Related papers: Envelopes for orbits around axially symmetric sour…
Spherically symmetric static fluid sources are endowed with rotation and embedded in Kerr empty space-time up to an including quadratic terms in an angular velocity parameter using Darmois junction conditions. Einstein's equation's for the…
Assuming that the dominant contribution, to the entropy due to entanglement across a spherical hypersurface, comes from the near horizon degrees of freedom, we analytically derive the entropy of a free massless scalar field in Minkowski…
In this work, two new axisymmetric models for the Galactic mass distribution are presented. Motivated by recent results, these two models include the contribution of a stellar thin disc and of a thick disc, as massive as the thin…
I first calculate the charged spherical Renyi entropy by a numerical method that does not require knowledge of any eigenvalue degeneracies, and applies to all odd dimensions. An image method is used to relate the full sphere values to those…
We have established the exact expression for the gravitational potential of a homogeneous polar cell - an elementary pattern used in hydrodynamical simulations of gravitating discs. This formula, which is a closed-form, works for any…
We consider embedded ring-type surfaces (that is, compact, connected, orientable surfaces with two boundary components and Euler-Poincar\'{e} characteristic zero) in ${\bold R}^3$ of constant mean curvature which meet planes $\Pi_1$ and…
In a previous paper, I demonstrated the accuracy of simple, precessing, power ellipse (p-ellipse) approximations to orbits of low-to-moderate eccentricity in power-law potentials. Here I explore several extensions of these approximations to…
There is apparently a widespread belief that the gravitational field (and subsequently the rotation curve) ``inside'' razor-thin, axially symmetric disks can not be determined accurately from elliptic integrals because of the singular…
Extreme mass ratio inspirals (EMRIs), where a compact object orbits a massive black hole, are a key source of gravitational waves for the future Laser Interferometer Space Antenna (LISA). Due to their small mass ratio, ($\epsilon \sim…
Computing the envelope of deforming planar domains is a significant and challenging problem with a wide range of potential applications. We approximate the envelope using circular arc splines, curves that balance geometric flexibility and…
Measurements of exoplanetary masses and radii have revealed a population of massive super-Earths --- planets sufficiently large that, according to one dimensional models, they should have turned into gas giants. To better understand the…
A family of potential-density pairs that represent spherical shells with finite thickness is obtained from the superposition of spheres with finite radii. Other families of shells with infinite thickness with a central hole are obtained by…
We present an accurate approximation of the full gravitational radiation waveforms generated in the merger of non-eccentric systems of two non-spinning black holes. Utilizing information from recent numerical relativity simulations and the…
We analyze a new numerical relativity dataset of spinning but nonprecessing binary black holes on eccentric orbits, with eccentricities from approximately $0.1$ to $0.5$, with dimensionless spins up to $0.75$ included at mass ratios…
The properties of filamentary interstellar clouds observed at sub-millimetre wavelengths, especially by the Herschel Space Observatory, are analysed with polytropic models in cylindrical symmetry. The observed radial density profiles are…
Convection in rotating spherical geometries is an important physical process in planetary and stellar systems. Using continuation methods at low Prandtl number, we find both strong equatorially asymmetric and symmetric polar nonlinear…
Shapes of relative emission sources can be accessed by expanding shapes of correlations at low relative velocities in pair center of mass in Cartesian harmonics. Coefficients of expansion for correlations are related to the respective…
Radiation from a narrow circular ring shows a characteristic double-horn profile dominated by photons having energy around the maximum or minimum of the allowed range, i.e. near the extremal values of the energy shift. The energy span of a…
We calculate stationary configurations of rapidly rotating compact stars in general relativity, to study the properties of circular orbits of test particles in the equatorial plane. We search for simple, but precise, analytical formulae for…
The article presents the mathematical sequences describing circle packing densities in four different geometric configurations involving a hexagonal lattice based equal circle packing in the Euclidian plane. The calculated sequences take…