For one, it's going to produce a metric where all the diagonal elements are positive (or zero) - different from the -+++ or +--- signature of "normal" spacetime.
The paper's calculation reminds me of Kaluza-Klein theory, which uses a similar construction as part of extending the metric from four dimensions to five:
The paper's calculation reminds me of Kaluza-Klein theory, which uses a similar construction as part of extending the metric from four dimensions to five:
https://en.wikipedia.org/wiki/Kaluza–Klein_theory