The Minimal Geometric Deformation Approach Extended

TL;DR

This paper extends the minimal geometric deformation approach to include modifications of both metric components, providing new solutions for spherically symmetric systems in brane-world scenarios, including a modified Schwarzschild geometry.

Contribution

The paper develops a consistent extension of the minimal geometric deformation approach, incorporating modifications to both time and radial metric components in brane-world models.

Findings

Derived a modified Schwarzschild geometry as an example.

Presented a new solution for star modeling in brane-worlds.

Extended the applicability of the minimal geometric deformation approach.

Abstract

The minimal geometric deformation approach was introduced in order to study the exterior space-time around spherically symmetric self-gravitating systems, like stars or similar astrophysical objects as well, in the Randall-Sundrum brane-world framework. A consistent extension of this approach is developed here, which contains modifications of both the time component and the radial component of a spherically symmetric metric. A modified Schwarzschild geometry is obtained as an example of its simplest application, and a new solution potentially useful to describe stars in the brane-world is also presented.