The Limit Tenson Equation and Quantum Gravity: Black Holes and Extreme Energy–Information States

We present a mathematical expansion and selected analytic solutions of the Limit Tenson Equation ∇∞·LT = ε∞, a formalism that joins energy and information in a complex-valued tenson field. After defining the field decomposition and the interpretation of the limit divergence operator, we derive real/imaginary component equations, construct spherically symmetric solu- tions relevant to black-hole spacetimes (including the explicit derivation of the C/r2 profile in the homogeneous limit), and introduce a time-dependent energy–information coupling model. We discuss boundary conditions at the event horizon and the role of the limit state ε∞ for information bookkeeping in black-hole contexts. The aim is to provide a clear, self-contained mathematical presentation of the expansions and solu- tion ans¨atze that can serve as the basis for subsequent numerical and field-theoretic work.