Quantum Einstein Gravity as a Topological Field Theory

General covariance in quantum gravity is seen once one integrates over all possible metrics. In recent years topological field theories have given us a different route to general covariance without integrating over all possible metrics. Here we argue that Einstein quantum gravity may be viewed as a topological field theory provided a certain constrant from the path integral measure is satisfied.Comment: 10 pages, LaTe

Black Strings and Classical Hair

We examine the geometry near the event horizon of a family of black string solutions with traveling waves. It has previously been shown that the metric is continuous there. Contrary to expectations, we find that the geometry is not smooth, and the horizon becomes singular whenever a wave is present. Both five dimensional and six dimensional black strings are considered with similar results.Comment: 14 pages, harvma

Topology, Quantum Gravity and Particle Physics

It is argued that quantum gravity has an interpretation as a topological field theory provided a certain constraint from the path intergral measure is respected. The constraint forces us to couple gauge and matter fields to gravity for space - time dimensions different from 3. We then discuss possible models which may be relevant to our universe.Comment: 18 pages, LaTeX. Replaced version corrects typos and has additional reference

Where is the Information Stored in Black Holes?

It is shown that many modes of the gravitational field exist only inside the horizon of an extreme black hole in string theory. At least in certain cases, the number of such modes is sufficient to account for the Bekenstein-Hawking entropy. These modes are associated with sources which carry Ramond-Ramond charge, and so may be viewed as the strong coupling limit of D-branes. Although these sources naturally live at the singularity, they are well defined and generate modes which extend out to the horizon. This suggests that the information in an extreme black hole is not localized near the singularity or the horizon, but extends between them.Comment: 21 pages, reference corrected and comment adde

An Equivalence Between Momentum and Charge in String Theory

It is shown that for a translationally invariant solution to string theory, spacetime duality interchanges the momentum in the symmetry direction and the axion charge per unit length. As one application, we show explicitly that charged black strings are equivalent to boosted (uncharged) black strings. The extremal black strings (which correspond to the field outside of a fundamental macroscopic string) are equivalent to plane fronted waves describing strings moving at the speed of light.Comment: 10 page

DIMINISHING MARGINAL VALUE

The notion of diminishing marginal value has had a profound impact on the development of neoclassical theory. Early neoclassical scholars had considerable difficulty convincing contemporaries of the new paradigm's value until political economists, including Jevons and Walras, used the critical assumption of diminishing marginal value to link utility and demand. While diminishing marginal value remains a key component of modern economic intuition, there is surprisingly little empirical verification of its existence or level. This paper gathers field data across a myriad of subject pools--from undergraduate students to PTA members to sportscard enthusiasts--to examine several aspects of preferences in both price and exchange institutions. Examining behavior of nearly 900 subjects across several treatments, we find strong evidence of diminishing marginal value.Research Methods/ Statistical Methods,

Black Holes with Multiple Charges and the Correspondence Principle

We consider the entropy of near extremal black holes with multiple charges in the context of the recently proposed correspondence principle of Horowitz and Polchinski, including black holes with two, three and four Ramond-Ramond charges. We find that at the matching point the black hole entropy can be accounted for by massless open strings ending on the D-branes for all cases except a black hole with four Ramond-Ramond charges, in which case a possible resolution in terms of brane-antibrane excitations is considered.Comment: 26 pages, harvmac, minor correction

A Correspondence Principle for Black Holes and Strings

For most black holes in string theory, the Schwarzschild radius in string units decreases as the string coupling is reduced. We formulate a correspondence principle, which states that (i) when the size of the horizon drops below the size of a string, the typical black hole state becomes a typical state of strings and D-branes with the same charges, and (ii) the mass does not change abruptly during the transition. This provides a statistical interpretation of black hole entropy. This approach does not yield the numerical coefficient, but gives the correct dependence on mass and charge in a wide range of cases, including neutral black holes.Comment: 24 pages, one typo correcte