The sky invariant: A new conformal invariant for Schwarzschild spacetime

A new class of conformal invariants for a given spacetime $M$ is introduced exploiting the geometry any light ray $\Gamma$. Each congruence rays passing through point $p$ defines sky $S(p)$ such point. The are defined on bundle skies $M$, being called accordingly. natural covariant derivative and its associated calculus allows us show existence invariant differential arc that, together with restriction curvature derivative, can be used to construct that will curvature. An algorithm, implemented symbolic manipulation software system, compute discussed main ideas explicit computation illustrated in Schwarzschild spacetime.