  It has often been suggested (especially by Carlip) that spacetime symmetries
in the neighborhood of a black hole horizon may be relevant to a statistical
understanding of the Bekenstein-Hawking entropy. A prime candidate for this
type of symmetry is that which is exhibited by the Einstein tensor. More
precisely, it is now known that this tensor takes on a strongly constrained
(block-diagonal) form as it approaches any stationary, non-extremal Killing
horizon. Presently, exploiting the geometrical properties of such horizons, we
provide a particularly elegant argument that substantiates this highly
symmetric form for the Einstein tensor. It is, however, duly noted that, on
account of a "loophole", the argument does fall just short of attaining the
status of a rigorous proof.
