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We prove that the blowup term of a blowup solution of Jang's equation on aninitial data set (M,g,k) near an arbitrary strictly stable MOTS $ \Sigma $ isexactly $ -\frac{1}{\sqrt{\lambda}}\log \tau $, where $ \tau $ is the distancefrom $ \Sigma $ and $ \lambda $ is the principal eigenvalue of the MOTSstability operator of $ \Sigma $. We also prove that the gradient of thesolution is of order $ \tau^{-1} $. Moreover, we apply these results to get aPenrose-like inequality under additional assumptions.

Blowup rate control for solution of Jang's equation and its application on Penrose inequality