
Abstract 
1 
Introduction 
2 
Entanglement Entropy in Minkowski
Spacetime 

2.1 
Definition 

2.2 
Shortdistance correlations 

2.3 
Thermal
entropy 

2.4 
Entropy of a system of finite size at finite temperature 

2.5 
Entropy
in (1+1)dimensional spacetime 

2.6 
The Euclidean path integral representation
and the replica method 

2.7 
Uniqueness of analytic continuation 

2.8 
Heat kernel
and the Sommerfeld formula 

2.9 
An explicit calculation 

2.10 
Entropy of massive
fields 

2.11 
An expression in terms of the determinant of the Laplacian on the
surface 

2.12 
Entropy in theories with a modified propagator 

2.13 
Entanglement
entropy in nonLorentz invariant theories 

2.14 
Arbitrary surface in curved
spacetime: general structure of UV divergences 
3 
Entanglement Entropy of
NonDegenerate Killing Horizons 

3.1 
The geometric setting of blackhole
spacetimes 

3.2 
Extrinsic curvature of horizon, horizon as a minimal
surface 

3.3 
The wave function of a black hole 

3.4 
Reduced density matrix
and entropy 

3.5 
The role of the rotational symmetry 

3.6 
Thermality of
the reduced density matrix of a Killing horizon 

3.7 
Useful mathematical
tools 

3.8 
General formula for entropy in the replica method, relation
to the Wald entropy 

3.9 
UV divergences of entanglement entropy for
a scalar field 

3.10 
Entanglement Entropy of the Kerr–Newman black
hole 

3.11 
Entanglement entropy as oneloop quantum correction 

3.12 
The
statement on the renormalization of the entropy 

3.13 
Renormalization in
theories with a modified propagator 

3.14 
Area law: generalization to higher spin
fields 

3.15 
Renormalization of entropy due to fields of different spin 

3.16 
The
puzzle of nonminimal coupling 

3.17 
Comments on the entropy of interacting
fields 
4 
Other Related Methods 

4.1 
Euclidean path integral and thermodynamic
entropy 

4.2 
’t Hooft’s brickwall model 
5 
Some Particular Cases 

5.1 
Entropy of
a 2D black hole 

5.2 
Entropy of 3D Banados–Teitelboim–Zanelli (BTZ) black
hole 

5.3 
Entropy of ddimensional extreme black holes 
6 
Logarithmic Term
in the Entropy of Generic Conformal Field Theory 

6.1 
Logarithmic terms in
4dimensional conformal field theory 

6.2 
Logarithmic terms in 6dimensional
conformal field theory 

6.3 
Why might logarithmic terms in the entropy be
interesting? 
7 
A Holographic Description of the Entanglement Entropy of
Black Holes 

7.1 
Holographic proposal for entanglement entropy 

7.2 
Proposals
for the holographic entanglement entropy of black holes 

7.3 
The holographic
entanglement entropy of 2D black holes 

7.4 
Holographic entanglement
entropy of higher dimensional black holes 
8 
Can Entanglement Entropy
Explain the Bekenstein–Hawking Entropy of Black Holes? 

8.1 
Problems
of interpretation of the Bekenstein–Hawking entropy as entanglement
entropy 

8.2 
Entanglement entropy in induced gravity 

8.3 
Entropy in braneworld
scenario 

8.4 
Gravity cutoff 

8.5 
Kaluza–Klein example 
9 
Other Directions
of Research 

9.1 
Entanglement entropy in string theory 

9.2 
Entanglement
entropy in loop quantum gravity 

9.3 
Entropy in noncommutative theories
and in models with minimal length 

9.4 
Transplanckian physics and
entanglement entropy 

9.5 
Entropy of more general states 

9.6 
Nonunitary
time evolution 
10 
Concluding remarks 
11 
Acknowledgments 

References 

Footnotes 

Tables 