New interpretation of the Extended Geometric Deformation in Isotropic Coordinates

TL;DR

This paper explores a new interpretation of Extended Geometric Deformation in isotropic coordinates, presenting methods to generate physically acceptable anisotropic solutions from seed metrics, with applications to Tolman IV and Gold III solutions.

Contribution

It introduces two inequivalent methods for applying 2-step geometric deformation in isotropic coordinates, adaptable to various seed solutions.

Findings

Generated four physically acceptable anisotropic solutions in isotropic coordinates.

Demonstrated two distinct methods for 2-step geometric deformation.

Applied the methods to Tolman IV and Gold III seed solutions.

Abstract

We study the particular case in which Extended Geometric Deformation does consists of consecutive deformations of temporal and spatial components of the metric, in Schwarzschild-like and isotropic coordinates. In the latter, we present two inequivalent ways to perform this 2-steps GD. This was done in such a way that the method may be applied to different seed solutions. As an example, we use Tolman IV as seed solution, in order to obtain two inequivalent physical solutions with anisotropy in the pressures in Schwarzschild-like coordinates. In the isotropic sector, we obtained four different solutions with anisotropy in the pressures that satisfy physical acceptability conditions, using Gold III as seed solution.