Exotic Lovelock black holes and extended quasitopological electromagnetism

TL;DR

The paper addresses the extension of Birkhoff's theorem to Lovelock gravity in higher dimensions, enabling black holes with nonconstant-curvature horizons (exotic horizons). It develops a universal polynomial description for the metric function $f(r)$ in arbitrary-order Lovelock theories coupled to extended QT electromagnetism, and provides explicit Gauss–Bonnet ($p_{max}=2$) and third-order Lovelock solutions. The authors compute the thermodynamics, verify a generalized first law and Smarr relation, and perform a detailed stability analysis via the heat capacity $C_H$ under variations of electric and magnetic charges and topological parameters. The work highlights how horizon topology and nonlinear electromagnetism interact with higher-curvature corrections to shape extremal masses, horizon structure, and phase behavior in AdS and dS spacetimes, offering a framework for exploring quasi-topological gravities in higher dimensions.

Abstract

The generalization of Birkhoff's theorem for higher dimensions in Lovelock gravity permits us to investigate the black hole solutions with horizon geometries of nonconstant curvature. We present a new class of exotic dyonic black holes in the context of Lovelock gravity and generalized quasitopological electromagnetism. First, we derive the polynomial equation that describes exotic dyonic black holes in Lovelock gravity with an arbitrary order. Next, the solutions that characterize dyonic exotic black holes of the Gauss-Bonnet and third order Lovelock gravities are worked out. Then we compute the basic thermodynamic quantities for these exotic dyonic black holes. It is also verified that these quantities satisfy the generalized first law and Smarr's relation. Furthermore, the impact of generalized quasitopological electromagnetism and topological parameters on the local stability of the resulting objects are also investigated.

Figures (22)

• Figure 1: The behaviour of resultant exotic black hole solution (Eq. (\ref{['37a']})) for different values of mass $M$. The fixed values of the other parameters are taken as $d=5$, $G_N=1$, $\Sigma_{\beta}=1$, $q=0.5$, $\zeta=2$, $e=0.5$$\beta_1=1$, $\beta_2=1$, $\alpha_2=0.05$ and $\Lambda=-0.1$.
• Figure 2: Effect of the magnetic charge $q$ on the horizon structure of exotic black solution (Eq. (\ref{['37a']})). The fixed values of the other parameters are taken as $d=5$, $G_N=1$, $\Sigma_{\beta}=1$, $M=0.2$, $\zeta=2$, $e=0.5$$\beta_1=1$, $\beta_2=1$, $\alpha_2=0.05$ and $\Lambda=-0.1$.
• Figure 3: Effect of the electric charge $e$ on the horizon structure of exotic black solution (Eq. (\ref{['37a']})). The fixed values of the other parameters are taken as $d=5$, $G_N=1$, $\Sigma_{\beta}=1$, $M=0.2$, $\zeta=2$, $q=0.6$$\beta_1=1$, $\beta_2=1$, $\alpha_2=0.05$ and $\Lambda=-0.1$.
• Figure 4: Effect of the topological parameters on the horizon structure of exotic black solution (Eq. (\ref{['37a']})). The fixed values of the other parameters are taken as $d=5$, $G_N=1$, $\Sigma_{\beta}=1$, $M=0.2$, $\zeta=2$, $q=0.6$, $e=0.5$, $\alpha_2=0.05$ and $\Lambda=-0.1$.
• Figure 5: The behaviour of resultant exotic black hole solution (Eq. (\ref{['37a']})) in de Sitter space. The fixed values of the other parameters are taken as $d=6$, $G_N=1$, $\Sigma_{\beta}=1$, $q=0.5$, $\zeta=2$, $e=0.5$, $\alpha_2=0.05$ and $\Lambda=-0.1$.