## Curvature coupling to spin

Kepler discovered empirically that for each planet, its radius vector traces area increasing linearly with time. Newton realized that the projection of this rate of change on each of the coordinate surfaces xaxb defines a vector, the specific angular momentum. While test particles by definition move along geodesics, spinning objects bring along angular momentum and, by Kepler, a rate of change of surface area. They hereby couple to curvature on the basis of dimensionality. In geometric units,...

## True GRB supernova event rate

The observed redshift distribution of Table 11.1 can be contrasted with the underlying redshift distribution of the cosmological star-formation rate. The latter provides the redshift distribution of the true GRB event rate, up to an overall scaling factor. This comparison can be used to infer the orientation averaged GRB-luminosity function. To leading order, the intrinsic GRB-luminosity function can be assumed to be redshift-independent, neglecting any intrinsic cosmological evolution of...

## Stability diagram

Given the potential (10.30-10.31), the boundary conditions (10.35) define an eigenvalue problem in m' for wave-modes of mode number m in tori of arbitrary width. Suppose we choose an outer torus boundary x+ b a, leaving the associated inner boundary x determined by numerical root-finding of He(x ) 0 as a function of q. We can solve (10.35) simultaneously for (m',A) at x x for a given value of q. Eigenvalues m' are distinct and real, or appear in pairs of complex conjugates. Hence, double zeros...

## Introduction

Observations of gravitational radiation from black holes and neutron stars promise to dramatically transform our view of the universe. This new topic of gravitational-wave astronomy will be initiated with detections by recently commissioned gravitational-wave detectors. These are notably the Laser Interferometric Gravitational wave Observatory LIGO (US), Virgo (Europe), TAMA (Japan) and GEO (Germany), and various bar detectors in the US and Europe. This book is intended for graduate students...

## Phenomenology of GRB supernovae

Since you are now studying geometry and trigonometry, I will give you a problem. A ship sails the ocean. It left Boston with a cargo of wool. It grosses 200 tons. It is bound for Le Havre. The mainmast is broken, the cabin boy is on deck, there are 12 passengers aboard, the wind is blowing East-North-East, the clock points to a quarter past three in the afternoon. It is the month of May. How old is the captain Gustave Flaubert (1821-80), in a letter to his sister Cavoline, 1843. Discovery of...

## Gravitational Radiation Luminous Black Holes and Gamma Ray Burst Supernovae

Black holes and gravitational radiation are two of the most dramatic predictions of general relativity. The quest for rotating black holes - discovered by Roy P. Kerr as exact solutions to the Einstein equations - is one of the most exciting challenges currently facing physicists and astronomers. Gravitational Radiation, Luminous Black Holes and Gamma-ray Burst Supernovae takes the reader through the theory of gravitational radiation and rotating black holes, and the phenomenology of GRB...

## LIGO and Virgo detectors

LIGO consists of two 4 km detectors, located at Livingston, Louisiana, and Hanford, Washington (Figure 16.1). The Livingston site houses a single laser beam interferometer (LL1), while the Hanford site houses two laser beam interferometers (LH1 and LH2). Virgo consists of a single 3 km detector in Cascina (near Pisa), Italy. TAMA in Mitaka, Tokyo, and GEO at Hanover are detectors of comparable design, except their arm lengths are 300 and 600 m, respectively. Gingin at Perth is an 80 m test...