  Barrow proposed that quantum gravity effects might introduce fractal
corrections to the area of the event horizon of black holes. The area law gets
modified as $S \propto A^{1+\Delta/2}$, with $0\leq\Delta\leq 1$. It was so far
unclear whether this assumption could lead to meaningful quantum gravity
theories beyond general relativity. In this paper, we argue that this is indeed
the case. In particular, assuming $\Delta$ to be a radial function, we show
that the Barrow hypothesis, together with the Jacobson's approach can generate
non-trivial modified gravity theories.
