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

Shaping black holes with free fields

Starting from a metric Ansatz permitting a weak version of Birkhoff's theorem we find static black hole solutions including matter in the form of free scalar and p-form fields, with and without a cosmological constant \Lambda. Single p-form matter fields permit multiple possibilities, including dyonic solutions, self-dual instantons and metrics with Einstein-Kaelher horizons. The inclusion of multiple p-forms on the other hand, arranged in a homogeneous fashion with respect to the horizon geometry, permits the construction of higher dimensional dyonic p-form black holes and four dimensional axionic black holes with flat horizons, when \Lambda<0. It is found that axionic fields regularize black hole solutions in the sense, for example, of permitting regular -- rather than singular -- small mass Reissner-Nordstrom type black holes. Their cosmic string and Vaidya versions are also obtained.Comment: 38 pages. v2: minor changes, published versio

Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography

For a specific action supporting z = 2 Lifshitz geometries we identify the Lifshitz UV completion by solving for the most general solution near the Lifshitz boundary. We identify all the sources as leading components of bulk fields which requires a vielbein formalism. This includes two linear combinations of the bulk gauge field and timelike vielbein where one asymptotes to the boundary timelike vielbein and the other to the boundary gauge field. The geometry induced from the bulk onto the boundary is a novel extension of Newton-Cartan geometry that we call torsional Newton-Cartan (TNC) geometry. There is a constraint on the sources but its pairing with a Ward identity allows one to reduce the variation of the on-shell action to unconstrained sources. We compute all the vevs along with their Ward identities and derive conditions for the boundary theory to admit conserved currents obtained by contracting the boundary stress-energy tensor with a TNC analogue of a conformal Killing vector. We also obtain the anisotropic Weyl anomaly that takes the form of a Hořava-Lifshitz action defined on a TNC geometry. The Fefferman-Graham expansion contains a free function that does not appear in the variation of the on-shell action. We show that this is related to an irrelevant deformation that selects between two different UV completions