Representation of compact stars using the black string set-up

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. In our model, due to the action of the function A(z), the 5D geometry no longer has traslational symmetry along the z coordinate, as occurs for the Kaluza Klein black string. Furthermore, a form for the matching conditions is provided. 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. This clearly motivates the study of the impact of this methodology on some particular 4-dimensional models. In this concern, we have considered as a toy model the well-known isotropic Buchdahl model, showing by a graphical analysis how the mentioned properties are altered. It is worth mentioning that the resulting solution is well-behaved, satisfying all the physical criteria to represent a toy physical stellar model. Besides, the topology of this model is S2 x S1 and not the S3 topology of the 5-dimensional structures.