
Abstract 
1 
Introduction 
2 
EnergyMomentum and Angular Momentum of Matter
Fields 

2.1 
Energymomentum and angularmomentum 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 observables in general relativity 
4 
Tools to
Construct and Analyze QuasiLocal Quantities 

4.1 
The geometry of spacelike
twosurfaces 

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 Nester–Witten 2Form 

8.1 
The Ludvigsen–Vickers construction 

8.2 
The
Dougan–Mason constructions 

8.3 
A specific construction for the Kerr
spacetime 
9 
QuasiLocal Spin Angular Momentum 

9.1 
The Ludvigsen–Vickers
angular momentum 

9.2 
Holomorphic/antiholomorphic spin angular
momenta 

9.3 
A specific construction for the Kerr spacetime 
10 
The
Hamilton–Jacobi Method 

10.1 
The Brown–York expression 

10.2 
Kijowski’s
approach 

10.3 
Epp’s expression 

10.4 
The expression of Liu and Yau 

10.5 
The
expression of Wang 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 
Expressions in 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 general
relativity 

13.6 
Potential applications in cosmology 
14 
Summary: Achievements,
Difficulties, and Open Issues 

14.1 
On the Bartnik mass and Hawking
energy 

14.2 
On the Penrose mass 

14.3 
On the Dougan–Mason energymomenta
and the holomorphic/antiholomorphic spin angular momenta 

14.4 
On
the Brown–York–type expressions 
15 
Acknowledgments 

References 

Footnotes 

Updates 