Topologically nontrivial black holes in Lovelock-Born-Infeld gravity

We present the black hole solutions possessing horizon with nonconstant-curvature and additional scalar restrictions on the base manifold in Lovelock gravity coupled to Born-Infeld (BI) nonlinear electrodynamics. The asymptotic and near origin behavior of the metric is presented and we analyze different behaviors of the singularity. We find that, in contrast to the case of black hole solutions of BI-Lovelock gravity with constant curvature horizon and Maxwell-Lovelock gravity with non constant horizon which have only timelike singularities, spacelike, and timelike singularities may exist for BI-Lovelock black holes with nonconstant curvature horizon. By calculating the thermodynamic quantities, we study the effects of nonlinear electrodynamics via the Born-Infeld action. Stability analysis shows that black holes with positive sectional curvature, $\kappa$, possess an intermediate unstable phase and large and small black holes are stable. We see that while Ricci flat Lovelock-Born-Infeld black holes having exotic horizons are stable in the presence of Maxwell field or either Born Infeld field with large born Infeld parameter $\beta$, unstable phase appears for smaller values of $\beta$, and therefore nonlinearity brings in the instability.

Figure 1

$m(r)$ versus $r$ for $n=9$, ${\widehat{\alpha }}_0=0.5$, ${\widehat{\alpha }}_2=2$, ${\widehat{\alpha }}_3=5$, ${\widehat{\eta }}_2=0.5$, ${\widehat{\eta }}_3=0.006$, $q=20$, and $\beta =1$ (solid line), $\beta =20$ (dotted line), and $\beta =60$ (dashed line).

Figure 2

$T$ versus $r_{+}$ for $n=9$, ${\widehat{\alpha }}_0=0.1$, ${\widehat{\alpha }}_2=2$, ${\widehat{\alpha }}_3=5$, ${\widehat{\eta }}_2=1$ and ${\widehat{\eta }}_3=5$, for uncharged solution (solid line), charged solution with $q=1$ (dashed line) and BI solution with $q=1$ and $\beta =0.5$ (dotted line).

Figure 3

$T$ (solid line) and $C_Q$ (dashed line) versus $r_{+}$ for $n=8$, $\kappa =1$, ${\widehat{\alpha }}_0=0.1$, ${\widehat{\alpha }}_2=1$, ${\widehat{\alpha }}_3=1/3$, ${\widehat{\eta }}_2=1$, ${\widehat{\eta }}_3=5$, $q=2$, and $\beta =5$.

Figure 4

$C_Q$ versus $r_{+}$ for $n=9$, ${\widehat{\alpha }}_0=0.1$, ${\widehat{\alpha }}_2=1$, ${\widehat{\alpha }}_3=1/3$, ${\widehat{\eta }}_2=1$, ${\widehat{\eta }}_3=5$, and $q=0.1$.

Figure 5

$C_Q$ versus $r_{+}$ for $n=9$, ${\widehat{\alpha }}_0=0.1$, ${\widehat{\alpha }}_2=1$, ${\widehat{\alpha }}_3=1/3$, ${\widehat{\eta }}_2=1$, ${\widehat{\eta }}_3=5$, $q=0.1$, and $\beta =0.3$ (solid line), $\beta =0.1$ (dashed line).