Curing Black Hole Singularities with Local Scale Invariance

Figure 2

The figure shows a nongeneric nature of Schwarzschild singularity and also a singular nature of -gauge (GR description) by plotting solutions in -plane. The black thick line represents a BH solution with generic space-like (-gauge) singularity which is in regular gauges characterised by and (independently of values of scalar fields in asymptotic infinity). The dashed line represents Schwarzschild BH which is in all gauges characterised by . The point in which two solutions coincide corresponds to asymptotic infinity . Solutions in -gauge are obtained by projecting on a hyperbola (thin gray line). We see that, for generic solution, this projection (thick gray line) is ill-defined when in regular gauge, and this manifests itself as space-time singularity in -gauge. The dotted thick line represents a white hole extension (in region with negative and ). Thin grey diagonal lines are straight lines .