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

A search for near infrared counterparts of 3 pulsar wind nebulae

While pulsar wind nebulae (PWNe) and their associated isolated pulsars are commonly detected at X-ray energies, they are much rarer at near infrared (nIR) and optical wavelengths. Here we examine three PWN systems in the Galactic plane - IGR J14003-6326, HESS J1632-478 and IGR J18490-0000 - in a bid to identify optical/nIR emission associated with either the extended PWNe or their previously detected X-ray point sources. We obtain optical/nIR images of the three fields with the ESO - New Technology Telescope and apply standard photometric and astrometric calibrations. We find no evidence of any extended emission associated with the PWNe in any of the fields; neither do we find any new counterparts to the X-ray point sources, except to confirm the magnitude of the previously identified counterpart candidate of IGR J18490-0000. Further observations are required to confirm the association of the nIR source to IGR J18490-0000 and to detect counterparts to IGR J14003-6326 and HESS J1632-478, while a more accurate X-ray position is required to reduce the probability of a chance superposition in the field of the latter.Comment: Accepted to A&A (4 pages, 1 figure

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

Duality theory and slackness conditions in multiobjective linear programming

AbstractThe aim of this paper is to develop a duality theory for linear multiobjective programming verifying similar properties as in the scalar case. We use the so-called “strongly proper optima” and we characterize such optima and its associated dual solutions by means of some complementary slackness conditions. Moreover, the dual solutions can measure the sensitivity of the primal optima