The Globally Trapped Future: A Fate for Black Holes and Wormholes

TL;DR

The paper addresses the dynamic evolution of non-singular spacetimes, such as regular black holes, and their relation to wormholes by introducing a framework to generate arbitrary spherically symmetric metrics from two scalar fields coupled to an electromagnetic field. It analyzes non-stationary spacetimes with tractable global causal structure and trapping horizons, revealing a three-fold classification of ultimate fates and highlighting the globally trapped future as a novel possibility. Through concrete models, including a Schwarzschild-like black hole and an Ellis-Bronnikov wormhole, the authors demonstrate transitions between black-hole and wormhole regimes and introduce the concept of an unattainable minimal throat, the Endless Throat, embedded in a regular black hole. The work offers a new lens on regular black holes and horizon dynamics, with potential implications for causal structure and the end-state of gravitational collapse, while outlining future work to realize Schwarzschild-like limits with preserved Killing horizons and Endless Throats.

Abstract

We demonstrate, for the first time, that arbitrary spherically symmetric metrics can be derived within a framework based on the coupling of two scalar fields and an electromagnetic field. We then specialize to a class of non-stationary spacetimes characterized by analytically tractable global causal structure and trapping horizons, which is particularly suited for investigating black holes and wormholes. Within this framework, we find that the fate of spacetime can be categorized into three distinct classes: those without a globally trapped future; those without a globally trapped future but containing bounded, Cauchy-foliated trapped regions; and those with a future that becomes completely trapped. The evolution of a geometrically Schwarzschild-like black hole and a horizonless wormhole demonstrates these possible fates, thus revealing the globally trapped outcome as a novel theoretical possibility. Finally, we propose that a regular black hole may contain an Unattainable Minimal Throat -- a minimal-radius throat that is causally unreachable -- and refer to it henceforth as the Endless Throat.

Figures (3)

• Figure 1: The Penrose diagram for parameters $a=0.4, m=1.4, k=1/(2am)$. Regions: $\mathrm{T}$ (trapped), $\mathrm{AT}$ (anti-trapped), $\mathrm{UT}$ (untrapped). Blue and red lines indicate marginally trapping horizons of $k^a_+$ and $k^a_-$, thick and thin gray lines denote null infinities and constant $R$ surfaces (larger $R$ closer to null infinity). The null energy condition (NEC) and the strong energy condition (SEC) are satisfied in the region between the two dashed lines.
• Figure 2: Penrose diagram for $a=0.4, m=2, k=1/(2am)$. $\rho\geq0$ inside the regions enclosed by the four dotted lines. The label $\mathrm{UT}$ is not shown. The NEC and the SEC are satisfied in the region between the two dashed lines.
• Figure 3: Penrose diagram for $a=2, L=1, k=1/(2a(a-L)^2), mk=4, n=0$. Note that the thick gray lines do not represent conformal boundaries but merely coordinate boundaries, while the thin gray lines indicate surfaces of constant $R$; closer to the boundaries, these surfaces correspond to smaller $R$. The weak energy condition (WEC) is satisfied in the region between the two dashed lines.