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 $\lambda \mathrm{\ne }0$ separating it from a Schwarxzschild black hole (BH) ($\lambda =0$). 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 $\mathit{\text{the}}\mathit{\text{identity}}\mathit{\text{of}}\mathit{\text{the}}\mathit{\text{observed}}\mathit{\text{object}}\mathit{\text{will}}\mathit{\text{depend}}\mathit{\text{on}}\mathit{\text{the}}\mathit{\text{probabilistic}}\mathit{\text{outcome}}\mathit{\text{of}}\mathit{\text{photon}}\mathit{\text{motion}}\mathit{\text{probing}}\mathit{\text{the}}\mathit{\text{object}}$. 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 $\lambda \mathrm{\ne }0$. (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 $\lambda \mathrm{\ne }0$.