Excising Curvature Singularities from General Relativity

This thesis operates within the framework of general relativity withoutcurvature singularities. The motivation for this framework is explored,and several conclusions are drawn with a look towards future research.

There are many ways to excise curvature singularities from general relativity; a full list of desirable constraints on candidate geometries is presented. Several specific candidate spacetimes in both spherical symmetryand axisymmetry are rigorously analysed, typically modelling (charged oruncharged) regular black holes or traversable wormholes. Broadly, theseare members of the family of black-bounce spacetimes, and the familyof black holes with asymptotically Minkowski cores. Related thin-shelltraversable wormhole constructions are also explored via the Darmois–Israel formalism, as well as a brief look at the viability of thin-shell Dysonmega-spheres. The eye of the storm geometry is analysed, and discoveredto be very close to an idealised candidate geometry within this framework.

It is found to contain highly desirable features, and is not precluded bycurrently available measurements. For all spacetimes discussed, particular focus is placed on the extraction of (potential) astrophysical observables in principle falsifiable/verifiable by the observational and experimental communities. An examination of the spin one and spin zero quasinormal modes on a background regular black hole with asymptoticallyMinkowski core is performed by employing the relativistic Cowling approximation. A cogent effort is made to streamline the discourse betweentheory and experiment, and to begin filling the epistemological gap, whichwill enable the various communities involved to optimise the advancement of physics via the newly available observational technologies (suchas LIGO/Virgo, and the upcoming LISA). Furthermore, three somewhatgeneral theorems are presented, and two new geometries are introducedfor the first time to the literature.