Date post: | 26-May-2015 |
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Time Travel in the Schwarzschild Space-time
Yuhao YangSept 2010
Outline
Introduction to general relativity The Schwarzschild wormhole Dynamic properties of the
wormholeTime travel through the wormholeSummary and future
developments
Introduction to General Relativity
Special theory of relativity General
theory of relativityClassical
law of gravitation
the space-time near a massive object → bended / curved
the equation of motion → the shortest path (geodesic line)
Einstein & Schwarzschild
Karl Schwarzschild (October 9, 1873 – May 11, 1916)
Albert Einstein (March 14,1879 – April 18, 1955)
The Schwarzschild Solution
Schwarzschild Solution
Predictions
Conditions
Spherical
Non-rotating
Vacuum
Black Hole
Wormhole
A Wormhole is built!
A bridge which connects two distant flat regions in the space-time
The Einstein-
Rosen Bridge
Two types of Einstein-Rosen Bridges
The key to the construction of the bridge is the existence of an event horizon!
{Neutral bridge
(massive, chargeless)
Quasi-charged bridge
(charged, massless)
Generalized bridge
m<0 → no event horizon → construction
×
ε>0 → no event horizon
→ construction ×
Wormhole for Time Travel?Dynamic
Properties of the Bridge
Creation
Expansion
Contraction
Too rapid!Impossible
to pass through!
Possible Solutions
Establish a relation between singularities
→ contradiction with Einstein’s equations?Modify the space-time topology → creation of conical singularity? → violation of causality?
Summary and Future DevelopmentsThe Schwarzschild Geometry
suggests the existence of a wormhole
The Schwarzschild wormhole cannot be used to realize time travel because of its rapid dynamic motions
Future developmentso → Topological structureso → Quantum gravity
Thank you!