Is a planet with varying fields of gravity possible? Yes. Earth has varying gravitational fields at various different times due to various factors, mainly location based.
How extreme can I make these varying gravity fields, before the planet becomes uninhabitable?
The difference between the observed gravity and expected gravity, if the Earth was a perfect sphere, provides us with a handy visual aid of Gravity Anomaly Maps.
image below from NASA earth observatory using GRACE.
The Planetary Society posted an interesting and extremely helpful blogpost about using results from GRAIL to investigate the gravity anomalies on the Moon.
Differences in Earth Gravity are not only just due to location near the equator or the poles. Interpretations of recent GRACE findings have determined the following:
The model pinpoints more extreme differences in gravitational acceleration than previously seen. Standard models predict a minimum gravitational acceleration of 9.7803 metres per second squared at the equator and 9.8322 m/s2 at the poles. Hirt’s model pinpoints unexpected locations with more extreme differences. Mount Nevado Huascarán in Peru has the lowest gravitational acceleration, at 9.7639 m/s2, while the highest is at the surface of the Arctic Ocean, at 9.8337 m/s2.
However, these anomalies are very VERY small and can only be detected with sensitive machinery. Going to weigh yourself at the top of Mount Nevado Huascarán does not make any discernible difference from your own personal perspective.
How extreme can I make these gravity field anomalies, before the planet becomes uninhabitable?
- before the planet's gravity either starts to equalize through Isostasy and other natural forces, or
possibly tears itself apart
I am hoping that it is possible to have areas of the planet with gravity differences that are noticeable to humans (even if just slightly) and still allow for life to evolve and continue to live on planet.
- ie would it be possible to have ~1.1 or ~0.8 g environment in one region and a typical Earth gravity at another, on the same planet, at the same time.
These gravity anomaly maps are often representative of an average over a period of a month or year of time. For the purposes of this question, using the long-term averages is more than acceptable. Especially as the gravity anomalies are largely due to semi-permanent location factors and not that affected by temporal factors.
For reference you can use Earth-like parameters, as I'm building a planet far far away, where normal physics holds sway.
I'm also not looking for answers that explain how it would be possible. This question about a planet with changing gravity is the closest I could find on SE about what I am after. However it focused on changing gravity fields over a period of time (which would be cool) as well as how to explain how it would be possible. Not on how much actual change would be possible between 2 locations. It was a helpful question but doesn't answer my problem. Most of the 7 pages worth of [gravity] tagged questions were related to adjusting to different gravities, travelling from one to another, or changes over time (mostly centuries) etc.
I am aware that there are a lot of factors that influence the gravity anomalies. For the purposes of this question, I am mainly focused on how extreme these variations can be (due to whatever factors) before the planet becomes uninhabitable.
Extra constraint: As I am not worried about the 'how', right now, answers are open to terraforming and artificial initial causes. As long as the actual day to day location-based gravity anomalies are following normal physics, don't rely on tech to constantly interfer/stabilise, don't tear the planet apart and the planet is still inhabitable. I don't mind an artificial start to the process. As natural processes will always try to equalize, it may be difficult to have a planet with such weird conditions at such a late stage (life evolution etc). Just need to figure out how extreme these values can be before the natural equalizing processes start to kick in. Obviously answers that rely on an artificial initiating conditions should mention this 'how' factor.