Damour–Solodukhin Wormhole as a Black Hole Mimicker: The Role of Observers’ Location

It has been recently argued that in semi-classical gravity, a minimal 2-sphere is not a horizon but a tiny throat of a wormhole, such as the Damour–Solodukhin wormhole (DSWH), with a free parameter λ≠0 separating it from a Schwarxzschild black hole (BH) (λ=0). As shown by DS, their horizonless WH can mimic many properties of a black hole (BH). Assuming that observing a BH mimicker is equivalent to observing a BH itself, we ask the question as to which identity of the object, a WH or a BH, an observer is likely to observe in a single experiment. To answer this, we introduce Tangherlini’s new concept of indeterminacy in the gravitational field by portraying the field as a refractive medium. We then postulate that the identity of the observed object will depend on the probabilistic outcome of photon motion probing the object. The probabilities will be described by Fresnel reflection (R) and transmission (T) coefficients derived by Tangherlini on the basis of a non-quantum statistical indeterminacy of photon motion in ordinary optical media. By adapting this approach to a gravitational “effective optical medium,” we obtain two intriguing results: (i) The Fresnel coefficients at the DSWH throat are independent of mass M but dependent solely on the parameter λ≠0. (ii) Depending on the location of the observer, what is a DSWH to one observer may appear as a BH to another observer for the same value of λ≠0.