Some fundamental limitations of mathematical software revealed by the calculation of spacetime curvature

摘要

The use of library mathematical software will, ideally, provide solutions to problems in science and engineering without the user having to become invovled in the details of the software. In practice, some knowledge of the characteristics of the problem is often required to arrive at an acceptable solution. We illustrate this requirement with the solution of the Einstein field equations to calculate spacetime curvature. These equations under certain circumstances can become more difficult to solve with increasing problem time, and eventually cause a failure in the calculations, which we think will occur no matter what mathematical software is used.