  We have different definitions of the surface gravity (SG) of a horizon since
we can say we have distinct classifications of horizons. The SG has an
underlying role in the laws of black hole (BH) thermodynamics, being constant
in the event horizon. The SG also acts in the emission of Hawking radiation
being connected to its temperature. Concerning this last issue, the quantum
features that permeate Hawking radiation provide us a direct indication that a
BH has its temperature directly connected to its area and that its entropy is
proportional to the horizon area. In this work we analyzed some aspects of
event horizons. Analyzing how the SG can be classically defined for stationary
BHs together with the radial pressure computation. So, the SG, through the laws
of BH mechanics is connected to the real thermodynamical temperature of a
thermal spectrum. We discussed these subjects in two different BHs scenarios,
the five dimensional Gauss-Bonnet one and the recently developed Barrow entropy
construction. We discussed how the quantum fluctuations affect these both
quantities.
