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Course: Introduction to Galaxies and Large Scale Structure (Astronomy 2)

Semester: Winter semester 2026/2027

Institution: Goethe-Universität Frankfurt

Lecturers: Tanja Heftrich & Laura Sagunski

Textbook: Carroll & Ostlie, An Introduction to Modern Astrophysics (2nd ed.)

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Chapter 1 · Relativistic Foundations for Astrophysics

22 October 2026 · Carroll & Ostlie, Kap. 17

Learning Objectives

• Understand the key predictions of special relativity relevant to astrophysics
• Apply redshift and time dilation to astrophysical observations
• Describe light deflection in a gravitational field
• Identify how relativistic effects shape compact objects and AGN

1.1 Special Relativity – Key Concepts

Lorentz factor:

$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$

Time dilation:

$\Delta t = \gamma \, \Delta t_0$

Length contraction:

$L = \frac{L_0}{\gamma}$

1.2 Relativistic Redshift

Doppler redshift (relativistic):

$z + 1 = \sqrt{\frac{1 + v/c}{1 - v/c}}$