Compact objects in astrophysics

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Compact objects are a crucial focus in contemporary astronomical research. Supermassive black holes are key to understanding galaxy formation in the early Universe, while old white dwarfs serve as benchmarks for determining the Universe's age. Mergers of neutron stars and black holes generate intense gravitational waves, which will soon be measured by upcoming detectors. This work provides a thorough introduction and current overview of the physical processes governing these objects, encompassing everything from foundational concepts to the latest findings and observations. It begins with a classification of compact objects, followed by essential principles of general relativity. The author delves into the physics and observations of white dwarfs and neutron stars, presenting the latest equations of state for neutron star matter, and explores the gravitational fields of rapidly rotating compact objects and black holes, including ray tracing and magnetospheres. Additionally, the text covers gravitational waves and new insights into accretion processes through magnetorotational instability in accretion disks. Utilizing a 3+1 split approach to Einstein's equations and relativistic hydrodynamics, each chapter includes problems and solutions to enhance comprehension. This advanced textbook will be valuable for both students and researchers in the field of astrophysics.