Related papers: Random complex zeroes, III. Decay of the hole prob…
The spacetime singularities in classical general relativity are inevitable, which are also predicated by the celebrated singularity theorems. However, it is general belief that singularities do not exist in the nature and they are the…
We obtain the asymptotic behavior of hole probability for random holomorphic sections on a compact Riemann surface with respect to the hole size.
We consider the evolution of a warped disc around a Kerr black hole, under conditions such that the warp propagates in a wavelike manner. This occurs when the dimensionless effective viscosity, alpha, that damps the warp is less than the…
We establish a convergence speed estimate for hole probabilities of zeros of random holomorphic sections on compact Riemann surfaces.
Quantization of the gravitational field may allow the existence of a decay channel of black holes into white holes with an explicit time-reversal symmetry. The definition of a meaningful decay probability for this channel is studied in…
A {\em convex hole} (or {\em empty convex polygon)} of a point set $P$ in the plane is a convex polygon with vertices in $P$, containing no points of $P$ in its interior. Let $R$ be a bounded convex region in the plane. We show that the…
The probability that a zero of a random real polynomial of increasing degree is real tends to zero. However, passing from polynomials to Laurent polynomials yields a surprising result: the probability that a root is real tends not to zero,…
The Kiselev model describes a black hole surrounded by a fluid with equations of state $p_r/\rho=-1$ and $p_t/\rho=(3w+1)/2$ respectively in radial and tangential directions. It has been extensively studied in the parameter region…
We examine spherical gravitational collapse of a matter model with vanishing radial pressure and non-zero tangential pressure. It is seen analytically that the collapsing cloud either forms a black hole or disperses depending on values of…
We give a full metric describing the gravitational field of a static and axisymmetric thin disk without radial pressure encircling a Schwarzschild black hole. The disk density profiles are astrophysically realistic, stretching from the…
In this article, we propose a few sufficient conditions on polynomials having integer coefficients all of whose zeros lie outside a closed disc centered at the origin in the complex plane and deduce the irreducibility over the ring of…
We show that with high probability the number of real zeroes of a random polynomial is bounded by the number of vertices on its Newton-Hadamard polygon times the cube of the logarithm of the polynomial degree. A similar estimate holds for…
We employ a late-time expansion to study the interior of rotating black holes coupled to a massless scalar field in asymptotically flat spacetime. We find that decaying fluxes of scalar radiation into the black hole necessitate the…
The theory of coronal evaporation predicts the formation of an inner hole in the cool thin accretion disk for mass accretion rates below a certain value (~ 1/50 of the Eddington mass accretion rate) and the sudden disappearance of this hole…
The probability of a random polygon (or a ring polymer) having a knot type $K$ should depend on the complexity of the knot $K$. Through computer simulation using knot invariants, we show that the knotting probability decreases exponentially…
A compact packing is a set of non-overlapping discs where all the holes between discs are curvilinear triangles. There is only one compact packing by discs of size $1$. There are exactly $9$ values of $r$ which allow a compact packing by…
We study asymptotic clustering of zeros of random polynomials, and show that the expected discrepancy of roots of a polynomial of degree $n$, with not necessarily independent coefficients, decays like $\sqrt{\log n/n}$. Our proofs rely on…
We consider packings of the plane using discs of radius 1 and r=0.545151... . The value of r admits compact packings in which each hole in the packing is formed by three discs which are tangent to each other. We prove that the largest…
Using the Hartle-Hawking no-boundary proposal for the wave function of the universe, we can study the wave function and probability of a single black hole created at the birth of the universe. The black hole originates from a constrained…
How likely is the high level of a continuous Gaussian random field on an Euclidean space to have a "hole" of a certain dimension and depth? Questions of this type are difficult, but in this paper we make progress on questions shedding new…