Quantum Black Holes Theory and Solved Problems

This manual provides a systematic and accessible introduction to the study of micro black holes, also known as quantum black holes. It is designed as a short reference book for both advanced students and researchers interested in exploring the fundamentals of quantum gravity from a phenomenological perspective.

 

The book is structured in 13 chapters, each combining theoretical development with a collection of solved exercises that reinforce concepts and develop the necessary calculation skills. Fundamental topics covered throughout the text include:

 

1. Introduction: The Planck Scale and the Hierarchy Problem
2. Classical Black Holes in Four Dimensions 
3. Hawking Radiation 
4. Black Holes in Extra Dimensions
5. Production of Micro Black Holes 
6. Evaporation of Micro Black Holes 
7. Black Hole Thermodynamics and Phase Transitions 
8. The Information Paradox and the Page Curve 
9. Primordial Micro Black Holes 
10. Quantum Corrections and the Generalised Uncertainty Principle
11. Black Hole Complementarity and the Firewall Paradox 
12. Kaluza-Klein Modes, Black String Instability, and the Gregory-Laflamme Transition
13. Observational Constraints and Experimental Signatures

Appendix: Selected Problems with Solutions.

As this is the first edition, this version is under review and subject to errors in both form and content. Readers are encouraged to use this material critically and report any corrections or suggestions to the author to help improve future editions.