Pseudo-Riemannian manifolds of balanced signature which are both spacelike and timelike Jordan Osserman nilpotent of order 2 and of order 3 have been constructed previously. In this short note, we shall construct pseudo-Riemannian manifolds of signature (2s, s) for any s ≥ 2 which are spacelike Jordan Osserman nilpotent of order 3 but which are not timelike Jordan Osserman. Our example and tech...

We explore some foundational issues regarding the splitting of D-dimensional Einstein Field Equations (EFE’s) with respect to timelike and spacelike (D 1)-dimensional hypersurfaces, first without and then with thin matter sheets such as branes. We begin to implement methodology, that is well-established for the GR Cauchy and initial value problems (CP and IVP), in the new field of GR-based bran...

In the appearance of absorption material, the quantum vacuum fluctuations of all kinds of fields may be smoothed out and the spacetime with time machine may be stable against vacuum fluctuations. The chronology protection conjecture might break down, and the anti-chronology protection conjecture might hold: There is no law of physics preventing the appearance of closed timelike curves. PACS num...

Let s ≥ 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s, s) which are not locally homogeneous but whose curvature tensors never the less exhibit a number of important symmetry properties. They are curvature homogeneous; their curvature tensor is modeled on that of a local symmetric space. They are spacelike Jordan Osserman with a Jacobi operator which is nilpotent of ord...

By extending Ashtekar and Romano’s definition of spacelike infinity to the timelike direction, a new definition of asymptotic flatness at timelike infinity for an isolated system with a source is proposed. The treatment provides unit spacelike 3-hyperboloid timelike infinity and avoids the introduction of the troublesome differentiability conditions which were necessary in the previous works on...

It is known that a party with access to Deutschian closed timelike curve (DCTC) can perfectly distinguish multiple nonorthogonal quantum states. In this paper we propose practical method for discriminating states, by using previously circuit designed simulate DCTCs. This relies on copies of an input state, iterations the circuit, and fixed set unitary operations. We first characterize performan...

In this paper, using pseudo-spherical Frenet frame of pseudospherical curves in hyperbolic space, we define the notion of the structure functions on the non-developable ruled surfaces with timelike ruling. Then we obtain the properties of the structure functions and a complete classification of the non-developable ruled surfaces with timelike ruling in Minkowski 3-space by the theories of the s...

We show that isothermic surfaces and S-Willmore surfaces are also the solutions to the corresponding Blaschke’s problem for both spacelike and timelike surfaces in pseudoRiemannian space forms. For timelike surfaces both Willmore and isothermic, we obtain a description by minimal surfaces similar to the classical results of Thomsen.