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Let $(M^{n}, g)$ denote a Riemannian spin manifold of dimension $n$ withDirac operator $D$ induced from the Levi-Cevita connection acing on the spinorbundle, $S$ ($D$ is also called the Atiyah-Singer Operator). Let $c: Cl(TM^{n})\rightarrow End(S)$ be the standard representation of the Clifford Algebra asendomorphisms of the spinor bundle. Let $B \in End(S)$ be a zeroth-orderendomorphism of the spinor bundle; given an in an orthonormal frame, $e_{j} \inTM^{n}$ by the expression $B=f^{\alpha}c(e_{\alpha})$ where the sum is takenover multi-indices, $\alpha = (i_{j_{m}}), \ m = 1, \, 2, \, 3 \, ... ,\ k$,$j_{1}< j_{2} < ... < j_{k}$ and each $f^{\alpha} \in C^{\infty}(M^{n})$. Thepurpose of this paper is investigate when the Dirac-Schrodinger operator $D +B$ has an integrating factor, i.e. when does there exist an invertibleendomorphism $A \in End(S)$ such that $D(AB)=AD+AB$. This has applications toimproving eigenvalue estimates for Dirac-Schrodinger operators and provingpositive charged positive mass theorems where such operators appear on theboundary. Of particular interest is the case $n = 2$, for boundary Diracoperators of this form appear in charged positive mass theorems based on theinitial data formulation in mathematical general relativity. It allows us togeneralize a theorem of M. Herzlich (set-forth in his attempt to prove theRiemannian Penrose-inequality using spinors, cf. [1]) to a manifold ofdimension $n \geq 3$ containing an electric field and symmetric two-tensorrepresenting the second-fundamental form.

Integrating Factors for Dirac-Schrodinger Operators: Improving  Eigenvalue Estimates and Applications to Charged Positive Mass Theorems  Outside Horizon(s)