Containing the latest, groundbreaking discoveries in the field, this text outlines the basics of Einstein’s theory of gravity with a focus on its most important astrophysical consequences, including stellar structures, black holes and the physics of gravitational waves. Blending advanced topics - usually not found in introductory textbooks - with examples, pedagogical boxes, mathematical tools and practical applications of the  theory, this textbook maximises learning opportunities and is ideal for master and graduate students in Physics and Astronomy.

Key features:
• Provides a self-contained and consistent treatment of the subject that does not require advanced previous knowledge of the field.
• Explores the subject with a new focus on gravitational waves and astrophysical relativity, unlike current introductory textbooks.
• Fully up-to-date, containing the latest developments and discoveries in the field.

chapter Chapter 1|16 pages


chapter Chapter 2|46 pages

Elements of differential geometry

chapter Chapter 3|24 pages

Affine connection and parallel transport

chapter Chapter 4|10 pages

The curvature tensor

chapter Chapter 5|12 pages

The stress-energy tensor

chapter Chapter 6|12 pages

The Einstein equations

chapter Chapter 7|14 pages

Einstein’s equations and variational principles

chapter Chapter 8|16 pages


chapter Chapter 9|30 pages

The Schwarzschild solution

chapter Chapter 10|16 pages

Geodesic motion in Schwarzschild’s spacetime

chapter Chapter 11|24 pages

Kinematical tests of General Relativity

chapter Chapter 12|22 pages

Gravitational waves

chapter Chapter 13|24 pages

Gravitational waves in the quadrupole approximation

chapter Chapter 14|32 pages

Gravitational wave sources

chapter Chapter 15|22 pages

Gravitational waves from oscillating black holes

chapter Chapter 16|50 pages

Compact stars

chapter Chapter 17|24 pages

The far-field limit of an isolated, stationary object

chapter Chapter 18|26 pages

The Kerr solution

chapter Chapter 19|26 pages

Geodesic motion in Kerr’s spacetime

chapter Chapter 20|14 pages

Black hole thermodynamics