1,935 research outputs found
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
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)].
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