2. Certain gravitational plane wave spacetimes provide good examples of this phenomenon: an observer traveling along the incomplete timelike geodesic constituting the singular structure would experience unbounded tidal acceleration, whereas any observer traveling arbitrarily close by would not (Ellis and Schmidt 1977).
In many cases, however, the singular structure of the solution is known, and its form may be exploited by the spectral element method.
For smooth domains the singular structure at Dirichlet Neumann junctions is incorporated as part of our corresponding numerical algorithm which otherwise relies on use of the cosine change of variables, trigonometric polynomials and, to avoid the Gibbs phenomenon that would arise from the solution singularities, the Fourier Continuation method (FC).
The construction method used in its execution (cantilevered erection in a congested urban area), so as the characteristics of the bolted steel structure and the way it is anchored to the concrete core walls, employing post-tensioning systems and stud shear connectors, transform this building into a singular structure in the field of construction.
At the same time, the ground-breaking work predicting the existence of such pathological paths produced no consensus on what ought to count as a necessary condition for singular structure according to this criterion, and thus no consensus on a fixed definition for it.
Many eminent physicists believe that general relativity's prediction of singular structure signals a serious deficiency in the theory; singularities are an indication that the description offered by general relativity is breaking down.
It is perhaps this fact that lies behind much of the urgency surrounding the attempt to define singular structure as "missing points".
As we have seen, there is no commonly accepted, strict definition of singularity, no physically reasonable definition of missing point, and no necessary connection of singular structure, at least as characterized by the presence of incomplete paths, to the presence of curvature pathology.
Many discussions of singular structure in relativistic spacetimes, therefore, are premised on the idea that a singularity represents a point or set of points that in some sense or other is "missing" from the spacetime manifold, that spacetime has a "hole" or "tear" in it that we could fill in or patch by the appendage of a boundary to it.
