REGISTRATION: Upon arrival, Visitors not staying in the ICTP Guest Houses, are kindly requested  to complete registration formalities at the Leonardo Building (Lobby) from 8.30 till 9.30

TRAVEL UNIT (Only for those Visitors receiving daily living allowance/travel reimbursement)  
Only after having completed registration formalities, please go to the Travel Unit, EF, Main     Entrance, Room T17, ground floor, open two days:  Monday and Friday, 08.30 - 12.00 and 13.30 - 14.30  
Please bring with you: badge/identity card or passport/any travel tickets and boarding passes, if reimbursement due.

1.1 History and Spacetime
1.2 Properties (horizon, ergo-sphere, singularity)
1.3 Geodesics

Various approaches to the definition of total mass and energy in general relativity for 
asymptotically flat and asymptotically hyperbolic Riemannian manifolds, and sketch various       elementary proofs of positivity will be described.

These lectures will give a comprehensive introduction to black hole thermodynamics. The basic properties of black holes will be reviewed. The first law of black hole mechanics will be derived, and the notion of black hole entropy will be thereby introduced. The notion of canonical energy will be introduced and used to show that dynamical stability of a black hole is equivalent to its thermodynamic stability. A brief discussion will be given of quantum aspects of black hole thermodynamics.

The Einstein equations imply certain curvature inequalities on spacelike hypersurfaces in spacetime. These inequalities are responsible for successful notions of gravitational mass and energy, and they impose certain local constraints on the 
geometry. In the simplest case this leads to the study of Riemannian manifolds with non-negative scalar curvature. From a physical point of view, notions of quasi-local mass and their positivity, are a reflection of such local constraints. From a geometric point of view comparison with a model space is a basic notion. In recent years both of these directions have been very active, and some of the results that have been obtained will be introduced and compared. In many of these results involving scalar curvature, the theory of stable minimal hypersurfaces plays a key role. In the general case this is replaced by the theory of stable MOTS (marginally outer trapped surfaces). This more general theory and some of its applications will be discussed.

2.1 Formation Scenarios and Gravitational Wave Modeling
2.2 The Semi-Relativistic Approximation
2.3 Kludge Waveforms
2.4 The Self-Force

3.1 The Landau-Lifshitz Formulation of General Relativity
3.2 The Relaxed Einstein Equations
3.3 The DIRE Approach
3.4 Post-Newtonian Waveforms

4.1 Scalar Field Example
4.2 Schwarzschild Perturbation Theory

It will be given an introduction to the cosmic censorship conjectures (both weak and strong) in
classical general relativity and related issues concerning the structure of spacetime singularities. 
The collapse of self gravitating matter under spherical symmetry will provide an elementary setting for understanding many of the issues involved. The course will review basic material (initial value problem, Penrose diagrams) as necessary.

Effective field theories of gravity; the initial value problem for GR; the initial value problem for theories beyond GR

The aim is to give a pedagogical introduction to AdS-CFT emphasising the GR and geometrical aspects of it. Description of how the conjecture relates certain field theories (CFTs) to certain quantum gravitational theories in asymptotically Anti-deSitter (AdS) spacetimes. Discussion about why this is interesting, and why the conjecture should be taken seriously. Focus on the explicit map between the two theories when the gravitational side has classical geometric character. Description of how certain field theory observables are mapped to geometric objects, and how geometry can then constrain and determine their behaviour. Discussion on some interesting open geometric questions which fall in the remit of mathematical GR.

Static black hole uniqueness theorems, including newer developments about higher dimensions, non-vacuum settings, and photon sphere uniqueness.