Strings and Spacetime Geometry
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The
classical theory of spacetime geometry that we call gravity consists of
the Einstein equation, which relates the curvature of spacetime to the
distribution of matter and energy in spacetime. But how do the Einstein
equations come out of string theory?
If a closed string is traveling in a curved spacetime, then the coordinates of the string in spacetime feel this curvature as the string propagates. Once again, the answer lies on the string worldsheet. In order for their to be a consistent quantum theory in this case, the curved space in which the string travels must be a solution to the Einstein equations. Now this is really something! This was a very convincing result for string theorists. Not only does string theory predict the graviton from flat spacetime physics alone, but string theory also predicts the Einstein equation will be obeyed by a curved spacetime in which strings propagate. What about strings and black
holes?
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