Scalar Fields In Rindler Spacetime And The Near Horizon Black Hole Entropy

Abstract

One constructs the Feynman propagator for real scalar fields in both Minkowski and Rindler spacetimes. This is done using the Poincaré invariant vacuum state in Minkowski space and a thermal state in the Rindler case. One shows that both results are a function of the invariant distance, and therefore onecan beobtained from theother bya coordinatetransformation. Since thenear horizon limit of a Schwarzschild black hole has the same geometry as a Rindler observer, the Rindler frame is used to study the near horizon limit. The observer at constant acceleration in the Rindler frame is similar to an observer of constant radial distance to the black hole horizon and has no access to information inside the horizon. One constructs the reduced density matrix by tracing out the degrees of freedom inside the black hole. For a Rindler observer, this corresponds to tracing out the left Rindler wedge. One also constructs a projected Statistical function in order to express the reduced density matrix in terms of spacetime coordinates. One uses these calculations to make important steps towards calculating Remyi entropy in the near horizon limit of a black hole, however this calculation is not yet completed.