We already have a very good, and nearly complete, understanding of all the ingredients responsible for the formation of low pressure systems, as seen in Hurricanes.

But because a hurricane is quite a massive thing, a force of gravity (albeit a quite weak one) will contribute to the contraction of the space occupied by a hurricane.

Similar to a galaxy, this force will contract space and matter from both a hurricanes periphery as well as from its centre. It is of course only a weak contribution, but still important to understand.

Gravity is basically the cause of the low pressure that occurs, later in the process, the coriolis force takes part, and the rising heat speeds up the velocity.

Let's imaging a low pressure area of 500 km²,  carrying an average of  100 kg water per m²  (total 5 * 10¹³ kg ). This is a pretty heavy mass.  

Near the centre of a such low pressure we should (according to this theory) expect acceleration due to gravity about 0,00002 m/s².

Even though this is not much, we have to remember that wind blowing towards the centre of a low pressure will keep accelerating (second by second / day by day) due to the force of gravity.

After one  day/night (86400 seconds) a such low pressure therefore must reach  a wind velocity about 1.73 m/s². After 10 days  17,3 m/s². (62 km/h) etc...only caused by gravity

The time a low pressure exist  is therefore very  important regarding to how fast wind it will create. 

Because we have underestimated the strength and importance  of central gravity, we have also failed to understand a very important factor responsible for low pressure (and hurricanes).