Feynman’s iϵ prescription, almost real spacetimes, and acceptable complex spacetimes

Spacetimes admitting quasi-conformal curvature tensor

‎The object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎At first we prove that a quasi-conformally flat spacetime is Einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎Einstein's field equation with cosmological constant is covariant constant‎. ‎Next‎, ‎we prove that if the perfect flui...

Combinatorial Spacetimes

Kundt Spacetimes

Kundt spacetimes are of great importance in general relativity in 4 dimensions and have a number of topical applications in higher dimensions in the context of string theory. The degenerate Kundt spacetimes have many special and unique mathematical properties, including their invariant curvature structure and their holonomy structure. We provide a rigorous geometrical kinematical definition of ...

Waves on Noncommutative Spacetimes

Waves on “commutative” spacetimes like Rd are elements of the commutative algebra C0(Rd) of functions on Rd. When C0(Rd) is deformed to a noncommutative algebra Aθ(R) with deformation parameter θ (A0(R) = C0(Rd)), waves being its elements, are no longer complex-valued functions on Rd. Rules for their interpretation, such as measurement of their intensity, and energy, thus need to be stated. We ...

Geodesics in Margulis Spacetimes

Let M be a Margulis spacetime whose associated complete hyperbolic surface Σ has compact convex core. Generalizing the correspondence between closed geodesics on M and closed geodesics on Σ, we establish an orbit equivalence between recurrent spacelike geodesics on M and recurrent geodesics on Σ. In contrast, no timelike geodesic recurs in neither forward nor backwards time.