Violation of Energy Bounds in Designer Gravity

We continue our study of the stability of designer gravity theories, where one considers anti-de Sitter gravity coupled to certain tachyonic scalars with boundary conditions defined by a smooth function W. It has recently been argued there is a lower bound on the conserved energy in terms of the global minimum of W, if the scalar potential arises from a superpotential P and the scalar reaches an extremum of P at infinity. We show, however, there are superpotentials for which these bounds do not hold.Comment: 16 pages, 4 figures, v2: discussion of vacuum decay included, typos corrected, reference adde

New hairy black hole solutions with a dilaton potential

We consider black hole solutions with a dilaton field possessing a nontrivial potential approaching a constant negative value at infinity. The asymptotic behaviour of the dilaton field is assumed to be slower than that of a localized distribution of matter. A nonabelian SU(2) gauge field is also included in the total action. The mass of the solutions admitting a power series expansion in $1/r$ at infinity and preserving the asymptotic anti-de Sitter geometry is computed by using a counterterm subtraction method. Numerical arguments are presented for the existence of hairy black hole solutions for a dilaton potential of the form $V(\phi)=C_1 \exp(2\alpha_1 \phi)+C_2 \exp(2\alpha_2 \phi)+C_3$, special attention being paid to the case of ${\cal N}=4, D=4$ gauged supergravity model of Gates and Zwiebach.Comment: 12 pages, 4 figures; v2:references added, typos corrected, small changes in Section