Searching Exact Solutions for Compact Stars in Braneworld: a conjecture

In the context of the braneworld, a spherically symmetric, static and nonhomogeneous stellar distribution with local and non-local bulk terms is studied. Using a toy solution, it is shown how the general relativistic limit could be lost while a solution is being generated on the brane. The source of this problem is clearly identified and solved by a general solution where a constraint can be identified. This constraint is physically interpreted as a necessary condition to regain general relativity, and a particular solution for it is used to find an exact analytical internal solution to no-uniform stellar distributions on the brane. It is shown that such an exact solution is possible due to the fact that bulk corrections to pressure, density and a metric component are a null source of anisotropic effects on the brane. A conjecture is proposed about the possibility of finding physically relevant exact solutions to non-uniform stellar distributions on the brane. ∗[email protected]; [email protected]