Thermo field dynamics on BTZ spacetime

A thin dust shell contracting from infinity to near its gravitational radius r + , in a spacetime AdS 3 is analyzed; its equation of motion is determined and the solution R ( t ) as seen by a FIDO observer is estimated. It is concluded that this Shell's exterior looks like a BTZ black hole with similar properties. Based on the Thermo Field Dynamics technique, a scalar field Φ in the proximity of a non-rotating BTZ (2 + 1) black hole is studied. From the corresponding Killing-Boulware 0 KB * and Hartle-Hawking 0 HH * vacuum states, the associated Wightman function W x , x ′ HH * − W x , x ′ KB * is determined and based on it, the time component of the momentum-energy tensor of the system ∂ 0 ∂ 0 ′ W HH * − W KB * ( x , x ′ ) ≈ T 00 ( x , x ′ ) = σ ( r ) is calculated. Which allows establishing the origin and location of the degrees of freedom responsible for the entropy that describes a source for the Bekenstein-Hawking S BH entropy. The thermal environment described by this model manifests itself with a well-defined and concentrated energy density near the event horizon, according to a FIDO observer.