Quasinormal modes, scattering, and Hawking radiation in the vicinity of an Einstein-dilaton-Gauss-Bonnet black hole

Classical (quasinormal) and quantum (Hawking) radiations are investigated for test fields in the background of a four dimensional, spherically symmetric and asymptotically flat black hole in the Einstein-dilaton-Gauss-Bonnet (EdGB) theory. The geometry of the EdGB black hole deviates from the Schwarzschild geometry only slightly. Therefore, here we observe that the quasinormal spectrum also deviates from its Schwarzschild limit at most moderately, allowing for a 9% decrease in the damping rate and up to a 6% decrease in the real oscillation frequency. However, the intensity of Hawking radiation of an electromagnetic and Dirac fields turned out to be much more sensitive characteristic than its quasinormal spectrum, allowing for a 57% and 48% increase of the energy emission rate respectively. The analytical formula for the eikonal regime of quasinormal modes is derived for test fields and it is shown that the correspondence between the eikonal quasinormal modes and null geodesics is indeed fulfilled for test fields, but is not expected for the gravitational one.

Figure 1

Dependence of the effective potentials $V(r)$ with $r_0=1$; blue line is $p=0$, red line is $p=0.4$ and green line is $p=0.97$: (a) $s=1$, $\ell =1$; (b) $s=0$, $\ell =0$.

Figure 2

The fundamental quasinormal mode ($n=0$) for the electromagnetic field ($s=1$), blue line is real part of frequencies, red line is imaginary part: (a) $\ell =1$; (b) $\ell =2$; (c) $\ell =3$.

Figure 3

The fundamental quasinormal mode ($n=0$) for the scalar field ($s=0$), blue line is real part of frequencies, red line is imaginary part: (a) $\ell =1$; (b) $\ell =2$.

Figure 4

Imaginary part of the quasinormal modes for a massive scalar field $\ell =15$, $p=0.5$.

Figure 5

Real part of the quasinormal modes for a massive scalar field $\ell =15$, $p=0.5$.

Figure 6

Time-domain profile for the scalar field’s perturbation: $\ell =0$, $p=0.97$.

Figure 7

The gray-body factor dependence in $\omega$, for the electromagnetic field ($s=1$), blue line corresponds to $p=0$, it is Schwarzschild limit, orange line corresponds to $p=0.3$, green line corresponds to $p=0.6$, red line is a maximum value of $p=0.9$: (a) $l=1$; (b) $l=2$; (c) $l=3$.

Figure 8

The Hawking temperature $T_H(p)$.

Figure 9

Energy emission rate of the electromagnetic field for different values $\ell$, $p=0.97$: blue line corresponds to $\ell =1$, green line corresponds to $\ell =2$, red line is $\ell =3$.

Figure 10

Total energy emission rate (after summation over all degrees of freedom and quantum numbers) of the electromagnetic field for $p=0$ (green), 0.9 (red), and 0.97 (blue).

Figure 11

Energy emission rate of the Dirac field for different values $\ell$, $p=0.97$: blue line corresponds to $\ell =1$, green line corresponds to $\ell =2$, red line is $\ell =3$.

Figure 12

Total energy emission rate (after summation over all degrees of freedom and quantum numbers) of the Dirac field for $p=0$ (green), 0.9 (red), and 0.97 (blue).