Abstract:
In this paper, we investigate nonlinearly charged AdS black holes in four-dimensional critical gravity and
study more exact black hole thermodynamics under the effect of small statistical fluctuations. We compute
the correction to the thermodynamics of nonlinearly charged AdS black hole up to the leading order. We
discuss the stability of black holes under the circumstances of fluctuation and find that fluctuation causes
instability in the black holes. Moreover, both the isothermal and adiabatic compressibilities are also derived.
Finally, we estimate the role of small fluctuations on the equation of states and study the P − v diagram of
nonlinearly charged AdS black hole.
