3 Entanglement Entropy of Non-Degenerate Killing Horizons

 3.1 The geometric setting of black-hole 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
  3.7.1 Curvature of space with a conical singularity
  3.7.2 The heat kernel expansion on a space with a conical singularity
 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
  3.9.1 The Reissner–Nordström black hole
  3.9.2 The dilatonic charged black hole
 3.10 Entanglement Entropy of the Kerr–Newman black hole
  3.10.1 Euclidean geometry of Kerr–Newman black hole
  3.10.2 Extrinsic curvature of the horizon
  3.10.3 Entropy
 3.11 Entanglement entropy as one-loop 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 non-minimal coupling
 3.17 Comments on the entropy of interacting fields

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