Educational Materials

Geodesic Equations for the Schwarzschild Metric

William Collins

Author

William Collins

Title

Geodesic Equations for the Schwarzschild Metric

Description

Using MathTensor(Parker&Christensen) the geodesic equations and the constants of the motion for the Schwarzschild metric are developed.

Category

Educational Materials

Keywords

URL

http://www.notebookarchive.org/2018-10-10qi9i1/

DOI

https://notebookarchive.org/2018-10-10qi9i1

Date Added

2018-10-02

Date Last Modified

2018-10-02

File Size

120.96 kilobytes

Supplements

2018-10-10qi9i1_Supplements.zip

Rights

Redistribution rights reserved

Cite this as: William Collins, "Geodesic Equations for the Schwarzschild Metric" from the Notebook Archive (2006), https://notebookarchive.org/2018-10-10qi9i1

Introduction

MathTensor package

SchwarzschildOut file

Coordinates,
α
x
; Differentials,
α
d
; Four Velocity,
α
u
.

Schwarzschild Metric Tensor: MetricS =
g
αβ
= Metricg[-α,-β]

Affine Connection: AffineS =
α
Γ
βγ

Constants of the motion and the coordinate derivitives

Geodesic equation:
2
d
α
x
d
2
τ
+
α
Γ
βγ

β
dx
dτ
γ
dx
dτ
= 0

Riemann curvature tensor

Ricci, Einstein and Weyl tensors