I Difference between Schwarzschild metric and Gravity well.

Victor Escudero
I would like to know the difference between this two concepts, specially the difference between the geometry deformations of space-time that they descript. As far as I know the Schawrzschild metric can be represent by Flamm’s paraboloid, but this shape is not the same that the deformation of space-time descripted by the Gravity well. So I would like to know the difference, which one describes exactly de deformation of space-time due to the gravity and if there exist any formulas that can give us the shape of this deformation.
 
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It is unclear what you mean by "gravity well". Do you refer to a well in the gravitational potential? In that case it is only a valid description for very weak gravitational fields and the Schwarzschild solution is a better description (assuming that you want a spherically symmetric distribution) outside of the matter distribution.

Flamm's paraboloid only describes a particular space-like two-dimensional submanifold of the Schwarzschild space-time so neither it nor a gravitational potential well describes the geometry of 4D space-time very well.
 
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