Casimir/squeezed vacuum breaks Lorentz symmetry, by allowing light to propagate faster than $c$. We looked at the possible transformation  symmetry group such vacuum could obey. By solving the semi-classical Einstein field equation in squeezed vacuum, we have found that the background geometry describes an Anti-deSitter (AdS) geometry. Therefore, the proper transformation symmetry group is the (A)dS group. One can describe quantum field theory in a finite volume  as a quantum field theory (QFT) on AdS background, or vice versa.

In this paper, a four dimensional  rotating Kaluza Klien (K-K) black hole was deformed using rainbow functions derived from loop quantum gravity and non-commutative geometry. We studied the thermodynamic properties and critical phenomena of this deformed black hole. The deformed temperature and entropy showed the existence of a Planckian remnant.  The calculation of Gibbs free energy $ G$ for the ordinary and deformed black holes showed that both share a similar critical behaviour. 

In this paper, we construct and calculate a non-perturbative path integrals in a multiply-connected space-time. This is done by by summing over homotopy classes of paths. The topology of the space-time is defined by Einstein-Rosen bridges (ERB) forming from the entanglement of quantum foam described by virtual black holes. As these `bubbles' are entangled, they ar econnected by Plankian ERB's because of the ER=EPR conjecture. Hence the space-time will possess a large first Betti number B1.