Difference between Schwarzschild metric and Gravity well.

Click For Summary
SUMMARY

The discussion clarifies the distinction between the Schwarzschild metric and the concept of a gravity well in the context of general relativity. The Schwarzschild metric, represented by Flamm's paraboloid, provides a more accurate depiction of the geometry of space-time around a spherically symmetric mass. In contrast, a gravity well is a simplified model applicable primarily in weak gravitational fields and does not adequately represent the complexities of 4D space-time geometry. The Schwarzschild solution is preferred for describing gravitational effects outside matter distributions.

PREREQUISITES
  • Understanding of general relativity principles
  • Familiarity with the Schwarzschild metric
  • Knowledge of Flamm's paraboloid representation
  • Concept of gravitational potential wells
NEXT STEPS
  • Research the mathematical formulation of the Schwarzschild metric
  • Explore the implications of Flamm's paraboloid in space-time geometry
  • Study gravitational potential wells and their limitations in strong fields
  • Examine the differences between 2D and 4D representations of space-time
USEFUL FOR

Physicists, students of general relativity, and anyone interested in the mathematical descriptions of gravitational fields and space-time geometry.

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.
 
Physics news on Phys.org
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.
 

Similar threads

  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 13 ·
Replies
13
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 6 ·
Replies
6
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 13 ·
Replies
13
Views
6K
Replies
1
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 18 ·
Replies
18
Views
3K