
Abstract 
1 
Introduction 
2 
EnergyMomentum and Angular Momentum of
Matter Fields 

2.1 
Energymomentum and angular momentum density of
matter fields 

2.2 
Quasilocal energymomentum and angular momentum of
the matter fields 
3 
On the EnergyMomentum and Angular Momentum of
Gravitating Systems 

3.1 
On the gravitational energymomentum and angular
momentum density: The difficulties 

3.2 
On the global energymomentum and
angular momentum of gravitating systems: The successes 

3.3 
The necessity
of quasilocality for the observables in general relativity 
4 
Tools to Construct
and Analyze the QuasiLocal Quantities 

4.1 
The geometry of spacelike
2surfaces 

4.2 
Standard situations to evaluate the quasilocal quantities 

4.3 
On
lists of criteria of reasonableness of the quasilocal quantities 
5 
The Bartnik
Mass and its Modifications 

5.1 
The Bartnik mass 

5.2 
Bray’s modifications 
6 
The
Hawking Energy and its Modifications 

6.1 
The Hawking energy 

6.2 
The Geroch
energy 

6.3 
The Hayward energy 
7 
Penrose’s QuasiLocal EnergyMomentum
and Angular Momentum 

7.1 
Motivations 

7.2 
The original construction for
curved spacetimes 

7.3 
The modified constructions 
8 
Approaches Based on
the NesterWitten 2Form 

8.1 
The LudvigsenVickers construction 

8.2 
The
DouganMason constructions 

8.3 
A specific construction for the Kerr
spacetime 
9 
QuasiLocal SpinAngular Momentum 

9.1 
The LudvigsenVickers
angular momentum 

9.2 
Holomorphic/antiholomorphic spinangular
momenta 

9.3 
A specific construction for the Kerr spacetime 
10 
The
HamiltonJacobi Method 

10.1 
The BrownYork expression 

10.2 
Kijowski’s
approach 

10.3 
The expression of Epp 

10.4 
The expression of Liu
and Yau 
11 
Towards a Full Hamiltonian Approach 

11.1 
The 3 + 1
approaches 

11.2 
Approaches based on the doublenull foliations 

11.3 
The
covariant approach 
12 
Constructions for Special Spacetimes 

12.1 
The
Komar integral for spacetimes with Killing vectors 

12.2 
The effective mass
of Kulkarni, Chellathurai, and Dadhich for the Kerr spacetime 

12.3 
The
KatzLyndenBellIsrael energy for static spacetimes 
13 
Applications in
General Relativity 

13.1 
Calculation of tidal heating 

13.2 
Geometric inequalities
for black holes 

13.3 
Quasilocal laws of black hole dynamics 

13.4 
Entropy
bounds 

13.5 
Quasilocal radiative modes of GR 
14 
Summary: Achievements,
Difficulties, and Open Issues 

14.1 
On the Bartnik mass and the Hawking
energy 

14.2 
On the Penrose mass 

14.3 
On the DouganMason energymomenta
and the holomorphic/antiholomorphic spin angular momenta 

14.4 
On
the BrownYorktype expressions 
15 
Acknowledgments 

References 

Footnotes 

Updates 