In particular, there's this survey article: Brane-World Gravity.
What's interesting is that a couple of theorists have recently come up with a way that the "braneworld" idea can be tested observationally, and in such a way that would confirm the existence of at least one extra spatial dimension beyond the familiar three:
Scientists Predict How to Detect a Fourth Dimension of Space
Scientists at Duke and Rutgers universities have developed a mathematical framework they say will enable astronomers to test a new five-dimensional theory of gravity that competes with Einstein's General Theory of Relativity.
Charles R. Keeton of Rutgers and Arlie O. Petters of Duke base their work on a recent theory called the type II Randall-Sundrum braneworld gravity model. The theory holds that the visible universe is a membrane (hence "braneworld") embedded within a larger universe, much like a strand of filmy seaweed floating in the ocean. The "braneworld universe" has five dimensions -- four spatial dimensions plus time -- compared with the four dimensions -- three spatial, plus time -- laid out in the General Theory of Relativity.
The framework Keeton and Petters developed predicts certain cosmological effects that, if observed, should help scientists validate the braneworld theory. The observations, they said, should be possible with satellites scheduled to launch in the next few years.
I'm not going to tackle at this moment trying to explain the details, but I will give a few references, in addition to the survey article already mentioned.
I'll just make a few comments. First, the gravitational theory this work is based on (the Randall-Sundrum braneworld gravity model) is not exactly a rival that would completely replace Einstein's general relativity. It does not invalidate Einstein's theory. Rather, it's a generalization that assumes the existence of additional spatial dimensions beyond the familiar three. (These are spatial dimensions, not to be confused with the idea of time as a fourth dimension.) Since these additional dimensions are "compact", i. e. very small, their effect is to contribute small corrections to general relativity which are significant only under special circumstances. Additionally, this kind of model may explain facts that general relativity doesn't even address, such as why gravity is so weak compared to the other three main physical forces (electromagnetism and the "weak" and "strong" nuclear forces).
Second, what Keeton and Petters have done is to use the braneworld theory to predict that the universe could contain a significant number of small primordial black holes, i. e. black holes which were created in the original big bang. Under classical general relativity, as Stephen Hawking demonstrated, all such small black holes must have "evaporated" long ago. Under the new theory, these black holes could make up several percent of the mass of the universe. And they would be numerous enough that some could even exist in our solar system. They would also be numerous enough to affect the properties of gamma rays emitted in distant gamma ray bursts. And such effects are how the existence of these black holes may be observed within a few years.
Third, evidence for the existence of at least one additional spatial dimension would also be evidence for a major prediction of superstring theory and/or its generalization, M-theory. This is not a small deal, since these theories have been criticized as untestable. Of course, finding extra dimensions does not come close to "proving" these theories, but it certainly would be some evidence for one of their rather striking predictions.
Fourth, one of the originators of the Randall-Sundrum braneworld gravity model is Lisa Randall, who recently published a popular book, Warped Passages, that (among other things) explains a bit about the model, and a lot of the background ideas about "branes", superstring theory, and M-theory. (Refernces on Randall: home page, Wikipedia article. References on the book: home page, Wikipedia article, Amazon page.)
- NewScientist article: Satellite could open door on extra dimension
- Wikipedia articles: Randall-Sundrum model, Brane cosmology, M-theory
- Keeton-Petters article: Formalism for testing theories of gravity using lensing by compact objects. III. Braneworld gravity -- abstract at Physical Review D, full text at arXiv.org.
- Randall-Sundrum article: A Large Mass Hierarchy from a Small Extra Dimension
- Randall article at Science: Extra Dimensions and Warped Geometries (subscription or fee required)
- Some blog articles: The Randall-Sundrum 'Braneworld' Model, Of ‘Braneworlds’ and Nearby Black Holes, Exploring the fourth dimension (also here, here), Science…Sort Of, I Want Black Holes for Christmas, more
Tags: braneworld, black holes, fourth dimension, Randall-Sundrum model
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