New algorithms to obtain analytical solutions of Einstein's equations in isotropic coordinates

The main objective of this work, is to show two inequivalent methods to obtain new spherical symmetric solutions of Einstein's Equations with anisotropy in the pressures in isotropic coordinates. This was done inspired by the MGD method, which is known to be valid for line elements in Schwarzschild coordinates. As example, we obtained four analytical solutions using Gold III as seed solution. Two solutions, out of four, (one for each algorithm), satisfy the physical acceptability conditions.Comment: 14 pages, 24 figures, results were improve

Complexity factor of spherically anisotropic polytropes from gravitational decoupling

In this work we will analyse the complexity factor, proposed by L. Herrera, of spherically symmetric static matter distributions satisfying a polytropic equation through the gravitational decoupling method. Specifically, we will use the 2-steps GD, which is a particular case of the Extended Geometric Deformation (EGD), to obtain analytic polytropic solutions of Einstein's equations. In order to give an example, we construct a model satisfying a polytropic equation of state using Tolman IV as seed solution

Estrategias para un desarrollo cognitivo a través de la apreciación artística.

Sin resume

Can Maxwell's equations be obtained from the continuity equation?

We formulate an existence theorem that states that given localized scalar and vector time-dependent sources satisfying the continuity equation, there exist two retarded fields that satisfy a set of four field equations. If the theorem is applied to the usual electromagnetic charge and current densities, the retarded fields are identified with the electric and magnetic fields and the associated field equations with Maxwell's equations. This application of the theorem suggests that charge conservation can be considered to be the fundamental assumption underlying Maxwell's equations.Comment: 14 pages. See the comment: "O. D. Jefimenko, Causal equations for electric and magnetic fields and Maxwell's equations: comment on a paper by Heras [Am. J. Phys. 76, 101 (2008)].