**Table of Contents**

*.......The Elegant Universe*

**THE ELEGANT UNIVERSE,****Brian Greene,**1999, 2003

```(annotated and with added

**bold highlights by Epsilon=One**)

**Chapter 13 - Black Holes: A String/M-Theory Perspective**

Returning to Black Holes and Elementary Particles

What does this have to do with black holes and elementary particles? A lot. To see this, we must ask ourselves the same question we posed in Chapter 11. What are the observable physical consequences of such tears in the fabric of space? For flop transitions, as we have seen, the surprising answer to this question was that not much happens at all. For

Two related notions underlie these observable consequences; we will explain each in turn. First, as we have discussed, Strominger's initial breakthrough was his realization that a three-dimensional sphere inside a Calabi-Yau space can collapse without an ensuing disaster, because a three-brane wrapped around it provides a perfect protective shield. But what does such a wrapped-brane configuration look like? The answer comes from earlier work of Horowitz and Strominger, which showed that to persons such as ourselves who are directly cognizant only of the three extended spatial dimensions, the three-brane "smeared" around the three-dimensional sphere will set up a gravitational field that looks like that of a black hole.

The second ingredient we need to recall is that the number of holes in a Calabi-Yau shape, as discussed in Chapter 9, determines the number of low-energy, and hence low-mass, vibrational string patterns, the patterns that can possibly account for the particles in Table 1.1 as well as the force carriers. Since the space-tearing conifold transitions change the number of holes (as, for example in Figure 13.3, in which the hole of the doughnut is eliminated by the tearing/repairing process), we expect a change in the number of low-mass vibrational patterns. Indeed, when Morrison, Strominger, and I studied this in detail, we found that as a new two-dimensional sphere replaces the pinched three-dimensional sphere in the curled-up Calabi-Yau dimensions, the number of massless string vibrational patterns increases by exactly one. (The example of the doughnut turning into a beach ball in Figure 13.3 would lead you to believe that the number of holes—and thus the number of patterns—decreases, but this proves to be a misleading property of the lower-dimensional analogy.)

To combine the observations of the preceding two paragraphs, imagine a sequence of snapshots of a Calabi-Yau space in which the size of a particular, three-dimensional sphere gets smaller and smaller. The first observation implies that a three-brane wrapping around this three-dimensional sphere—which appears to us as a black hole—will have ever smaller mass until, at the final point of collapse, it will be massless. But, as we asked above, what does this mean? The answer became clear to us by invoking the second observation. Our work showed that the new massless pattern of string vibration arising from the space-tearing conifold transition

*cortifold transitions*—the technical name for the drastic space-tearing transitions we had now found—there is, once again, no physical catastrophe (as there would be in conventional general relativity), but there are more pronounced observable consequences.Two related notions underlie these observable consequences; we will explain each in turn. First, as we have discussed, Strominger's initial breakthrough was his realization that a three-dimensional sphere inside a Calabi-Yau space can collapse without an ensuing disaster, because a three-brane wrapped around it provides a perfect protective shield. But what does such a wrapped-brane configuration look like? The answer comes from earlier work of Horowitz and Strominger, which showed that to persons such as ourselves who are directly cognizant only of the three extended spatial dimensions, the three-brane "smeared" around the three-dimensional sphere will set up a gravitational field that looks like that of a black hole.

**This is***2**not*obvious and becomes clear only from a detailed study of the equations governing the branes. Again, it's hard to draw such higher-dimensional configurations accurately on a page, but Figure 13.4 conveys the rough idea with a lower-dimensional analogy involving two-dimensional spheres. We see that a two-dimensional membrane can smear itself around a two-dimensional sphere (which itself is sitting inside a Calabi-Yau space positioned at some location in the extended dimensions). Someone looking through the extended dimensions toward this location will sense the wrapped brane by its mass and the force charges it carries, properties that Horowitz and Strominger had shown would look just like those of a black hole. Moreover, in Strominger's 1995 breakthrough paper, he argued that the mass of the three-brane—the mass of the black hole, that is—is proportional to the volume of the three-dimensional sphere it wraps: The bigger the volume of the sphere, the bigger the three-brane must be in order to wrap around it, and the more massive it becomes. Similarly, the smaller the volume of the sphere, the smaller the mass of the three-brane that wraps it. As this sphere collapses, then, a three-brane that wraps around**the sphere, which is perceived as a black hole**, appears to become ever lighter. When the three-dimensional sphere has**collapsed to a pinched point, the corresponding black hole—brace yourself—is massless.**Although it sounds completely mysterious—what in the world is a*massless*black hole?—we will soon connect this enigma with more familiar string physics.**Figure 13.4**When a brane wraps around a sphere that is within the curled-up dimensions, it appears as a black hole in the familiar extended dimensions.

To combine the observations of the preceding two paragraphs, imagine a sequence of snapshots of a Calabi-Yau space in which the size of a particular, three-dimensional sphere gets smaller and smaller. The first observation implies that a three-brane wrapping around this three-dimensional sphere—which appears to us as a black hole—will have ever smaller mass until, at the final point of collapse, it will be massless. But, as we asked above, what does this mean? The answer became clear to us by invoking the second observation. Our work showed that the new massless pattern of string vibration arising from the space-tearing conifold transition

*is the microscopic description of a massless particle into which the black hole has transmuted.*We concluded that as a Calabi-Yau shape goes through a space-tearing conifold transition, an initially massive black hole becomes ever lighter until it is massless and then it transmutes into a massless particle—such as**a massless photon—which in string theory is nothing but a single string executing a particular vibrational pattern.****(Epsilon=One: NO! Quantum electrodynamics (QED) indicates that a photon has many different oscillations; "a particular vibrational pattern is only one form of oscillation. In fact, a photon is an orbital Resoloid (electron) that is ejected from the dual envelopes of a Pulsoid ("dark" matter) when critically compressed. A Pulsoid that has one or more ejected Resoloids is referred to as an atom.)**In this way, for the first time, string theory explicitly establishes a direct, concrete, and quantitatively unassailable connection between black holes and elementary particles.**(Epsilon=One: Strong words: "explicitly establishes a direct, concrete, and quantitatively unassailable" for a "connection between black holes and elementary particles" when neither the "holes" nor "particles" have ever been directly observed nor precisely understood.)**