Related papers: Exact Results for the Kepler Problem in General Re…
The manuscripts provides a novel starting guess for the solution of Kepler's equation for unknown eccentric anomaly E given the eccentricity e and mean anomaly M of an elliptical orbit.
In this second paper, we develop an analytical theory of quasi-equatorial lensing by Kerr black holes. In this setting we solve perturbatively our general lens equation with displacement given in Paper I, going beyond weak-deflection Kerr…
On a quantum particle in the unit interval $[0,1]$, perform a position measurement with inaccuracy $1/n$ and then a quantum measurement of the projection $|\phi\rangle\langle\phi|$ with some arbitrary but fixed normalized $\phi$. Call the…
The timelike geodesic equations resulting from the Kerr gravitational metric element are derived and solved exactly including the contribution from the cosmological constant. The geodesic equations are derived, by solving the…
The present paper establishes the correspondence between the properties of the solutions of a class of PDEs and the geometry of sets in Euclidean space. We settle the question of whether (quantitative) absolute continuity of the elliptic…
The meaning of "linear expansion" is explained. Particularly accurate relative distances are compiled and homogenized a) for 246 SNe Ia and 35 clusters with v<30,000 km/s, and b) for relatively nearby galaxies with 176 TRGB and 30 Cepheid…
As an extension of a previous work in which perihelion advances are considered only and as an attempt to find more stringent constraints on its parameters, we investigate effects on astronomical observation and experiments conducted in the…
We investigate the asymptotic behavior of solutions to a class of weighted quasilinear elliptic equations which arise from the Euler--Lagrange equation associated with the Caffarelli--Kohn--Nirenberg inequality. We obtain sharp pointwise…
Classical general relativity predicts that a contracting, spherically symmetric matter system with a large-enough mass will result in the formation of a trapped region whose outer boundary is an apparent horizon where the gravitational…
Black holes are an ubiquitous end state of stellar evolution and successfully explain some of the most extreme physics encountered in astronomical observations. The Kerr geometry is the known exact solution to Einstein's equations for a…
Closed-Form Kepler solutions in projective coordinates are used to define a corresponding set of eight orbit elements and obtain their governing equations for arbitrarily-perturbed two-body dynamics. The elements and their dynamics are…
Very recently authors in [1] proposed a new Generalized Uncertainty Principle (or GUP) with a linear term in Plank length. In this Letter the effect of this linear term is studied perturbatively in the context of Keplerian orbits. The angle…
The redshift-distance modulus relation, the Hubble Diagram, derived from Cosmological General Relativity has been extended to arbitrarily large redshifts. Numerical methods were employed and a density function was found that results in a…
The Schwarzschild geometry is investigated within the context of effective-field-theory models of gravity. Starting from its harmonic-coordinate expression, we derive the metric in standard coordinates by keeping the leading one-loop…
We extract elegant and concise analytic formulae for the mass and rotation parameters of the Kerr black hole as well as its distance from the Earth only in terms of directly measurable quantities of the accretion disk revolving in the black…
This paper considers an extremal version of the Erd\H{o}s distinct distances problem. For a point set $P \subset \mathbb R^d$, let $\Delta(P)$ denote the set of all Euclidean distances determined by $P$. Our main result is the following: if…
The collective dynamics of objects moving through a viscous fluid is complex and counterintuitive. A key to understanding the role of nontrivial particle shape in this complexity is the interaction of a pair of sedimenting spheroids. We…
This work arose as an aftermath of Cassini's 2002 experiment \cite{bblipt03}, in which the PPN parameter $\gamma$ was measured with an accuracy $\sigma_\gamma = 2.3\times 10^{-5}$ and found consistent with the prediction $\gamma =1$ of…
It is argued that, for motion in a central force field, polar reciprocals of trajectories are an elegant alternative to hodographs. The principal advantage of polar reciprocals is that the transformation from a trajectory to its polar…
The cosmological constant sets certain scales important in cosmology. We show that Lambda in conjunction with other parameters like the Schwarzschild radius leads to scales relevant not only for cosmological but also for astrophysical…