Exact black hole formation in asymptotically (A)dS and flat spacetimes

We consider four-dimensional Einstein gravity minimally coupled to a dilaton scalar field with a supergravity-inspired scalar potential. We obtain an exact time-dependent spherically symmetric solution describing gravitational collapse to a static scalar-hairy black hole. The solution can be asymptotically AdS, flat or dS depending on the value of the cosmological constant parameter Λ in the potential. As the advanced time u increases, the metric approaches the static limit in an exponential fashion, i.e., e−u/u0 with u0∼1/(α4M0)1/3 , where M0 is the mass of the final black hole and α is the second parameter in the potential. Similarly to the Vaidya solution, at u=0 , the spacetime can be matched to an (A)dS or flat vacuum except that at the origin a naked singularity may occur. Moreover, a limiting case of our solution with α=0 gives rise to an (A)dS generalization of the Roberts solution. Our results provide a new model for investigating formation of real life black holes with Λ≥0 . For Λ<0 , it can be instead used to study non-equilibrium thermalization of certain strongly-coupled field theory

Electrically-charged Lifshitz spacetimes, and hyperscaling violations

Electrically-charged Lifshitz spacetimes are hard to come by. In this paper, we construct a class of such solutions in five dimensional Einstein gravity coupled to Maxwell and SU(2) Yang-Mills fields. The solutions are electrically-charged under the Maxwell field, whose equation is sourced by the Yang-Mills instanton(-like) configuration living in the hyperbolic four-space of the Lifshitz spacetime. We then introduce a dilaton and construct charged and colored Lifshitz spacetimes with hyperscaling violations. We obtain a class of exact Lifshitz black holes. We also perform similar constructions in four dimensions

Charged black holes in colored Lifshitz spacetimes

We consider Einstein gravities coupled to a cosmological constant and SU(2) Yang–Mills fields in four and five dimensions. We find that the theories admit colored Lifshitz solutions with dynamic exponents z>1 . We study the wave equations of the SU(2) scalar triplet in the bulk, and find that the vacuum color modifies the scaling dimensions of the dual operators. We also introduce a Maxwell field and construct exact solutions of electrically-charged black holes that approach the D=4 , z=3 and D=5 , z=4 colored Lifshitz spacetimes. We derive the thermodynamical first law for general colored and charged Lifshitz black holes

SU(2)-colored (A)dS black holes in conformal gravity

We consider four-dimensional conformal gravity coupled to the U(1) Maxwell and SU(2) Yang-Mills fields. We study the structure of general black hole solutions carrying five independent parameters: the mass, the electric U(1) and magnetic SU(2) charges, the massive spin-2 charge and the thermodynamical pressure associated with the cosmological constant, which is an integration constant in conformal gravity. We derive the thermodynamical first law of the black holes. We obtain some exact solutions including an extremal black hole with vanishing mass and entropy, but with non-trivial SU(2) Yang-Mills charges. We derive the remainder of the first law for this special solution. We also reexamine the colored black holes and derive their first law in Einstein-Yang-Mills gravity with or without a cosmological constant

Charged black holes with scalar hair

We consider a class of Einstein-Maxwell-Dilaton theories, in which the dilaton coupling to the Maxwell field is not the usual single exponential function, but one with a stationary point. The theories admit two charged black holes: one is the Reissner-Nordstrøm (RN) black hole and the other has a varying dilaton. For a given charge, the new black hole in the extremal limit has the same AdS 2 ×Sphere near-horizon geometry as the RN black hole, but it carries larger mass. We then introduce some scalar potentials and obtain exact charged AdS black holes. We also generalize the results to black p -branes with scalar hair

Scalar charges in asymptotic AdS geometries

We show that for n -dimensional Einstein gravity coupled to a scalar field with mass-squared m20=−n(n−2)/(4ℓ2) , the first law of thermodynamics of (charged) AdS black holes will be modified by the boundary conditions of the scalar field at asymptotic infinity. Such scalars can arise in gauged supergravities in four and six dimensions, but not in five or seven. The result provides a guiding principle for constructing designer black holes and solitons in general dimensions, where the properties of the dual field theories depend on the boundary conditions

Thermodynamics of Lifshitz black holes

We specialize the Wald formalism to derive the thermodynamical first law for static black holes with spherical/torus/hyperbolic symmetries in a variety of supergravities or supergravity-inspired theories involving multiple scalars and vectors. We apply the formula to study the first law of a general class of Lifshitz black holes. We analyse the first law of three exact Lifshitz black holes and the results fit the general pattern. In one example, the first law is TdS + Φ dQ = 0 where (Φ , Q ) are the electric potential and charge of the Maxwell field. The unusual vanishing of mass in this specific solution demonstrates that super-extremal charged black holes can exist in asymptotic Lifshitz spacetimes

Lifshitz and Schrödinger vacua, superstar resolution in gauged maximal supergravities

We consider the subset of gauged maximal supergravities that consists of the SO( n  + 1) gauge fields A ij and the scalar deformation T ij of the S n in the spherical reduction of M-theory or type IIB. We focus on the Abelian Cartan subgroup and the diagonal entries of T ij . The resulting theories can be viewed as the STU models with additional hyperscalars. We find that the theories with only one or two such vectors can be generalized naturally to arbitrary dimensions. The same is true for the D  = 4 or 5 Einstein-Maxwell theory with such a hyperscalar. The gauge fields become massive, determined by stationary points of the hyperscalars a la the analogous Abelian Higgs mechanism. We obtain classes of Lifshitz and Schrödinger vacua in these theories. The scaling exponent z turns out to be rather restricted, taking fractional or irrational numbers. Tweaking the theories by relaxing the mass parameter or making a small change of the superpotential, we find that solutions with z  = 2 can emerge. In a different application, we find that the resolution of superstar singularity in the STU models by using bubbling-AdS solitons can be generalized to arbitrary dimensions in our theories. In particular, we obtain the smooth AdS solitons that can be viewed as the resolution of the Reissner-Nordstrøm superstars in general dimensions