The Kerr metric

This review describes the events leading up to the discovery of the Kerr metric in 1963 and the enormous impact the discovery has had in the subsequent 50 years. The review discusses the Penrose process, the four laws of black hole mechanics, uniqueness of the solution, and the no-hair theorems. It also includes Kerr perturbation theory and its application to black hole stability and quasi-normal modes. The Kerr metric's importance in the astrophysics of quasars and accreting stellar-mass black hole systems is detailed. A theme of the review is the 'miraculous' nature of the solution, both in describing in a simple analytic formula the most general rotating black hole, and in having unexpected mathematical properties that make many calculations tractable. Also included is a pedagogical derivation of the solution suitable for a first course in general relativity

Numerical relativity: maximizing the scientific payoff from gravitational wave detection

For many of the proposed LIGO sources, we are currently unable to produce reliable theoretical waveforms or event rates. Usually the difficulty is in performing numerical simulations. These problems seriously undermine our ability to extract science from LIGO, or in some cases even to detect sources at all. We describe two sources where these problems are present: the merger of a binary black hole system, and a newborn neutron star unstable to r-modes. We explain the origin of the difficulties, and how they might be overcome

The Kerr metric

This review describes the events leading up to the discovery of the Kerr metric in 1963 and the enormous impact the discovery has had in the subsequent 50 years. The review discusses the Penrose process, the four laws of black hole mechanics, uniqueness of the solution, and the no-hair theorems. It also includes Kerr perturbation theory and its application to black hole stability and quasi-normal modes. The Kerr metric's importance in the astrophysics of quasars and accreting stellar-mass black hole systems is detailed. A theme of the review is the 'miraculous' nature of the solution, both in describing in a simple analytic formula the most general rotating black hole, and in having unexpected mathematical properties that make many calculations tractable. Also included is a pedagogical derivation of the solution suitable for a first course in general relativity

Short note on the mass matrix for Gauss-Lobatto grid points

The mass matrix for Gauss-Lobatto grid points is usually approximated by Gauss-Lobatto quadrature because this leads to a diagonal matrix that is easy to invert. The exact mass matrix and its inverse are full. We show that the exact mass matrix \emph{and} its inverse differ from the approximate diagonal ones by a simple rank-1 update (outer product). They can thus be applied to an arbitrary vector in $O(N)$ operations instead of $O(N^2)$

The explanation of the Trouton–Noble experiment revisited

One class of explanations of the null result of the Trouton–Noble experiment uses the "standard" definitions of electromagnetic energy and momentum but is quite complicated. Another class is much simpler but appears to require new definitions of electromagnetic energy and momentum. We reconcile the two sets of explanations and show that they are both physically correct. We use the same arguments that have been used in discussions of the famous "4/3" factor in the electromagnetic mass of the classical electron

A Nonlinear Coupling Network to Simulate the Development of the r-mode Instablility in Neutron Stars I. Construction

R-modes of a rotating neutron star are unstable because of the emission of gravitational radiation. We explore the saturation amplitudes of these modes determined by nonlinear mode-mode coupling. Modelling the star as incompressible allows the analytic computation of the coupling coefficients. All couplings up to n=30 are obtained, and analytic values for the shear damping and mode normalization are presented. In a subsequent paper we perform numerical simulations of a large set of coupled modes.Comment: 15 pages 3 figure