Over the horizon: Distinguishing the Schwarzschild spacetime and the $\mathbb{R}{\mathbb{P}}^3$ spacetime using an Unruh-DeWitt detector

The ${\mathbb{RP}}^3$ geon and the Schwarzschild black hole are two black hole spacetimes which differ only behind the event horizon. We show that the thermal Hawking radiation emanating from the two black holes contains nontrivial correlations, that these correlations contain information about their interiors, and demonstrate that a particle detector can recover these correlations. In this manner, a simple particle detector can determine the structure behind the event horizon of an eternal black hole.

Figure 1

The ${\mathbb{RP}}^3$ geon from the extended Schwarzschild solution.

Figure 2

Response functions for black hole (blue), geon part (red), and geon total (green) versus $\mathrm{\Omega }$.

Figure 3

Response functions for varying detector radius (Hartle-Hawking vacuum).

Figure 4

Response functions for varying detector radius (Unruh vacuum).

Figure 5

Geon relative signal for varying switching width $\sigma$.

Figure 6

Response functions for black hole (blue) and geon part (red) versus time translation.

Figure 7

Transition rates for black hole versus gap, for the Hartle-Hawking (dot-dashed), Unruh (dashed), and Boulware (solid) vacuum states.

Figure 8

Transition rate for $\mathrm{\Omega }/T_{\mathrm{loc}}=-2$ (top), 0 (middle), 2 (bottom).