A self-tuning exact solution and the nonexistence of horizons in 5d gravity-scalar system

We present an exact thick domain wall solution with naked singularities to five-dimensional gravity coupled with a scalar field with exponential poten tial. In our solution we found exactly the special coefficient of the expon ent as coming from compactification of string theory with cosmological cons tant. We show that this solution is self-tuning when a 3-brane is included. In searching for a solution with horizon we found a similar exact solution with fine-tuned exponent coefficient with an integration constant. Failing to find a solution with horizon we prove the nonexistence of horizons. The se naked singularities actually cannot be resolved by horizon. We also comm ent on the physical relevance of this solution.