Spherical warp-based bubble with non–trivial lapse function and its consequences on matter content

In the present work, we study the consequences of including the lapse function as an additional degree of freedom for a general spherical warp-based geometry. By allowing a non-uniform lapse function to evolve, we find that it is possible to accommodate a fluid that includes heat flow. This broadens the range of fluid types that have been studied in these systems and is consistent with the spherical warp metric. Having added the lapse function, we solved the system of equations using an anisotropic fluid with heat flow. In this way, we can examine the different characteristics of the variables of the system. Next, we study the energy conditions and establish how these are modified by including heat flux for an appropriate generic observer in a locally flat spacetime. Finally, we explore all energy conditions using the numerical solutions and verify the regions where they are satisfied.