Jason Bates

Noise kernel for a quantum field in Schwarzschild spacetime under the Gaussian approximation

A method is given to compute the noise kernel, defined as the symmetrized connected 2-point function of the stress tensor, for the conformally invariant scalar field in the Hartle-Hawking state in Schwarzschild spacetime. We consider the two points to be separated in a timelike or a spacelike direction and use a Gaussian approximation of the same type as that used by Page to compute an approximate form of the stress tensor for this field in Schwarzschild spacetime. Several components of the noise kernel have been explicitly computed and the expression for one of them is displayed.

Noise kernel near the horizon of de Sitter space

The symmetric two point correlation function of the stress–energy tensor, also known as the noise kernel, for the conformally invariant scalar field is computed in the static region of de Sitter space in terms of the usual static coordinates. Its behavior near the cosmological horizon is investigated. The exact expression is then compared to an approximate expression derived using a quasi-local expansion in order to test the validity of that expansion in a static spherically symmetric spacetime containing a horizon. This gives insight into the likely range of validity of the quasi-local expansion for the noise kernel in Schwarzschild spacetime which has been previously computed.