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We apply quantum statistics to our quantized versions of Schwarzschild-AdSand Kerr-AdS black holes and also to the quantized globally hyperbolicspacetimes having an asymptotically Euclidean Cauchy hypersurface by firstproving, 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 spatialHamiltonian $H_1$, which has the same eigenvalues but with largermultiplicities. Since the lowest eigenvalue is strictly positive the extensionof $e^{-\beta H_1}$ to the corresponding symmetric Fock space is also of traceclass and we are thus able to define a partition function $Z$, the operatordensity $\rho$, 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 thesource of the dark matter and that the dark energy density is a multiple of theeigenvalue of $\rho$ with respect to the vacuum vector which is $Z^{-1}$.

A partition function for Schwarzschild-AdS and Kerr-AdS black holes and  for quantized globally hyperbolic spacetimes with a negative cosmological  constant