Static topological black hole with nonminimal derivative coupling and nonlinear electromagnetic field of Born-Infeld type

Understand

We consider scalar-tensor gravity with nonminimal derivative coupling and Born-Infeld electromagnetic field which is minimally coupled to gravity.

• Since cosmological constant is taken into account it allowed us not only derive static black hole with spherical horizon but also to obtain topological solutions with non-spherical horizons.
• The obtained metrics are thoroughly analyzed, namely for different distances and types of topology of horizon.
• To investigate singularities of the metrics Kretschmann scalar is used and it is shown that the character of singularity depends on the type of topology of horizon and dimension of space.