Transformation on the minkowsky metric

Click For Summary
SUMMARY

The discussion centers on a problem involving a linear bijective map T from R^4 to R^4 that preserves the light cone in the context of the Minkowski metric. The objective is to demonstrate that the pullback of the metric, denoted as T* ds^2, is equal to a constant squared multiplied by ds^2. This relationship is crucial in understanding transformations in spacetime geometry, particularly in the realm of special relativity.

PREREQUISITES
  • Understanding of Minkowski metric in R^4
  • Knowledge of linear bijective maps and their properties
  • Familiarity with the concept of pullback in differential geometry
  • Basic principles of light cone preservation in physics
NEXT STEPS
  • Study the properties of linear transformations in vector spaces
  • Explore the concept of pullbacks in differential geometry
  • Investigate the implications of light cone preservation in special relativity
  • Learn about the mathematical formulation of the Minkowski metric
USEFUL FOR

Mathematicians, physicists, and students studying differential geometry or special relativity who seek to deepen their understanding of transformations in spacetime.

michiherlin
Messages
2
Reaction score
0
hi,

in my textbook there ist a problem, i cannot solve: let T be a linear bijective map from R^4 to R^4, which preserves the light cone. show: T* ds^2 = (constant)^2 * ds^2, where ds^2 ist the minkowsky metric and T* ist the pullback of the metric.

can someone show how to do it.

michiherlin
 
Physics news on Phys.org
hi,
does anyone have a hint for me :)?
 

Similar threads

Diagonalizing a metric by a coordinate transformation
  • · Replies 12 ·
Replies
12
Views
2K
Diagonalizing a metric by a coordinate transformation
  • · Replies 1 ·
Replies
1
Views
2K
Initial conditions for orbits around a wormhole
  • · Replies 4 ·
Replies
4
Views
987
Coordinate transformation into a standard flat metric
  • · Replies 3 ·
Replies
3
Views
2K
General relativity- Coordinate/metric transformations
  • · Replies 3 ·
Replies
3
Views
3K
Transform Metric to Flat Spacetime: Advice & Hints
  • · Replies 2 ·
Replies
2
Views
1K
How to Derive Radial Geodesics in Kerr Metric?
  • · Replies 11 ·
Replies
11
Views
4K
Form of radial velocity along null geodesic under the Kerr metric
  • · Replies 0 ·
Replies
0
Views
1K
How Do You Calculate the Ricci Tensor for the AdS Metric in 4 Dimensions?
  • · Replies 1 ·
Replies
1
Views
4K
Graduate Characterizing GR Traj in Minkowski Space
  • · Replies 17 ·
Replies
17
Views
2K