The history of black holes is an evolution both science and imagination. Although the physicist, who coined the term *‘black hole*’, was John A. Wheeler in the 1960s, A. Einstein first predicted the existence of black holes in 1916 with his theory of General Relativity. For many years, black holes have been considered as a pure mathematical construction in General Relativity. The possible existence of black holes has always fascinated and perplexed scientists. In fact, black holes are among the most fascinating predictions of Einstein’s theory of General Relativity. Today, we have indirect evidence for black holes, because they do not emit any electromagnetic radiation. However, Einstein’s theory of General Relativity tells us that they must emit gravitational waves. The detection of gravitational waves from cosmic inflation – if confirmed — may open a new chapter in cosmology. The idea to write this book, and the desire to do so, is an outgrowth of my sustained interest in black hole physics. This book provides students with basic information, and some additional knowledge about the effect of gravity, which is needed to understand black holes properly. It is designed for students who have learned the fundamental principles of astrophysics, as taught to undergraduates in Physics, and are prepared to explore substantial topics in black hole physics.

For this purpose, this book recovers basic topics – such as the equivalence principle, the Jeans instability, and the gravitational collapse – and introduces others – such as the Hawking radiation, the QNMs, and the Penrose process –, making them accessible at undergraduate level.

My aim has been to develop the mathematics in a comprehensive (and rigorous) way, while at the same time keeping to a minimum the prerequisites needed for reading this book. However, a rudimentary knowledge of linear algebra and differential geometry is needed.

I have tried to present the mathematical theory of black holes in a form that might be useful for students who would like to investigate the black hole physics.

I have tried to break down the topics in a way that will help students to understand black hole a bit better…

… *At least I can say that I have tried!*

Valeria Mazzeo

Ps. “The Physics of Black Holes” is just published. You can buy it on Amazon (Kindle edition). I am grateful for your interest and your support. Thank you so much. This book will be available for free this weekend (on 21-22 November). Enjoy your reading!