‘Detection’ is one of the commonest words in the practising astronomer's vocabulary. It is the preliminary to much else that happens in astronomy, whether it means locating a spectral line, a faint star or a gamma-ray burst. Indeed, of its wide range of meanings, here we take the location, and confident measurement, of some sort of feature in a fixed region of an image or spectrum. When a detection is obvious to even the most sceptical referee, statistical questions usually do not arise in the first instance. The parameters that result from such a detection have signal-to-noise ratio so high that the detection finds its way into the literature as fact. However, elusive objects or features at the limit of detectability tend to become the focus of interest in any branch of astronomy. Then, the notion of detection (and non-detection) requires careful examination and definition.

Non-detections are especially important because they define how representative any catalogue of objects may be. This set of non-detections can represent vital information in deducing the properties of a population of objects; if something is never detected, that too is a fact, and can be exploited statistically.

The molecules which generate astrophysical masers form a small subset of those so far discovered in space. At the end of 2003, the total number of molecular species detected was 129, not including isotopic substitutions, with the largest containing 13 atoms (Lequeux, 2005). There is no indication that we have reached anything approaching an exhaustive list of astrophysical molecules. Indeed, there has been a recent detection of the fullerenes C60 and C70 (Cami et al., 2010). Of those known in space, only 11 molecules (and the hydrogen atom) are known to give rise to masers, and again I have not included isotopic substitutions in this count. The maser molecules tend to be small, ranging from hydrogen – the simplest atom – to methanol, the most complex maser molecule, which has six atoms. Despite their simplicity, the maser molecules have a surprising variety of structures, the basics of which are explained below.

Molecular spectroscopy

Broadly speaking, molecular transitions can be placed into the following energy hierarchy. Transitions of the highest energy result from re-arranging the electron wavefunction of the molecule. Such transitions between electronic states are analogous to those in individual atoms, and have typical wavelengths that range from the near infrared, through the visible, and into the ultraviolet region of the electromagnetic spectrum. Electronic transitions are rarely involved in the pumping of astrophysical masers, though there are examples of schemes which do employ them.

This chapter deals with the theory of astrophysical masers in some depth. It therefore contains considerable mathematical detail, and is the most fundamental chapter from the point of view of maser physics. Perhaps the most important point to make is that maser radiation behaves, in its interaction with matter, in a way which is in principle different from the behaviour of ‘ordinary’ radiation. This difference arises from the generation of the maser radiation through the stimulated, rather than spontaneous, emission process.

Introduction to semi-classical theory

The interaction of radiation with matter can be treated via a hierarchy of approximations. At each level of approximation, accuracy of the representation is traded for simpler analysis and greater ease of use. Choosing the level of approximation which provides the minimum level of accuracy for a particular situation is often non-trivial, and the various approximations available are detailed in, for example, Sargent et al. (1974).

The most accurate representation of radiation interacting with matter is the fully quantum-mechanical model, in which an ensemble of active molecules, together with a radiation field of a countable number of photons, forms a combined quantum state. In this representation, the gain of one photon by stimulated emission is accompanied by the loss of one molecule from the maser transition upper level, and the increase in the number of such molecules in the lower level, with a resulting state change.

Introduction

The existence of black p-branes in higher-dimensional general relativity hints at the possibility of large classes of black holes without any four-dimensional counterpart. Black rings provide a nice explicit example; in Chapter 6 they were introduced as the result of the bending of a black string into the shape of a circle and spinning it up to balance forces. One can naturally expect that this heuristic construction extends to other black branes. If the worldvolume of a black p-brane could be similarly bent into the shape of a compact hypersurface, for instance that of a torus Tp or a sphere Sp, we would obtain many new geometries and topologies of black hole horizons.

Unfortunately, the techniques that allow one to construct exact black hole solutions in four and five dimensions have not been successfully extended to more dimensions. Still, one may want to hold on to the intuition that a long circular black string, or more generally a smoothly bent black brane, could be obtained as a perturbation of a straight one.

The experience with brane-like objects in other areas of physics suggests that such approximate methods may be efficiently applied to this problem. Consider, for instance, the Abelian Higgs theory and its familiar string-like vortex solutions. These are first obtained in the form of static straight strings, but one would expect that they can also bend and vibrate.

Introduction

The goal of the present chapter is to introduce black holes and branes in supergravity in the simplest possible manner. As a result, we make no attempt to be complete and, in fact, we will intentionally omit many points dear to the hearts of practising string theorists and supergravity experts. In particular, spinors and supersymmetry will make only a passing appearance, in section 11.2.3, which can be skipped if the material seems too technical (though be sure to read the “executive summary” at the end of that section). Instead, we focus on bosonic spacetime solutions and the dynamics of the associated bosonic fields.

Even within this limited scope, our referencing of the original works will be rather sporadic. The interested reader can consult [1] for a more encyclopedic review of branes and black holes in string theory (as of 1997), with numerous references to the original works. We also refer the reader to [2] for a more recent review of black holes in four- and five-dimensional supergravity and for complimentary material in ten and eleven dimensions, to [3] for a partial guide to the literature as of 2004, and to various textbooks [4–9] for further reading.

Our treatment will focus on supergravity theories in ten and eleven dimensions, which are in many ways simpler than their lower-dimensional counterparts and which allow us to make direct contact with string theory.

In this chapter we will continue the exploration of black holes in higher dimensions with an examination of asymptotically flat black holes with spherical horizons, i.e., in d spacetime dimensions the topology of the horizon and of spatial infinity is an Sd-2. In particular, we will focus on a family of vacuum solutions describing spinning black holes, known as Myers–Perry (MP) metrics. In many respects these solutions admit the same remarkable properties as the standard Kerr black hole in four dimensions. However, studying these solutions also begins to provide some insight into the new and unusual features of event horizons in higher dimensions.

These metrics were discovered in 1985 as a part of my thesis work as a Ph.D. student at Princeton [1]. My supervisor,Malcolm Perry, and I had been led to study black holes in higher dimensions, in part by the renewed excitement in superstring theory that had so dramatically emerged in the previous year. We anticipated that examining black holes in d > 4 dimensions would be important in obtaining a full understanding of these theories. I should add that, amongst the subsequent developments, this family of spinning black hole metrics was further generalized to include a cosmological constant as well as Newman, Unti, and Tamburino (NUT) parameters. While I will not have space to discuss these extensions, the interested reader may find a description of the generalized solutions in [2].