  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.
