quantities is not possible locally. Nonlocality is indeed a fundamental feature of general relativity, and corresponding nonextesive thermodynamic phenomena have been known in cosmology and gravitation theory for a long time (see e.g. [@Landsberg1984; @cg1; @cg2; @cg3; @cg4; @cg5; @cg6; @cg7; @cg8; @cg9] and references therein). In fact, even as early as 1902, Gibbs already pointed out in his statistical mechanics book [@Gibbs], that systems with divergent partition function lie outside the validity of Boltzamann–Gibbs theory. He explicitly mentions gravitation as an example (see e.g. [@Tsallis:2012js] for more details). Therefore, the standard Boltzamann–Gibbs statistics may not be the best possible choice for defining the entropy function in strongly gravitating systems, and other statistical approaches, which could also take into account the long-range type property of the relevant interaction (i.e. gravitation) and the nonextensive nature of the problem, are also relevant and important to study.

The nonextensive nature of the Bekenstein-Hawking entropy of black hole event horizons has been noticed [@Davies:1978mf] very early on after the thermodynamic theory of black holes had been formulated [@Bekenstein:1973ur; @Bardeen:1973gs; @Hawking:1974sw; @Hawking:1976de], and the corresponding thermodynamic and stability problem has been investigated several times with various approaches (see e.g. [@landsberg1980entropies; @bishop1987thermodynamics; @Landsberg1984; @pavon1986some; @1993Natur.365..103M; @Gour:2003pd; 