Special relativity effects in general relativity

Click For Summary
SUMMARY

Special Relativity (SR) operates within a flat space-time framework, while General Relativity (GR) incorporates curved space-time. SR serves as an approximation in regions where curvature effects are negligible, allowing for the application of time dilation, length contraction, and relative simultaneity in locally flat tangent spaces of GR. The relationship between SR and GR can be understood through the analogy of navigating a curved surface, where curvature becomes significant over larger distances. The introduction of metric coefficients in GR accounts for variations in distances, emphasizing the need for a field of observers to extend SR concepts globally in curved space-time.

PREREQUISITES
  • Understanding of Special Relativity principles, including time dilation and length contraction.
  • Familiarity with General Relativity concepts, particularly curved space-time and geodesics.
  • Knowledge of Minkowski geometry and its application in flat space-time.
  • Basic grasp of metric coefficients and their role in describing distances in curved geometries.
NEXT STEPS
  • Study the differences between Minkowski geometry and the geometry of General Relativity.
  • Learn about the concept of geodesics and their significance in curved space-time.
  • Explore the mathematical formulation of metric coefficients in General Relativity.
  • Investigate the implications of tidal forces and their effects on objects in curved space-time.
USEFUL FOR

Students and researchers in physics, particularly those focusing on theoretical physics, cosmology, and anyone seeking to deepen their understanding of the relationship between Special and General Relativity.

  • #31
analyst5 said:
Ok, I guess I'm wrong, but kinematical time dilation and gravitational time dilation do add up?

Sort of, at least in simple circumstances. For example if we have an observer in circular free fall orbit in Schwarzschild space-time then the observer's "gamma factor" in Schwarzschild coordinates will be ##\gamma = (1 - 2M/R - R^2 \omega^2)^{-1/2}## where the ##2M/R## accounts for the gravitational part and the ##R^2 \omega^2## accounts for the kinematical part. Then ##\gamma^{-1}## represents the rate at which the circularly orbiting observer's clock ticks relative to a clock at spatial infinity.
 

Similar threads

Graduate Generalize Special Relativity for Flat Spacetime
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad SR-time dilation vs GR-time dilation on rotating Earth
  • · Replies 79 ·
3
Replies
79
Views
5K
High School General Relativity and the curvature of space: more space or less than flat?
  • · Replies 62 ·
3
Replies
62
Views
6K
Undergrad Confused about time dilation -- motion vs energy
  • · Replies 9 ·
Replies
9
Views
1K
Undergrad Relativity: the Special and General theories
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad The wave equation interpretation of special relativity
  • · Replies 10 ·
Replies
10
Views
913
High School Why Aren’t ALL SR Effects Cumulative?
  • · Replies 28 ·
Replies
28
Views
3K
Graduate Special Relativity Fiber Bundle: R^3 & Lorentz Metric
  • · Replies 10 ·
Replies
10
Views
2K
Undergrad Question about special relativity and magnetism
  • · Replies 5 ·
Replies
5
Views
882
Graduate Dirac's derivation of the action/Lagrangian for a free particle
  • · Replies 3 ·
Replies
3
Views
1K