The authors discuss a classification of four cases of time-like two dimensional submanifolds (also called surfaces) \(S\) of a Lorentzian manifold with respect to special algebraic properties of the second fundamental form of \(S\). They explain that physically such surfaces can considered as a track, and their time like curves as the worldliness of observers who are bound to that track. For application to relativity, they consider two types of surfaces, namely, photon surfaces (ruled by two families of light-like geodesics) and one-way photon surfaces (if one of the two families is geodesic and the other is not). Finally, they justify the results of this paper by an example of time-like surfaces in the Kerr-Newman space-time.
For the entire collection see [Zbl 1152.53002].