Extremal Myers-Perry black holes in Born-Infeld-dilaton theory

A class of perturbatively charged rotating dilaton black hole solutions coupled to the nonlinear Born-Infeld electrodynamics is presented. The strategy for obtaining these solutions is to start from Myers-Perry solutions and then, considering the effects of the dilaton field, Born-Infeld parameter as well as the electric charge as a perturbative parameter. We perform the perturbations up to fourth order in the extremal black holes of Einstein-Born-Infeld-dilaton gravity with two equal angular momenta and arbitrary dilaton coupling constant. We discuss the physical properties of these black holes and study their dependence on the perturbative parameter $q$, the dilaton coupling constant $\alpha$, and the Born-Infeld parameter $\beta$. One can see these black holes solutions satisfy a generalized Smarr relation.

Figure 1

The horizon radius $r_H$ versus the dilaton coupling constant $\alpha$ for $\nu =1.16$ and $q=0.09$.

Figure 2

The mass $M$ versus the BI parameter $\beta$ for $\nu =1.16$ and $q=0.09$. $\alpha =1$ (bold line), $\alpha =5000$ (continuous line), and $\alpha =10000$ (dotted line).

Figure 3

The magnetic moment ${\mu }_{\text{mag}}$ versus $\beta$ for $\nu =1.16$ and $q=0.09$. $\alpha =1$ (bold line), $\alpha =50$ (continuous line), and $\alpha =100$ (dotted line).

Figure 4

The gyromagnetic ratio $g$ versus the BI parameter $\beta$ for $\nu =1.16$ and $q=0.09$. $\alpha =1$ (bold line), $\alpha =50$ (continuous line), and $\alpha =100$ (dotted line).