Representation of compact stars using the black string set--up

TL;DR

This paper introduces a method to embed 4D spherically symmetric compact stars into 5D spacetime using the black string framework, simplifying equations and revealing effects of extra dimensions on stellar properties.

Contribution

It presents a novel approach to represent 4D compact stars in 5D space, reducing equations and analyzing the impact of extra dimensions on stellar characteristics.

Findings

The 5D equations reduce to 4D equations of motion.

The sign of pressure along the extra dimension depends on the 4D energy-momentum trace.

The model's topology is S^2 x S^1, differing from standard 5D topologies.

Abstract

This work is devoted to provide a way of representing $4D$ spherically symmetric and static compact stellar configurations into a $5D$ space time, using the black string framework. We write the four and five dimensional line elements and the four and five dimensional energy momentum tensor such that the four and five dimensional quantities are related by a function $A(z)$, where $z$ represents to the extra dimension. Remarkably, one consequence of our chosen form for the line element, for the energy momentum tensor and for $A(z)$, is the fact that the $5D$ equations are reduced to the usual form of the four dimensional equations of motion. Also, the five dimensional conservation equation adopts the form of the four dimensional conservation equation. It is worth mentioning that, although our methodology is simple, this form of reduction could serve to represent other types of four dimensional objects into an extra dimension in future works. Furthermore, under our assumptions the sign of the pressure along the extra dimension is given by the trace of the four dimensional energy momentum tensor. Furthermore, our simple election for the function $A(z)$ modifies some features of the induced 4--dimensional compact stellar configuration, such as the mass--radius relation, the momentum of inertia, the central values of the thermodynamic variables, to name a few. Besides, the topology of this model is ${S}^{2}\times {S}^{1}$ and not the ${S}^{3}$ topology of the 5--dimensional structures.