Black-bounce to traversable wormhole (1812.07114v3)

Abstract: So-called "regular black holes" are a topic currently of considerable interest in the general relativity and astrophysics communities. Herein we investigate a particularly interesting regular black hole spacetime described by the line element [ ds^{2}=-\left(1-\frac{2m}{\sqrt{r^{2}+a^{2}}}\right)dt^{2}+\frac{dr^{2}}{1-\frac{2m}{\sqrt{r^{2}+a^{2}}}} +\left(r^{2}+a^{2}\right)\left(d\theta^{2}+\sin^{2}\theta \;d\phi^{2}\right). ] This spacetime neatly interpolates between the standard Schwarzschild black hole and the Morris-Thorne traversable wormhole; at intermediate stages passing through a black-bounce (into a future incarnation of the universe), an extremal null-bounce (into a future incarnation of the universe), and a traversable wormhole. As long as the parameter $a$ is non-zero the geometry is everywhere regular, so one has a somewhat unusual form of "regular black hole", where the "origin" $r=0$ can be either spacelike, null, or timelike. Thus this spacetime generalizes and broadens the class of "regular black holes" beyond those usually considered.

• The paper introduces a novel spacetime metric that transitions from a Schwarzschild black hole (a=0) to a traversable wormhole (a>2m) while avoiding singularities.
• The authors analyze four distinct spacetime configurations using Carter-Penrose diagrams to illustrate photon spheres, ISCOs, and Regge-Wheeler potentials.
• Key violations of the Null Energy Condition emphasize the exotic matter needed to sustain these regular geometries and their unique causal structures.

Overview of "Black-bounce to traversable wormhole"

The paper by Alex Simpson and Matt Visser presents a detailed exploration of a novel family of spacetimes that serves to effectively bridge the concept of regular black holes with traversable wormholes. This is achieved via the introduction of specific spacetime metrics that interpolate between various well-known solutions in general relativity, notably the Schwarzschild black hole and the Morris-Thorne traversable wormhole. The formulation of this geometric progression provides significant insights into the nature of regular black holes, with specific attention to the avoidance of singularities at the core of these astrophysical objects.

Key Contributions

The authors define a line element characterized by a parameter, $a$, which controls the transitional behavior of the geometry from a Schwarzschild black hole at $a=0$ to a traversable wormhole at $a > 2m$. The spacetime remains regular for all non-zero values of $a$, significantly broadening the class of regular black holes while avoiding spacetime singularities. This approach allows the origin $r=0$ to be spacelike, null, or timelike depending on the parameter's value, thereby accommodating a unique form of regular black holes that can feature a bounce into a future universe.

The authors identify four distinct spacetime configurations based on the parameter $a$:

1. Schwarzschild spacetime for $a = 0$,
2. Regular black holes with a spacelike throat for $0 < a < 2m$,
3. One-way wormholes with an extremal null throat at $a = 2m$,
4. Canonical traversable wormholes for $a > 2m$.

Detailed Analysis

Through comprehensive analysis, the paper delineates the specific characteristics of these spacetimes including the locations of photon spheres, innermost stable circular orbits (ISCOs), and the evaluation of Regge-Wheeler potentials. The analysis also covers the behavior of the geometry's curvature tensors, which remain finite, confirming the absence of singularities.

Simpson and Visser proceed to perform a metric analysis using Carter-Penrose diagrams to illustrate the causal structures that form the geometry of these spacetimes. Such diagrams traditionally represent the maximal analytical extensions of black holes and wormholes, demonstrating the regularity and nature of the spacetime under varying conditions of the parameter $a$.

The paper discusses the violation of known energy conditions necessary to support such geometries, particularly highlighting the necessary violations of the Null Energy Condition (NEC) within this framework. This highlights the exotic nature of the matter-energy content required to sustain these solutions.

Implications and Future Work

The implications of this work extend into both theoretical and practical realms in general relativity and astrophysics. The concept of an underlying geometry that unifies black holes and wormholes paves the way for further experimental tests in high-energy astrophysics. Moreover, the work invites future theoretical investigations into the dynamics involved in the formation and stability of these geometries, as well as their potential observational signatures.

Future developments in this area may also explore the cosmological implications of such bounces and extensions into new universe incarnations, examining how this framework can integrate with current cosmological models and theories.

Overall, Simpson and Visser provide a robust foundation for deconstructing traditional concepts of black hole and wormhole physics, offering a tractable avenue for bridging these phenomena within a singular geometric description. Their paper expands the horizon for innovative explorations in gravitational physics, cosmology, and potentially quantum gravity, where the avoidance of singularities may be vital.