Explore advanced topics in general relativity and gravitational physics through this comprehensive school program from ICTP Mathematics. Delve into the fundamental concepts of mass and energy in general relativity, examining how these quantities behave in curved spacetime. Study the geometric properties of spacetime and their implications for understanding gravitational phenomena. Investigate black hole physics extensively, covering Kerr black holes, black hole thermodynamics across multiple detailed lectures, black hole perturbation theory, and stability analysis using both global and microlocal approaches. Learn about binary systems and gravitational waves, including extreme mass-ratio inspirals and comparable-mass binaries that produce detectable gravitational wave signals. Examine static black hole uniqueness theorems that establish fundamental constraints on black hole solutions. Explore the cosmic censorship conjectures, which address fundamental questions about singularities and the predictability of general relativity. Discover cosmological models with non-zero cosmological constant and their asymptotic behavior. Gain insights into the AdS-CFT correspondence from a general relativity perspective, connecting gravitational physics to quantum field theory through this important duality. Master both theoretical foundations and cutting-edge research topics in modern gravitational physics through systematic lecture series covering each major area in depth.

Syllabus

Black Holes, Binary Systems, and Gravitational Waves - 1. Kerr Black Hole
Introduction to mass and energy in general relativity - Lecture 1
Black Hole Thermodynamics - Lecture 1
Introduction to mass and energy in general relativity - Lecture 2
Some geometric properties of spacetime - Lecture 1
Black Holes, Binary Systems, and Gravitational Waves - 2. Extreme mass-ratio inspirals
Introduction to mass and energy in general relativity - Lecture 3
Some geometric properties of spacetime - Lecture 2
Black Hole Thermodynamics - Lecture 2
Black Holes, Binary Systems, and Gravitational Waves - 3. Comparable-Mass Binaries
Introduction to mass and energy in general relativity - Lecture 4
Black Holes, Binary Systems, and Gravitational Waves - 4. Black Hole Perturbation Theory
Some geometric properties of spacetime - Lecture 3
Black Hole Thermodynamics - Lecture 3
Black Hole Thermodynamics - Lecture 4
Black hole stability: global and microlocal analysis aspects
Some geometric properties of spacetime - Lecture 4
The cosmic censorship conjectures in general relativity - Lecture 1
Asymptotic Behaviour of Cosmologies with Lambda Major of 0
Introduction to the AdS-CFT conjecture from a GR perspective - Lecture 1
Static black hole uniqueness theorems - Lecture 1
Introduction to the AdS-CFT conjecture from a GR perspective - Lecture 2
The cosmic censorship conjectures in general relativity - Lecture 2
Introduction to the AdS-CFT conjecture from a GR perspective - Lecture 3
Static black hole uniqueness theorems - Lecture 2
The cosmic censorship conjectures in general relativity - Lecture 3
Static black hole uniqueness theorems - Lecture 3
Introduction to the AdS-CFT conjecture from a GR perspective - Lecture 4
Static black hole uniqueness theorems - Lecture 4
The cosmic censorship conjectures in general relativity - Lecture 4