Some Singular Spacetimes and Their Possible Alternatives

In this review, we begin with a historical survey of some singular solutions in the theory of gravitation, as well as a very brief discussion of how black holes could physically form. Some possible scenarios which could perhaps eliminate these singularities are then reviewed and discussed. Due to the vastness of the field, its coverage is not exhaustive; instead, the concentration is on a small subset of topics such as possible quantum gravity effects, non-commutative geometry, and gravastars. A simple singularity theorem is also reviewed. Although parts of the manuscript assume some familiarity with relativistic gravitation or differential geometry, the aim is for the broad picture to be accessible to non-specialists of other physical sciences and mathematics.