1st Edition

General Relativity and its Applications Black Holes, Compact Stars and Gravitational Waves

    494 Pages 92 B/W Illustrations
    by CRC Press

    494 Pages 92 B/W Illustrations
    by CRC Press

    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.

    1 Introduction

    2 Elements of Differential Geometry

    3 Affine Connection and Parallel Transport

    4 The Curvature Tensor

    5 The Stressenergy Tensor

    6 The Einstein Equations

    7 Einstein’s Equations and Variational Principles

    8 Symmetries

    9 The Schwarzschild Spacetime

    10 Geodesic Motion in Schwarzschild’s Spacetime

    11 Kinematical Tests of General Relativity

    12 Gravitational Waves.

    13 Gravitational Waves in the Quadrupole Approximation

    14 Gravitational Wave Sources

    15 Gravitational Waves from Oscillating Black Holes

    16 Compact Stars

    17 The Farfield Limit of an Isolated, Stationary Object

    18 The Kerr Solution

    19 Geodesic Motion in Kerr’s Spacetime

    20 Black Hole Thermodynamics


    Valeria Ferrari is Professor of Theoretical Physics at Sapienza, University of Rome (Italy). She performed research in the fields of General Relativity, with special focus on black hole and stellar perturbations, and gravitational wave sources. She has published over 125 papers in international journals, given over 100 invited talks, in addition to coordinating international research projects, the Virgo-Ego Scientific forum, and serving as part of several journal Editorial Boards. She co-authored textbooks in Physics for undergraduate students.

    Leonardo Gualtieri is Associate Professor at Sapienza, University of Rome (Italy). His main research interests are gravitational theory and gravitational waves, with special focus on gravitational wave sources as probes of fundamental physics. He has published over 100 papers in international journals and given over 30 invited talks, in addition to coordinating TEONGRAV, the INFN network of Italian groups studying gravitational wave sources.

    Paolo Pani is Associate Professor of Theoretical Physics at Sapienza, University of Rome (Italy) and Junior Fellow at Sapienza’s School for Advanced Studies. He coordinates the DarkGRA project "Unveiling the dark universe with gravitational waves" funded by the European Research Council (ERC). He received the SIGRAV Prize and the Outstanding Referee award from the American Physics Society. He is co-author of the book “Superradiance” and of over 100 scientific publications on black-hole physics and gravitational-wave phenomenology, and their connections to fundamental physics.

    "This textbook introduces the basics of Einstein’s theory of general relativity and of its astrophysical applications. The first half of the book is dedicated to a pedagogical, self-contained treatment of differential geometry. The second half deals with the structure and stability of compact objects (black holes and neutron stars), the classical tests of general relativity, and gravitational waves. The book is an excellent starting point for students interested in gravitational wave astronomy and relativistic astrophysics, introducing the reader to exciting recent developments, such as the first LIGO/Virgo observations of gravitational waves from the mergers of black holes and neutron stars. The choice of material is well-balanced and it includes important topics which are not usually covered in detail in introductory textbooks, such as black hole perturbation theory and geodesic motion in the Kerr spacetime."

    Dr. Emanuele Berti, Professor, Johns Hopkins University, USA

    "At a time when gravitational physics is at the center of many new scientific discoveries, there are many textbooks initiating students to the beauty of General Relativity. Yet, it is hard to find a book that manages so admirably to combine the introductory material with the more advanced topics. Written with skilled perspective of experts who have been teaching these topics for many years, the book provides the novice with a systematic and complete picture of what is arguably the most fascinating theory in physics. At the same time, the book does also offer a detailed account of more advanced and modern topics in relativistic astrophysics such as black holes, compact stars, and gravitational waves. The result is a self-contained and invaluable source for anyone interested in General Relativity. Highly recommended for students and teachers alike."

    Prof. Luciano Rezzolla, Institute for Theoretical Physcis, Frankfurt