astrophysics

Introduction to relativistic astrophysics and cosmology through Maple

Vladimir L. Kalashnikov ,

Belarussian Polytechnical Academy,

www.geocities.com/optomaplev

Abstract: The basics of the relativistic astrophysics including the celestial mechanics in weak field, black holes and cosmological models are illustrated and analyzed by means of Maple 6

Application Areas/Subjects: Science, Astrophysics, General Relativity, Tensor Analysis, Differential geometry, Differential equations

Introduction

A rapid progress of the observational astrophysics, which resulted from the active use of orbital telescopes, essentially intensifies the astrophysical researches at the last decade and allows to choose the more definite directions of further investigations. At the same time, the development of high-performance computers advances in the numerical astrophysics and cosmology. Against a background of these achievements, there is the renascence of analytical and semi-analytical approaches, which is induced by new generation of high-efficient computer algebra systems.

Here we present the pedagogical introduction to relativistic astrophysics and cosmology, which is based on computational and graphical resources of Maple 6. The pedagogical aims define the use only standard functions despite the fact that there are the powerful General Relativity (GR) oriented extensions like GRTensor. The knowledge of basics of GR and differential geometry is supposed. It should be noted, that our choice of metric signature (+2) governs the definitions of Lagrangians and energy-momentum tensors.

The computations in this worksheet take about of 6 min of CPU time (PIII-500) and 9 Mb of memory.

Contents:

1. Relativistic celestial mechanics in weak gravitational field

1.1. Introduction

1.2. Schwarzschild metric

1.3. Equation of motion

1.4. Light ray deflection

1.5. Planet's perihelion motion

1.6. Conclusion

2. Relativistic stars and black holes

2.1. Introduction

2.2. Geometric units