Quasitopological Reissner-Nordström black holes

We consider Reissner-Nordström solutions in quasitopological gravity, obtaining exact solutions to the field equations yielding charged quasitopological black holes. We study their thermodynamic behavior over a range of parameters that yield ghost-free and stable space times. We find that a sufficiently negative quasitopological parameter can yield black holes with two horizons, even for zero charge. We discuss the thermodynamic stability for the class of solutions we obtain. We also describe the structure of exact charged solutions to $k$th-order quasitopological gravity.

Figure 1

Comparison of Reissner-Nordström and uncharged black hole solutions’ metric functions versus radial coordinate for $k=0$. The solutions are $Q=0$ (solid), $Q=6$ (dotted), and $Q=12$ (dashed). The inset is zoomed in to enhance the near-horizon behavior of $g(r)$.

Figure 2

Reissner-Nordström black hole solutions for $k=-1$, $r_{+}=2.0$, where $Q=0$, 6, 12 are in (bottom to top) red, green, and blue, respectively. The dotted solutions are quasitopological, and the solid solutions are Einsteinian.

Figure 3

Reissner-Nordström black hole solutions for $k=0$, $r_{+}=2.0$, where $Q=0$, 6, 12 are in (bottom to top) red, green, and blue, respectively. The dotted solutions are quasitopological, and the solid solutions are Einsteinian.

Figure 4

Reissner-Nordström black hole solutions for $k=1$, $r_{+}=2.0$, where $Q=0$, 6, 12 are in (bottom to top) red, green, and blue, respectively. The dotted solutions are quasitopological, and the solid solutions are Einsteinian.

Figure 5

Solutions in de Sitter space for $k=1$, where $Q=0$, 0.2, 0.6, 0.7 are in (bottom to top) black, green, red, and blue, respectively. Here $\lambda =0.04$ and $\mu =-0.001$. Quasitopological gravity is dotted, Gauss-Bonnet is dashed, and Einsteinian is solid.

Figure 6

Solutions in asymptotically flat space for $k=1$, where $Q=0$, 0.2, 0.6, 0.7 are in (bottom to top) black, green, red, and blue, respectively. Here $\lambda =0.04$ and $\mu =-0.001$. Quasitopological gravity is dotted, Gauss-Bonnet is dashed, and Einsteinian is solid.

Figure 7

log(temperature) versus log(entropy) for quasitopological, Gauss-Bonnet, and Einsteinian (dotted, dashed, solid) asymptotically AdS RN black holes of $k=-1$, 0, 1 (red, blue, green; bottom to top) and $Q=6$, $\lambda =0.04$, $\mu =-0.001$; note that the dotted and dashed lines yield almost identical curves for $k=-1$ and that all three curves are effectively indistinguishable for $k=0$.

Figure 8

log(temperature) versus log(entropy) for quasitopological, Gauss-Bonnet, and Einsteinian (dotted, dashed, solid) asymptotically de Sitter (blue, bottom) and asymptotically flat (red, top) RN black holes of $k=1$; $Q=0.6$, $\lambda =0.04$, $\mu =-0.001$.

Figure 9

log(temperature) versus log(entropy) for asymptotically anti-de Sitter Reissner-Nordström black holes of $Q=6$ (dotted), $Q=3$ (dashed), $Q=0.5$ (dash-dot), $Q=0.1$ (long-dash), and $Q=0$ (solid) for $k=-1$, 0, 1 (red, blue, green; bottom to top); $\lambda =0.04$, $\mu =-0.001$.