Quasinormal modes are eigenmodes of dissipative systems. Perturbations of classical gravitational backgrounds involving black holes or branes naturally lead to quasinormal modes. The analysis and classification of the quasinormal spectra require solving non-Hermitian eigenvalue problems for the associated linear differential equations. Within the recently developed gauge-gravity duality, these modes serve as an important tool for determining the near-equilibrium properties of strongly coupled quantum field theories, in particular their transport coefficients, such as viscosity, conductivity and diffusion constants. In astrophysics, the detection of quasinormal modes in gravitational wave experiments would allow precise measurements of the mass and spin of black holes as well as new tests of general relativity. This review is meant as an introduction to the subject, with a focus on the recent developments in the field.

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Quasinormal modes of black holes and black branes

The WMAP mission has produced sky maps from seven years of observations at L2. We present the angular power spectra derived from the seven-year maps and discuss the cosmological conclusions that can be inferred from WMAP data alone. With the seven-year data, the temperature (TT) spectrum measurement has a signal-to-noise ratio per multipole that exceeds unity for l 2.7(95%CL). Also, using WMAP data alone, the primordial helium mass fraction is found to be Y He = 0.28+0.14 ?0.15, and with data from higher-resolution cosmic microwave background experiments included, we now establish the existence of pre-stellar helium at >3?. These new WMAP measurements provide important tests of big bang cosmology.

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Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Power Spectra and WMAP-Derived Parameters

Separable wave equations with source terms are presented for electromagnetic and gravitational perturbations of an uncharged, rotating black hole. These equations describe the radiative field completely, and also part of the nonradiative field. Nontrivial, source-free, stationary perturbations are shown not to exist. The barrier integral governing synchrotron radiation from particles in circular orbits is shown to be the same as for scalar radiation. Future applications (stability of rotating black holes, "spin-down," superradiant scattering, floating orbits) are outlined.

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Rotating black holes: separable wave equations for gravitational and electromagnetic perturbations.

A formalism is presented for the treatment of space‐times, which is intermediate between a fully covariant approach and the spin‐coefficient method of Newman and Penrose. With the present formalism, a pair of null directions only, rather than an entire null tetrad, is singled out at each point. The concept of a spin‐ and boost‐weighted quantity is defined, the formalism operating entirely with such quantities. This entails the introduction of modified differentiation operators, one of which represents a natural extension of the definition of the operator ð which had been introduced earlier by Newman and Penrose. For suitable problems, the present formalism should lead to considerable simplifications over that achieved by the standard spin‐coefficient method.

A space‐time calculus based on pairs of null directions

The cosmic microwave background (CMB) is the radiation left over from the Big Bang Recent analysis of the fluctuations in this radiation has given us valuable insights into our Universe and its parameters Examining the theory of CMB and recent developments, this textbook starts with a brief introduction to modern cosmology and its main successes, followed by a thorough derivation of cosmological perturbation theory It then explores the generation of initial fluctuations by inflation The Boltzmann equation governs the evolution of CMB anisotropies and polarization is derived using the total angular momentum method Cosmological parameter estimation and the lensing of CMB fluctuations and spectral distortions are also discussed This textbook is the first to contain a full derivation of the theory of CMB anisotropies and polarization Ideal for graduate students and researchers in this field, it includes end-of-chapter exercises, and solutions to selected exercises are provided

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The Cosmic Microwave Background

Recent work on the Bondi‐Metzner‐Sachs group introduced a class of functions sYlm (θ, φ) defined on the sphere and a related differential operator ð. In this paper the sYlm are related to the representation matrices of the rotation group R 3 and the properties of ð are derived from its relationship to an angular‐momentum raising operator. The relationship of the sTlm (θ, φ) to the spherical harmonics of R 4 is also indicated. Finally using the relationship of the Lorentz group to the conformal group of the sphere, the behavior of the sTlm under this latter group is shown to realize a representation of the Lorentz group.

A. J. Macfarlane

Papers

Spin‐s Spherical Harmonics and ð