Black hole solutions in R2 gravity

We find static spherically symmetric solutions of scale invariant R-2 gravity. The latter has been shown to be equivalent to General Relativity with a positive cosmological constant and a scalar mode. Therefore, one expects that solutions of the R-2 theory will be identical to that of Einstein theory. Indeed, we find that the solutions of R-2 gravity are in one-to-one correspondence with solutions of General Relativity in the case of non-vanishing Ricci scalar. However, scalar-flat R = 0 solutions are global minima of the R-2 action and they cannot in general be mapped to solutions of the Einstein theory. As we will discuss, the R = 0 solutions arise in Einstein gravity as solutions in the tensionless, strong coupling limit M-P -> 0. As a further result, there is no corresponding Birkhoff theorem and the Schwarzschild black hole is by no means unique in this framework. In fact, R-2 gravity has a rich structure of vacuum static spherically symmetric solutions partially uncovered here. We also find charged static spherically symmetric backgrounds coupled to a U(1) field. Finally, we provide the entropy and energy formulas for the R-2 theory and we find that entropy and energy vanish for scalar-flat backgrounds.