**Advanced course in general relativity **

*Sudipta Sarkar, IIT Gandhinagar*

Riemann, Ricci and Einstein Tensor, the Einstein field equation, Energy-Momentum tensor, Spherically symmetric asymptotically flat vacuum solution, The Schwarzschild Geometry, Eddington-Finkelstein coordinates. Timelike geodesics of Schwarzschild Geometry. Effective potential and nature of timelike obits. Null geodesics, Photon Sphere and shadow of Schwarzschild black hole. Introduction to Kerr solution. Dragging of Inertial Frames & ZAMO, Ergosphere, and the event horizon, Penrose Process. Linearized Einstein Equation. Gauge freedoms, Gravitational radiation, Energy loss by gravitation wave emission.

**References: **

- Sean Carrol,
*Lectures notes on general relativity*(gr-qc/9712019) - Eric Poisson,
*A Relativist’s Toolkit*(Cambridge University Press) - S Chandrasekhar,
*The Mathematical Theory of Black Holes*(Oxford)

**Primordial black holes and gravitational wave astronomy**

*Teruaki Suyama, Tokyo Institute of Technology*

Introduction: Why primordial black holes (PBHs) are important in cosmology. Formation of PBHs: Threshold of the PBH formation, abundance of PBHs, generating seeds of PBH from inflation. Observational constraints on the abundance of PBHs. PBHs as sources of gravitational waves:Mechanism of the PBH binary formation, merger rate, tests of the PBH hypothesis by the future GW observations

**References: **

- M. Sasaki et al, Class. Quant. Grav. 35 (2018), 063001 [arXiv:1801.05235]

**Gravitational radiation from post-Newtonian sources and inspiralling compact binaries**

*Luc Blanchet, Institute of Astrophysics of Paris*

Quadrupole formula, effect of GWs on matter, problem of the generation of GWs; and more advanced ones: post-Newtonian methods, the multipolar post-Minkowskian expansion, problem of motion, applications to compact binary systems, Fokker Lagrangian and Hamiltonian, effects of spins and internal structure.

**References: **

- L. Blanchet, Living Rev. Relativ. (2014) 17: 2. https://doi.org/10.12942/lrr-2014-2

**Preparatory material: **

- Kip S. Thorne, "Gravitational Radiation," in
*Three Hundred Years of Gravitation*, ed. S.W. Hawking and W. Israel (Cambridge University Press, 1987), pp. 330-458. - Michele Maggiore,
*Gravitational Waves: Volume 1: Theory and Experiments*(Cambridge University Press) - Misner, Thorne, Wheeler,
*Gravitation*(Princeton University Press) [Chapters 18 (weak gravitational fields), 35 (propagation of GWs), 36 (generation of GWs) and Exercises: 35.1, 35.2, 35.15, 36.2, 36.5, 36.6, 36.8, 36.9]

**Self-force and radiation reaction in general relativity**

*Adam Pound, University of Southampton*

Overview of extreme mass ratio inspirals. Perturbation theory in GR. Orbital dynamics in Schwarzschild and Kerr spacetime. The adiabatic approximation. Foundations of self-force theory: matched asymptotic expansions. Practical methods: puncture scheme and mode-sum regularization.

**References: **

- Leor Barack, Adam Pound,
*Self-force and radiation reaction in general relativity*, arXiv:1805.10385 [gr-qc].