Anti-evaporation and evaporation of an $n$-dimensional Reissner-Nordström black hole

We generalize the $f(R)$ theory of anti-evaporation and evaporation for a Reissner-Nordström black hole in $n$-dimensional spacetime. We consider nonlinear conformally invariant Maxwell field. By perturbing the fields over Nariai-like spacetime associated with degenerate horizon, we describe the dynamic behavior of the horizon. We show that $f(R)$ gravity can offer both anti-evaporation and evaporation in an $n$-dimensional Reissner-Nordström black hole depending on the dimension $n$ and the functional form of $f(R)$. Furthermore, we argue that, in one class of a nonoscillatory solution, stable and unstable anti-evaporation and evaporation exist. In the other class of oscillatory solutions, anti-evaporation and evaporation exist only with instability. The first class of solutions may explain a long-lived black hole.

Figure 1

Left and right plots are for $N(r)$ with respect to $r$ for positive and negative $N^{\prime \prime }(r_0)$ respectively with a degenerate horizon at $r_0=1$.

Figure 2

The plot of $1-4\alpha$ with dimension $n$ of spacetime for $r_0=0.1$ and $C_1=10$.