fR Gravity Effects on Charged Accelerating AdS Black Holes Using Holographic Tools

Abstract

We investigate numerically fR gravity effects on certain AdS/CFT tools including holographic entanglement entropy and two-point correlation functions for a charged single accelerated Anti-de Sitter black hole in four dimensions. We find that both holographic entanglement entropy and two-point correlation functions decrease by increasing the acceleration parameter A, matching perfectly with literature. Taking into account the fR gravity parameter η, the decreasing scheme of the holographic quantities persist. However, we observe a transition-like point where the behavior of the holographic tools changes. Two regions meeting at such a transit-like point are shown up. In such a nomination, the first one is associated with slow accelerating black holes while the second one corresponds to a fast accelerating solution. In the first region, the holographic entanglement entropy and two-point correlation functions decrease by increasing the η parameter. However, the behavioral situation is reversed in the second one. Moreover, a cross-comparison between the entropy and the holographic entanglement entropy is presented, providing another counterexample showing that such two quantities do not exhibit similar behaviors.

Analytically approximation solution to $$R^{2}$$ gravity

“…Similar to previous cases for near horizons and asymptotes, one can obtain the metric as 8 ) , (43) with c 0 = 1 and c 0 = −2/9. The metric is fully determined and there is no free parameter.…”

“…In Fig. 4, we have shown the full solutions of the field equations from center to infinity by starting from the near origin metric (43) and asymptotic solution (17), for c 0 = 1 (a solution without horizon 2 ) and for c 0 = −2/9 (black hole case).…”

“…Many applications have been developed in the framework of the f (R) gravity such as early-time inflation [12][13][14], cosmological phases [15][16][17][18][19][20][21], gravitational wave detection [22,23], the stability of the solutions [24][25][26] and other different issues [27]. Interestingly, the duality between gravity and quantum field theory that has been introduced in [28,29] and its applications considered in different theories and f (R) gravity such as [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. In addition, the different solutions of f (R) gravity have been studied.…”