Enhanced black hole horizon fluctuations

We discuss the possible role of quantum horizon fluctuations on black hole radiance, especially whether they can invalidate Hawking’s analysis based upon transplanckian modes. We are particularly concerned with “enhanced” fluctuations produced by gravitons or matter fields in squeezed vacuum states sent into the black hole after the collapse process. This allows for the possibility of increasing the fluctuations well above the vacuum level. We find that these enhanced fluctuations could significantly alter stimulated emission, but have little effect upon the spontaneous emission. Thus the thermal character of the Hawking radiation is remarkably robust.

Figure 1

The spacetime of a black hole formed by gravitational collapse is illustrated. The shaded region is the interior of the collapsing body, the $r=0$ line on the left is the world line of the center of this body, the $r=0$ line at the top of the diagram is the curvature singularity, and ${\mathcal{H}}^{+}$ is the future event horizon. An ingoing light ray with $v<v_0$ from ${\mathcal{I}}^{-}$ passes through the body and escapes to ${\mathcal{I}}^{+}$ as a $u=\mathrm{\text{constant}}$ light ray. Ingoing rays with $v>v_0$ do not escape and eventually reach the singularity.

Figure 2

Schwarzschild black hole spacetime formed via gravitational collapse. The separation vector characterizing geodesic deviation of the horizon, ${\mathcal{H}}^{+}$, and a nearby outgoing null geodesic, $\gamma$, is initially $n^{\nu }=n_0^{\nu }$ but then evolves as $n^{\nu }=n_0^{\nu }+{\delta }_s{n}^{\mu }$. The vector ${\ell }^{\mu }$ is tangent to the horizon. Perturbing fields fall into the black hole well after the horizon forms.