Semi-polynomial black hole solutions in the Schwarzschild black hole

F. F. C. Almeida, J. A. H. S. M. S. A. Alves, A. V. S. Junior
Comments: Version accepted in JHEP

We study the semi-polynomial black hole solutions in the Schwarzschild black hole in the presence of a non-interacting potential. We find the solutions in the presence of a non-interacting potential with a Planck mass, and we compute the corresponding energy. In particular we find that there are two solutions in the case where the non-interacting potential is large and we have a deterministic equation of state for the Planck mass. However, we also find that there are two solutions in the case where the non-interacting potential is small and we have a deterministic equation of state for the Planck mass. We describe the solution in the Schwarzschild black hole in terms of the Einstein equation, and show that the solution is an Einstein one, although it is a General Relativity one.