We construct a quantum field theory in noncommutative spacetime by twisting the algebra of quantum operators (especially, creation and annihilation operators) of the corresponding quantum field theory in commutative spacetime. The twisted Fock space and S-matrix consistent with this algebra have been constructed. The resultant S-matrix is consistent with that of Filk [37]. We find from this formulation that the spin-statistics relation is not violated in the canonical noncommutative field theories.

We twist the Hopf algebra of igl(n, R) to obtain the κ-deformed spacetime coordinates. Coproducts of the twisted Hopf algebras are explicitly given. The κ-deformed spacetime obtained this way satisfies the same commutation relation as that of the conventional κ-Minkowski spacetime, but its Hopf algebra structure is different from the well known κ-deformed Poincaré algebra in that it has larger symmetry algebra than the κ-Minkowski case. There are some physical models which consider this symmetry [42,43,44]. Incidentally, we obtain the canonical (θ-deformed) non-commutative spacetime from canonically twisted igl(n, R) Hopf algebra.

Based on the equivalence between the three dimensional gravity and the Chern-Simons theory, we obtain a noncommutative BTZ black hole solution as a solution of U(1, 1)×U(1, 1) noncommutative Chern-Simons theory using the Seiberg-Witten map. The Seiberg-Witten map is carried out in a noncommutative polar coordinates whose commutation relation is equivalent to the usual canonical commutation relation in the rectangular coordinates up to first order in the noncommutativity parameter θ. The solution exhibits a characteristic of noncommutative polar coordinates in such a way that the apparent horizon and the Killing horizon coincide only in the non-rotating limit showing the effect of noncommutativity between the radial and angular coordinates.

We have investigated the classical stability of magnetically charged black p-brane solutions for string theories that include the case studied by Gregory and Laflamme. It turns out that the stability behaves very differently depending on a coupling parameter between dilaton and gauge fields. In the case of Gregory and Laflamme, it has been known that the black brane instability decreases monotonically as the charge of black branes increases and finally disappears at the extremal point. For more general cases we found that, when the coupling parameter is small, black brane solutions become stable even before reaching to the extremal point. On the other hand, when the coupling parameter is large, black branes are always unstable and moreover the instability does not continue to decrease, but starts to increase again as they approach to the extremal point. However all extremal black branes are shown to be stable even in this case. It has also been shown that main features of the classical stability are in good agreement with the local thermodynamic behavior of the corresponding black hole system through the Gubser-Mitra conjecture. Some implications of our results are also discussed. *

We study four dimensional κ-Minkowski spacetime constructed by the twist deformation of U (igl(4, R)). We demonstrate that the differential structure of such twist-deformed κ-Minkowski spacetime is closed in four dimensions contrary to the construction of κ-Poincaré bicovariant calculus which needs an extra fifth dimension. Our construction holds in arbitrary dimensional spacetimes.