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!