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How Can Mathematicians Compare Different Models of Spacetime?
April 28, 2026
Assistant Professor of Mathematics Brian Allen has authored a new paper in Letters in Mathematical Physics that describes a novel mathematical tool for comparing different models of spacetime.
When mathematicians use equations to describe the physical world—our three dimensions plus time—they need to know not only whether a solution works, but whether it is stable. In general relativity, this question is especially complicated because the model is not just measuring or describing something happening in space and time. It is describing the shape of spacetime itself. To study whether one spacetime model is similar to another, mathematicians need a reliable way to compare them.
One method, called the null distance, was introduced by Lehman Professor Christina Sormani and her colleague Carlos Vega in 2016. Allen’s paper continues the study of this tool, focusing on how the null distance works for static spacetime, a model that plays an important role in general relativity.