Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A partition function for Schwarzschild-AdS and Kerr-AdS black holes and
  for quantized globally hyperbolic spacetimes with a negative cosmological
  constant   We apply quantum statistics to our quantized versions of Schwarzschild-AdS
and Kerr-AdS black holes and also to the quantized globally hyperbolic
spacetimes having an asymptotically Euclidean Cauchy hypersurface by first
proving, for the temporal Hamiltonian $H_0$, that $e^{-\beta H_0}$, $\beta>0$,
is of trace class and then, that this result is also valid for the spatial
Hamiltonian $H_1$, which has the same eigenvalues but with larger
multiplicities. Since the lowest eigenvalue is strictly positive the extension
of $e^{-\beta H_1}$ to the corresponding symmetric Fock space is also of trace
class and we are thus able to define a partition function $Z$, the operator
density $\rho$, the entropy $S$, and the average energy $E$. We prove that $S$
and $E$ tend to infinity if the cosmological constant $\Lambda$ tends to $0$
and vanish if $|\Lambda|$ tends to infinity. We also conjecture that $E$ is the
source of the dark matter and that the dark energy density is a multiple of the
eigenvalue of $\rho$ with respect to the vacuum vector which is $Z^{-1}$.

17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
2
The categories of this paper are: math
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org