Dynamical model for black hole to white hole transitions

TL;DR

The paper develops a smooth, dynamical, non-singular, asymptotically flat metric in Painlevé-Gullstrand coordinates that describes a black hole to white hole transition driven by a matter bounce, incorporating a mass function $m(r,t)$ and a sign-changing shift $N^{r}$. It demonstrates a BH→WH transition within a single asymptotic region by tuning the shift, producing transient horizons and a finite-bounce evolution. The analysis shows dominant energy condition violations localized near the bounce and horizon regions, with the energy density $\rho$ remaining positive elsewhere, framing the model as a phenomenological quantum-gravity-inspired scenario. The results offer a minimal dynamical framework that could arise in effective theories, and they motivate potential observational signatures through geodesics and connections to dark-matter phenomenology in a broader quantum-gravity context.

Abstract

We present an asymptotically flat spherically symmetric non-singular metric that describes gravitational collapse and matter bounce with transient black hole and white hole regions. The metric provides a dynamical counterpart to proposed static non-singular black holes, and a phenomenological model for possible black hole to white hole transitions in quantum gravity.

Figures (4)

• Figure 1: Null expansion scalars $\theta_\pm$ that exhibit a transition from a black hole ($\theta_+<0$ for some range of $r$ and $\theta_-<0$ for all $r$) to a white hole ($\theta_->0$ for some range of $r$ and $\theta_+>0$ for all $r$) at the times indicated: a BH of radius $r=32$ forms at $t=-800$ and disappears at $t=0$; a WH of radius $r=32$ has formed at $t=20$ and disappears at $t=1200$.
• Figure 2: A view of the black hole and white hole regions: the left frame shows the inner and outer horizons and the peak of the density profile; the right frame is a close up showing the separation between the BH and WH regions with a sample of light cones.
• Figure 3: Schematic conformal diagram of the black hole (lower region) to white hole (upper region) transition.
• Figure 4: Radial (a,c) and azimuthal (b,d) components of the dominant energy condition: the second row is a close up of the upper row; the radial direction shows small violations of the DEC near the matter bounce point; the azimuthal direction shows violations at larger radial values.