Scalar Hair from a Derivative Coupling of a Scalar Field to the Einstein Tensor

We consider a gravitating system of vanishing cosmological constant consisting of an electromagnetic field and a scalar field coupled to the Einstein tensor. A Reissner-Nordstr\"om black hole undergoes a second-order phase transition to a hairy black hole of generally anisotropic hair at a certain critical temperature which we compute. The no-hair theorem is evaded due to the coupling between the scalar field and the Einstein tensor. Within a first order perturbative approach we calculate explicitly the properties of a hairy black hole configuration near the critical temperature and show that it is energetically favorable over the corresponding Reissner-Nordstr\"om black hole.Comment: 24 pages, 13 figures, title changed, improved discussion of the first order perturbative analysis, reference added, published versio

Charged C-metric with conformally coupled scalar field

We present a generalisation of the charged C-metric conformally coupled with a scalar field in the presence of a cosmological constant. The solution is asymptotically flat or a constant curvature spacetime. The spacetime metric has the geometry of a usual charged C-metric with cosmological constant, where the mass and charge are equal. When the cosmological constant is absent it is found that the scalar field only blows up at the angular pole of the event horizon. The presence of the cosmological constant can generically render the scalar field regular where the metric is regular, pushing the singularity beyond the event horizon. For certain cases of enhanced acceleration with a negative cosmological constant, the conical singularity disappears all together and the scalar field is everywhere regular. The black hole is then rather a black string with its event horizon extending all the way to asymptotic infinity and providing itself the necessary acceleration.Comment: regular article, no figures, typos corrected, to appear in Classical and Quantum Gravit

A New Class of Exact Hairy Black Hole Solutions

We present a new class of black hole solutions with minimally coupled scalar field in the presence of a negative cosmological constant. We consider a one-parameter family of self-interaction potentials parametrized by a dimensionless parameter $g$. When $g=0$, we recover the conformally invariant solution of the Martinez-Troncoso-Zanelli (MTZ) black hole. A non-vanishing $g$ signals the departure from conformal invariance. All solutions are perturbatively stable for negative black hole mass and they may develop instabilities for positive mass. Thermodynamically, there is a critical temperature at vanishing black hole mass, where a higher-order phase transition occurs, as in the case of the MTZ black hole. Additionally, we obtain a branch of hairy solutions which undergo a first-order phase transition at a second critical temperature which depends on $g$ and it is higher than the MTZ critical temperature. As $g\to 0$, this second critical temperature diverges.Comment: 18 pages, 6 figures, minor changes, references added, published versio