Black holes from Myers-Perry solution

Abstract

From the five dimensional Myers-Perry solution and consider that de metric MP corresponding to the Kaluza-Klein ansatz (zero mode), we obtained $4D$ solution with non-minimally coupled scalar and electromagnetic fields, characterized by three parameters, $r_{0},a,b$, related to the mass, angular momentum and electromagnetic field, respectively and proposing that the $4D$ solution is a solution type black hole. Then for $a\neq 0$, $b=0$ the electromagnetic field vanishes and the black hole is stationary. For $a=0$, $b\neq 0$ the solution is static with electric field. If $a\neq 0$, $b\neq 0$ the solution is stationary with electric field and, due to the rotation, a magnetic field appears. The scalar field that arises from the dimensional reduction is present in all cases. At infinity the solution is asymptotically flat and the trace of the scalar field get lost, turning out that this solution is in agreement with the no hair conjecture.