size in typical disordered many-particle systems in the infinite-size limit (e.g., equilibrium liquid states) is non-zero. Such "hole" statistics are intimately…
We consider packings of the plane using discs of radius 1 and r. A packing is compact if every disc D is tangent to a sequence of discs D_1, D_2, ..., D_n such that D_i is tangent to D_{i+1}. We prove that there are only nine values of r…
There is a maximum for the gravity of a black hole in the vertical direction in the accretion disc. Outflows may probably be driven from the disc if the radiation flux of the disc is greater than a critical value corresponding to the…
We show that the apparent horizon and the region near $r=0$ of an evaporating charged, rotating black hole are timelike. It then follows that for black holes in nature, which invariably have some rotation, have a channel, via which…
Astrophysical black hole candidates are thought to be the Kerr black holes predicted by General Relativity, but the actual nature of these objects has still to be proven. The Kerr black hole hypothesis can be tested by observing strong…
Consider a random system $\mathfrak{f}_1(x)=0,\ldots,\mathfrak{f}_n(x)=0$ of $n$ random real polynomials in $n$ variables, where each $\mathfrak{f}_k$ has a prescribed set of exponent vectors in a set $A_k\subseteq \mathbb{Z}^n$ of size…
The expected number of real zeros of an algebraic polynomial $a_0+a_1x+a_2x^2+a_3x^3+....+a_{n-1}x^{n-1}$ depends on the types of random coefficients, with large $n.$ In this article, we show that when the random coefficients…
We suppose that linear optical polarization is due to multiple scattering in optically thick magnetized accretion disk around central black hole. The polarization degree is very sensitive to the spin of black hole - for Kerr rotating hole…
A star surrounded by a black hole generated by it is analyzed. For an outer static observer the black hole mass (and radius) depends on his position in the gravitational field of the star. In spite of the black hole presence, the geometry…
By a compact packing of the plane by discs, $P$, we mean a collection of closed discs in the plane with pairwise disjoint interior so that, for every disc $C\in P$, there exists a sequence of discs $D_{0},\ldots,D_{m-1}\in P$ so that each…
Let each of n particles starting at the origin in Z^2 perform simple random walk until reaching a site with no other particles. Lawler, Bramson, and Griffeath proved that the resulting random set A(n) of n occupied sites is (with high…
A disc packing in the plane is compact if its contact graph is a triangulation. There are $9$ values of $r$ such that a compact packing by discs of radii $1$ and $r$ exists. We prove, for each of these $9$ values, that the maximal density…
We provide an elementary geometric derivation of the Kac integral formula for the expected number of real zeros of a random polynomial with independent standard normally distributed coefficients. We show that the expected number of real…
We consider a rapidly spinning black hole surrounded by an equatorial, geometrically thin, slowly accreting disk that is stationary and axisymmetric. We analytically compute the broadening of electromagnetic line emissions from the…
Black holes represent outstanding astrophysical laboratories to test the strong gravity regime, since alternative theories of gravity may predict black hole solutions whose may differ distinctly from those of General Relativity. When higher…
In this chapter I focus on asking and answering the following questions: (1) What is a black hole? Answer: There are three types of black holes, namely mathematical black holes, physical black holes and astrophysical black holes. An…
The truncation of stellar discs is not abrupt but characterized by a continuous distancing from the exponential profile. There exists a truncation curve, $t(r)$, ending at a truncation radius, $r_t$. We present here a theoretical model in…
We define the knotting probability of a knot $K$ by the probability for a random polygon (RP) or self-avoiding polygon (SAP) of $N$ segments having the knot type $K$. We show fundamental and generic properties of the knotting probability…
We show that the problem of deciding positivity of Kronecker coefficients is NP-hard. Previously, this problem was conjectured to be in P, just as for the Littlewood-Richardson coefficients. Our result establishes in a formal way that…