arXiv subjects
Publications and source records attributed to Carlos Marín.
Light deviation around a rotating black hole is calculated using the Kerr metric for both small and large deviation angles. For small angles the Lindstedt-Poincaré method is employed to get well-behaved solutions, as well as Padé approximants. For large deviation angles numerical integration has been used.
Higher order corrections are obtained for the perihelion precession in binary systems like OJ287, Sagittarius A*-S2 and H1821+643 using both the Schwarzschild metric and the Kerr metric to take into account the spin effect. The corrections are performed considering the third root of the motion equation and developing the expansion in terms of $ε\equiv r_s/\left(a(1-e^2)\right)$ and $ε^{*} \equiv \left(1- \frac{2 αE'}{cJ}\right) ε$.The results are compared with those obtained in a previous paper.
Higher order corrections (up to n-th order) are obtained for the perihelion precession in binary systems like OJ287 using the Schwarzschild metric and complex integration. The corrections are performed considering the third root of the motion equation and developing the expansion in terms of $r_s/\left(a(1-e^2)\right)$.}The results are compared with other expansions that appear in the literature giving corrections to second and third order. Finally, we simulate the shape of relativistic orbits for binary systems with different masses.
From the Schwarzschild metric we obtain the higher-order terms (up to 20-th order) for the deflection of light around a massive object using the Lindstedt-Poincaré method to solve the equation of motion of a photon around the stellar object. Additionally, we obtain diagonal Padé approximants from the perturbation expansion, and we show how these are a better fit for the numerical data. Furthermore, we use these approximants in ray-tracing algorithms to model the bending of light around the massive object.
Let $X=(X_1,X_2, X_3)$ be a Gaussian random vector such that $X\sim \mathcal{N} (0,Σ)$. We consider the problem of determining the matrix $Σ$, up to permutation, based on the knowledge of the distribution of $X_{\mathrm{min}}:=\min(X_1, X_2, X_3)$. Particularly, we establish a connection between this identification problem and a geometric identification problem in the context of the theory of the circular radon transform.