Black hole squeezers

We show that the gravitational quasinormal modes (QNMs) of a Schwarzschild black hole play the role of a multimode squeezer that can generate particles. For a minimally coupled scalar field, the QNMs “squeeze” the initial state of the scalar field (even for the vacuum) and produce scalar particles. The maximal squeezing amplitude is inversely proportional to the cube of the imaginary part of the QNM frequency, implying that the particle generation efficiency is higher for lower decaying QNMs. Our results show that the gravitational perturbations can amplify Hawking radiation.

Figure 1

Reflection coefficient for the scalar field modes.

Figure 2

Modulus of the joint frequency distribution. QNM: ${\mathrm{\Omega }}_R=0.7474$, ${\mathrm{\Omega }}_I=0.178$, $(l_0,m_0)=(2,0)$. Scalar particle one: $(l,m)=(1,1)$; scalar particle two: $(l^{\prime },m^{\prime })=(2,-1)$.

Figure 3

Modulus of the joint frequency distribution for even-parity QNMs. QNM: ${\mathrm{\Omega }}_R=0.7474$, ${\mathrm{\Omega }}_I=0.178$, $(l_0,m_0)=(2,0)$. Scalar particle one: $(l,m)=(1,1)$; scalar particle two: $(l^{\prime },m^{\prime })=(3,-1)$.

Figure 4

The contour $C$ and branch cut when ${\omega }_R-\omega -{\omega }^{\prime }>0$. The two shaded regions are referred to as in (close to the horizon) and out (around $r=\infty$) regions, respectively.