4 research outputs found
Thermal partition function of photons and gravitons in a Rindler wedge
The thermal partition function of photons in any covariant gauge and
gravitons in the harmonic gauge, propagating in a Rindler wedge, are computed
using a local -function regularization approach. The correct Planckian
leading order temperature dependence is obtained in both cases. For the
photons, the existence of a surface term giving a negative contribution to the
entropy is confirmed, as earlier obtained by Kabat, but this term is shown to
be gauge dependent in the four-dimensional case and, therefore is discarded. It
is argued that similar terms could appear dealing with any integer spin in the massless case and in more general manifolds. Our conjecture is
checked in the case of a graviton in the harmonic gauge, where different
surface terms also appear, and physically consistent results arise dropping
these terms. The results are discussed in relation to the quantum corrections
to the black hole entropy.Comment: 29 pages, RevTeX, no figures. Minor errors corrected and a few
comments changed since first submission. To be published on Phys.Rev.
Euclidean Approach to the Entropy for a Scalar Field in Rindler-like Space-Times
The off-shell entropy for a massless scalar field in a D-dimensional
Rindler-like space-time is investigated within the conical Euclidean approach
in the manifold C_\be\times\M^N, C_\be being the 2-dimensional cone, making
use of the zeta-function regularisation. Due to the presence of conical
singularities, it is shown that the relation between the zeta-function and the
heat kernel is non trivial and, as first pointed out by Cheeger, requires a
separation between small and large eigenvalues of the Laplace operator. As a
consequence, in the massless case, the (naive) non existence of the Mellin
transform is by-passed by the Cheeger's analytical continuation of the
zeta-function on manifold with conical singularities. Furthermore, the
continuous spectrum leads to the introduction of smeared traces. In general, it
is pointed out that the presence of the divergences may depend on the smearing
function and they arise in removing the smearing cutoff. With a simple choice
of the smearing function, horizon divergences in the thermodynamical quantities
are recovered and these are similar to the divergences found by means of
off-shell methods like the brick wall model, the optical conformal
transformation techniques or the canonical path integral method.Comment: 17 pages, LaTex. A sign error corrected and few comments adde