Horizons and Singularities in Static, Spherically Symmetric Spacetimes
Foundations of Physics
We make a thorough study of the regions near finite-order metric-singularity boundaries of static, spherically symmetric spacetimes. After distinguishing curvature singularities from other types of metric breakdown, we examine the eigenvalues of the energy tensor near the singularities for positivity and energy dominance, find the causal class of the t-translation ("static") Killing field, and ascertain the presence or absence of timelike, null, and spacelike geodesic incompleteness for each spacetime. For a certain subclass of spacetimes, we also show the completeness of all timelike and spacelike curves despite the superficial failure of the metric.
Wheeler, J. T., Horizons and singularities in static, spherically symmetric spacetimes, Foundations of Physics, Vol. 25, No. 5, (1995) 645-679.