The Geroch-Held-Penrose Calculus

lt;p>Pedro Bargueño is an associate research professor at the Department of Applied Physics, Alicante University (Spain). His work mainly involves gravitational physics, with emphasis in black holes. He received two Ph. Ds, one from Salamanca University (Spain) in 2010 and other from Complutense University (Madrid, Spain) in 2012. After serving as a Juan de la Cierva researcher at Complutense University (2011-2013), he joined Los Andes University (Colombia), where he got his tenure as an associate professor (2014-2019). He joined the Group of Relativistic Astrophysics at the Department of Applied Physics, Alicante University, in 2019. Prof. Bargueño has authored or coauthored more than eighty publications in internationally recognized journals. He has mentored two postdoctoral researchers and supervised two PhD students, six MSc students and around twenty undergrads.

Ernesto Contreras is a theoretical physicist and professor at the Universidad San Francisco de Quito, Department of Physics, Quito, Ecuador. His wide-ranging interests include: General Relativity, Quantum Field Theory, High Energy Physics, Knot Theory and Quantum Gravity.

Part I. Fundamentals.- Chapter 1. Basics of General Relativity.- Chapter 2. The Newman-Penrose formalism.- Chapter 3. Tools for the GHP formalism.-  Chapter 4. The GHP equations, Bianchi identities and commutator relations.- Chapter 5. The Penrose-Rindler equation.- Part II. Applications.- Chapter 6. Spherically symmetric electro-vacuum solutions: a GHP approach.-  Chapter 7. Self-gravitating spheres and fluid distributions: a GHP approach.-  Chapter 8. Black hole thermodynamics through the GHP calculus.- Part III. Conclusions.- Chapter 9. Conclusions and Outlook.