What is the different between Minkowski Space an Semi Riemann Space?

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SUMMARY

Minkowski space is a specific type of semi-Riemannian geometry characterized by its flatness, primarily used in the context of special relativity. In contrast, semi-Riemannian spaces can be curved, accommodating more complex geometries such as Schwarzschild and Friedmann-Robertson-Walker (FRW) spacetimes, which incorporate matter. The key distinction lies in the curvature of the space, with Minkowski being flat and semi-Riemannian allowing for curvature. Understanding these differences is crucial for applications in general relativity and cosmology.

PREREQUISITES
  • Basic understanding of geometry, specifically Riemannian geometry
  • Familiarity with concepts of spacetime in physics
  • Knowledge of special relativity principles
  • Introduction to general relativity and its implications
NEXT STEPS
  • Study the properties of Minkowski spacetime in detail
  • Explore the Schwarzschild solution in general relativity
  • Investigate the Friedmann-Robertson-Walker (FRW) metric and its applications
  • Learn about the implications of curvature in semi-Riemannian geometry
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Students and professionals in theoretical physics, mathematicians specializing in geometry, and anyone interested in the foundations of general relativity and cosmology.

ber70
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Last summer I took Semi Riemann Geometry lesson. Almost all the definitions in Semi Riemann geometry are with the same Minkowski geometry. I don't understand what is the different between Minkowski Space an Semi Riemann Space.
 
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Minkowski spacetime is a semi-riemannian spacetime that is flat. Curved semi-riemannian spacetimes include the Schwarzschild spacetime, and the FRW spacetime with matter.
 

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