Inspired by the recent "Complexity = Action" conjecture, we use the approach proposed by Lehner et al. to calculate the rate of the action of the WheelerDeWitt patch at late times for static uncharged and charged black holes in f (R) gravity. Our results have the same expressions in terms of the mass, charge, and electrical potentials at the horizons of black holes as in Einstein's gravity. In the context of f (R) gravity, the Lloyd bound is saturated for uncharged black holes but violated for charged black holes near extremality. For charged black holes far away from the ground states, the Lloyd bound is violated in four dimensions but satisfied in higher dimensions.

Considering a canonical ensemble, in which the temperature and the charge on a wall of the cavity are fixed, we investigate the thermodynamics of a D-dimensional Gauss-Bonnet black hole in a finite spherical cavity. Moreover, it shows that the first law of thermodynamics is still satisfied. We then discuss the phase structure and transition in both five and six dimensions. Specifically, we show that there always exist two regions in the parameter space. In one region, the system possesses one single phase. However in the other region, there could coexist three phases and a van der Waals-like phase transition occurs. Finally, we find that there is a fairly close resemblance in thermodynamic properties and phase structure of a Gauss-Bonnet-Maxwell black hole, either in a cavity or in anti-de Sitter space.

In string theory, an important challenge is to show if the big-bang singularity could be resolved by the higher derivative α corrections. In this work, based on the Hohm-Zwiebach action, we construct a series of non-singular non-perturbative cosmological solutions with the complete α corrections, for the bosonic gravi-dilaton system. In the perturbative regime, these solutions exactly match the perturbative results given in literature. Our results show that the big-bang singularity indeed could be smoothed out by the higher derivative α corrections. 1 arXiv:1909.00830v3 [hep-th]

For the bosonic gravi-dilaton system, we provide systematical approaches to construct non-perturbative string cosmological solutions without curvature singularities, which can match the perturbative solution to any order in α ′ expansion. When higher order α ′ corrections are calculated, they can be straightforwardly plugged in to generate compatible non-perturbative evolutions without curvature singularities. We also give a (phenomenological) map between α ′ corrected EOM and loop corrected EOM. This map enables us to easily generate a loop corrected solution from an α ′ corrected solution, and vice versa, therefore substantially enlarges the solution space.

The original derivation of Hawking radiation shows the complete evaporation of black holes. However, theories of quantum gravity predict the existence of the minimal observable length. In this paper, we investigate the tunneling radiation of the scalar particles by introducing quantum gravity effects influenced by the generalized uncertainty principle. The Hawking temperatures are not only determined by the properties of the black holes, but also affected by the quantum numbers of the emitted particles. The quantum gravity corrections slow down the increase of the temperatures. The remnants are found during the evaporation.