This document discusses time travel through wormholes in Schwarzschild space-time. It introduces general relativity and how the Schwarzschild solution describes space-time near a non-rotating, spherically symmetric black hole. This forms a wormhole bridge that could connect distant regions. However, the dynamic properties of the Schwarzschild wormhole, with its rapid contractions and expansions, make it impossible to pass through and use for time travel. Future work may examine modifying the space-time topology or incorporating quantum gravity to enable time travel through wormholes.

1. Time Travel in the Schwarzschild Space-time Yuhao Yang Sept 2010

3. Outline Introduction to general relativity The Schwarzschild wormhole Dynamic properties of the wormhole Time travel through the wormhole Summary and future developments

4. Introduction to General Relativity Special theory of relativity General theory of relativity Classical law of gravitation the space-time near a massive object -> bended/ curved the equation of motion -> the shortest path (geodesic line)

5. Einstein & Schwarzschild Karl Schwarzschild (October 9, 1873 – May 11, 1916) Albert Einstein (March 14,1879 – April 18, 1955)

6. The Schwarzschild Solution Spherical Conditions Non-rotating Schwarzschild Solution Vacuum Black Hole Predictions Wormhole

7. A Wormhole is built! A bridge which connects two distant flat regions in the space-time The Einstein-Rosen Bridge

8. Two types of Einstein-Rosen Bridges m<0 -> no event horizon -> construction × { Neutral bridge (massive, chargeless) Generalized bridge Quasi-charged bridge (charged, massless) ε>0 -> no event horizon -> construction × The key to the construction of the bridge is the existence of an event horizon!

9. Wormhole for Time Travel? Dynamic Properties of the Bridge Too rapid! Impossible to pass through! Creation Contraction Expansion

10. Possible Solutions Establish a relation between singularities -> contradiction with Einstein’s equations? Modify the space-time topology -> creation of conical singularity? -> violation of causality?