Is there a maximum gravity? Lately I visited a 3T NMR machine (subject to a research project). It got me thinking about maxiums. I know the maximum magnetic fields we have observed are quite a lot stronger than that (field strenghts on some stars), and there seems to be a theoretical maximum value for magnetic fields although the exact value can be disputed. 
But, now for the questions: what is the maximum gravity field or value we have observed or possibly calculated? And is there a theoretical maximum?
 A: In general relativity, we don't measure the strength of the gravitational field as an acceleration $g$, the way we would do in Newtonian gravity. The equivalence principle tells us that $g$ can be anything we like, based on the frame of reference we choose. Instead, we measure gravitational fields using measures of curvature. These measures of curvature naturally have units of inverse length squared (in coordinates that have units of length). The strongest curvature that we expect to be describable by classical general relativity is $1/\ell_{Planck}^2$, where $\ell_{Planck}$ is the Planck length.
A: The maximal magnetic (and electric) field is likely set by the Schwinger limit where QED effects become appreciable and pair production starts. The corresponding limit for gravity is when quantum gravity starts mattering. This presumably starts to happen when we approach the Planck scale, for example when the field causes accelerations on the order of the Planck acceleration $5.560\cdot 10^{51}$ m/s$^2$.
These limits do not mean there cannot be stronger fields, just that very different kinds of physics will be going on. 
