Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem

We study gravitational perturbations of Schwarzschild spacetime by solving a hyperboloidal initial value problem for the Bardeen-Press equation. Compactification along hyperboloidal surfaces in a scri-fixing gauge allows us to have access to the gravitational waveform at null infinity in a general setup. We argue that this hyperboloidal approach leads to a more accurate and efficient calculation of the radiation signal than the common approach where a timelike outer boundary is introduced. The method can be generalized to study perturbations of Kerr spacetime using the Teukolsky equation.Comment: 14 pages, 9 figure

Numerical Relativity: A review

Computer simulations are enabling researchers to investigate systems which are extremely difficult to handle analytically. In the particular case of General Relativity, numerical models have proved extremely valuable for investigations of strong field scenarios and been crucial to reveal unexpected phenomena. Considerable efforts are being spent to simulate astrophysically relevant simulations, understand different aspects of the theory and even provide insights in the search for a quantum theory of gravity. In the present article I review the present status of the field of Numerical Relativity, describe the techniques most commonly used and discuss open problems and (some) future prospects.Comment: 2 References added; 1 corrected. 67 pages. To appear in Classical and Quantum Gravity. (uses iopart.cls

History of climate modeling

The history of climate modeling begins with conceptual models, followed in the 19th century by mathematical models of energy balance and radiative transfer, as well as simple analog models. Since the 1950s, the principal tools of climate science have been computer simulation models of the global general circulation. From the 1990s to the present, a trend toward increasingly comprehensive coupled models of the entire climate system has dominated the field. Climate model evaluation and intercomparison is changing modeling into a more standardized, modular process, presenting the potential for unifying research and operational aspects of climate science. WIREs Clim Change 2011 2 128–139 DOI: 10.1002/wcc.95 For further resources related to this article, please visit the WIREs websitePeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79438/1/95_ftp.pd

Stability Analysis of Difference Methods for Parabolic Initial Value Problems

Abstract A decomposition of the numerical solution can be defined by the normal mode representation, that generalizes further the spatial eigenmode decomposition of the von Neumann analysis by taking into account the boundary conditions which are not periodic. In this paper we present some new theoretical results on normal mode analysis for a linear and parabolic initial value problem. Furthermore we suggest an algorithm for the calculation of stability regions based on the normal mode theory