We have derived a necessary and sufficient condition for non-null normal spacelike curve lying in or timelike surface M ⊂ E13, so that the becomes K-type slant helix with K ∈ {1,2,3}. used Darboux frame to define conditions. An example is given 1-type having binormal.

Einstein’s field equations of gravitation are known to admit closed timelike curve (CTC) solutions. Deutsch approached the problem from the quantum information point of view and proposed a selfconsistency condition. In this work, the Deutsch equation is formulated as an eigenvalue problem. The disappearance of entanglement between two qubits in an Einstein-Podolsky-Rosen (EPR) state near a CTC ...

A constant angle surface in Minkowski space is a spacelike surface whose unit normal vector field makes a constant hyperbolic angle with a fixed timelike vector. In this work we study and classify these surfaces. In particular, we show that they are flat. Next we prove that a tangent developable surface (resp. cylinder, cone) is a constant angle surface if and only if the generating curve is a ...

We consider a unit speed timelike curve α in Minkowski 4-space E41 and denote the Frenet frame of α by {T,N,B1,B2}. We say that α is a generalized helix if one of the unit vector fields of the Frenet frame has constant scalar product with a fixed direction U of E41. In this work we study those helices where the function 〈B2, U〉 is constant and we give different characterizations of such curves....

A computer which has access to a closed timelike curve, and can thereby send the results of calculations into its own past, can exploit this to solve difficult computational problems efficiently. I give a specific demonstration of this for the problem of factoring large numbers, and argue that a similar approach can solve NP-complete and PSPACE-complete problems. I discuss the potential impact ...

We consider a toy model of the interaction of a qubit with an exotic space-time containing a timelike curve. Consistency seems to require that the global evolution of the qubit be nonunitary. Given that quantum mechanics is globally unitary, this then is an example of a quantum gravity information paradox. However, we show that a careful analysis of the problem in the Heisenberg picture reveals...

Causality violations are typically seen as unrealistic and undesirable features of a physical model. The following points out three reasons why causal-ity violations, which Bonnor and Steadman identified even in solutions to the Ein-stein equation referring to ordinary laboratory situations, are not necessarily undesirable. First, a space-time in which every causal curve can be extended into a ...

Recently it was discovered that null hypersurfaces can develop caustics outside the event horizon of super-entropic Kerr-AdS black holes, in contrast to usual case. In this work we explore a few more examples hole spacetimes which such exterior develop. If closed curve is present, e.g., case Taub-NUT and "transunital" spacetimes, then coincides with hypersurface caustic (NHC) minimal separation...

In this paper, we give the parametric equation of Bishop frame for a timelike sweeping surface with unit speed curve in Minkowski 3-space. We introduce new geometric invariant to explain properties and local singularities surface. derive sufficient necessary conditions be developable ruled Afterwards, take advantage singularity theory classification Furthermore, some representative examples sho...

The causal boundary of a strongly causal spacetime, introduced by Geroch, Kronheimer, and Penrose in [GKP], is a tool for examining the causal nature of a spacetime “at infinity”. As it is conformally invariant, it is a property of the conformal structure of the spacetime. The addition of the causal boundary to a spacetime results in an object whose structure might be most naturally characteriz...