The exponential metric represents a traversable wormhole

TL;DR

This paper analyzes an exponential spacetime metric, revealing it describes a traversable wormhole rather than a black hole, with implications for astrophysical models and the need for further phenomenological studies.

Contribution

The paper clarifies that the exponential metric corresponds to a traversable wormhole, not a black hole, highlighting its strong-field differences and astrophysical implications.

Findings

Exponential metric lacks horizons, indicating a wormhole structure.

Strong-field behavior differs significantly from black hole metrics.

Potential to replace black hole candidates with wormholes in astrophysics.

Abstract

For various reasons a number of authors have mooted an "exponential form" for the spacetime metric: \[ ds^2 = - e^{-2m/r} dt^2 + e^{+2m/r}\{dr^2 + r^2(d\theta^2+\sin^2\theta \, d\phi^2)\}. \] While the weak-field behaviour matches nicely with weak-field general relativity, and so also automatically matches nicely with the Newtonian gravity limit, the strong-field behaviour is markedly different. Proponents of these exponential metrics have very much focussed on the absence of horizons --- it is certainly clear that this geometry does not represent a black hole. However, the proponents of these exponential metrics have failed to note that instead one is dealing with a traversable wormhole --- with all of the interesting and potentially problematic features that such an observation raises. If one wishes to replace all the black hole candidates astronomers have identified with traversable wormholes, then certainly a careful phenomenological analysis of this quite radical proposal should be carried out.