Solution generating techniques for general relativity with a conformally (and minimally) coupled scalar field are pushed forward to build a wide class of asymptotically flat, axisymmetric and stationary spacetimes continuously connected to Kerr. This
family contains, amongst other things, rotating extensions of the Bekenstein black hole and also its angular and mass multipolar generalisations. Further addition of NUT charge is also discussed.
An exact and regular solution, describing a couple of charged and spinning black holes, is generated in an external electromagnetic field, via Ernst technique, in Einstein-Maxwell gravity. A wormhole instantonic solution interpolating between the two
black holes is constructed to discuss, at the semi-classical level, the quantum process of creation rate, in an external magnetic field, of this charged and spinning black hole pair.
In Einstein-Maxwell gravity with a conformally coupled scalar field, the black hole found by Bocharova, Bronnikov, Melnikov, and Bekenstein breaks when embedded in the external magnetic field of the Melvin universe. The situation improves in presence
of acceleration, allowing one to build magnetised and accelerating BBMB black hole with a thin membrane. But to overcome this and others disadvantages of BBMB spacetimes, a new class of black holes, including the rotating case, is proposed for the conformal matter coupling under consideration.
Ernsts solution generating technique is adapted to Einstein-Maxwell theory conformally (and minimally) coupled to a scalar field. This integrable system enjoys a SU(2,1) symmetry which enables one to move, by Kinnersley transformations, though the ax
isymmetric and stationary solution space, building an infinite tower of physically inequivalent solutions. As a specific application, metrics associated to scalar hairy black holes, such as the ones discovered by Bocharova, Bronnikov, Melnikov and Bekenstein, are embedded in the external magnetic field of the Melvin universe.
A C-metric type solution for general relativity with cosmological constant is presented in 2+1 dimensions. It is interpreted as a three-dimensional black hole accelerated by a strut. Positive values of the cosmological constant are admissible too. So
me embeddings of this metric in the 3+1 space-time are considered: accelerating BTZ black string and a black ring where the gravitational force is sustained by the acceleration.
