Quasinormal modes, scattering, and Hawking radiation of Kerr-Newman black holes in a magnetic field

We perform a comprehensive analysis of the spectrum of proper oscillations (quasinormal modes), transmission/reflection coefficients, and Hawking radiation for a massive charged scalar field in the background of the Kerr-Newman black hole immersed in an asymptotically homogeneous magnetic field. There are two main effects: the Zeeman shift of the particle energy in the magnetic field and the difference of values of an electromagnetic potential between the horizon and infinity, i.e. the Faraday induction. We have shown that “turning on” the magnetic field induces a stronger energy-emission rate and leads to “recharging” of the black hole. Thus, a black hole immersed in a magnetic field evaporates much quicker, achieving thereby an extremal state in a shorter period of time. Quasinormal modes are moderately affected by the presence of a magnetic field which is assumed to be relatively small compared to the gravitational field of the black hole.

Figure 1

The effective potentials for the charged scalar field ($l=m=2$) in the Schwarzschild background ($r_{+}=1$) with the magnetic field $eB=0.04$ (top [blue] curve), $eB=0.1$ (middle [green] curve), and $eB=0.25$ (bottom [red] curve). One can see that the potential is negative only deeply in the region $r\gg 1/\sqrt{eB}$, which is beyond the region of validity of the approximation equation (10).

Figure 2

Real (left panel, graphs from top to bottom) and imaginary (right panel, graphs from bottom to top) parts of the fundamental ($n=0$) QNM as a function of $eB$ for $l=m=0$, $Q=0$, $a=0.2$ (blue online), $a=0.4$ (green), $a=0.6$ (orange), $a=0.8$ (red), $a=0.99$ (magenta).

Figure 3

Real (left panel, graphs from top to bottom) and imaginary (right panel, graphs from bottom to top) parts of the fundamental ($n=0$) QNM as a function of $eB$ for $l=1$, $m=0$, $Q=0$, $a=0.2$ (blue online), $a=0.4$ (green), $a=0.6$ (orange), $a=0.8$ (red), $a=0.99$ (magenta).

Figure 4

Real (left panel, graphs from top to bottom) and imaginary (right panel, graphs from bottom to top) parts of the fundamental ($n=0$) QNM as a function of $eB$ for $l=1$, $m=1$, $Q=0$, $a=0.2$ (blue online), $a=0.4$ (green), $a=0.6$ (orange), $a=0.8$ (red), $a=0.99$ (magenta).

Figure 5

Real (left panel, graphs from top to bottom) and imaginary (right panel, graphs from bottom to top) parts of the fundamental ($n=0$) QNM as a function of $eB$ for $l=1$, $m=-1$, $Q=0$, $a=0.2$ (blue online), $a=0.4$ (green), $a=0.6$ (orange), $a=0.8$ (red), $a=0.99$ (magenta).

Figure 6

Real and imaginary parts of the fundamental ($n=0$) QNM as a function of $Q$ for $Q=0$, $2aMB/3$, $aMB$, $2aMB$, $B=0.2$, $a=0.6$, $\mu =0$, $e=+0.2$: $l=0$ (right panel bottom [red]), $l=1$ (left panel top [magenta]); and $e=-0.2$: $l=0$ (left panel bottom [blue]), $l=1$ (right panel top [green]), $m=0$.

Figure 7

Real (left panel) and imaginary (right panel) parts of the fundamental ($n=0$) QNM as a function of $Q$ for $Q=0$, $2aMB/3$, $aMB$, $2aMB$, $B=0.2$, $a=0.6$, and $\mu =0$, from top to bottom: $l=m=1$, $e=+0.2$ (red online) and $e=-0.2$ (blue); $l=-m=1$, $e=-0.2$ (green) and $e=+0.2$ (magenta).

Figure 8

Real and imaginary parts of the fundamental ($n=0$) QNM as a function of $e$ for $\mu =0.1$, $a=0.25$ $Q=0.9$, $B=1440/749\approx 1.92$, $l=m=0$ (blue, bottom horizontal) $l=1$, $m=0$ (red, top horizontal), $l=1$, $m=1$ (cyan, top), $l=1$, $m=-1$ (green).

Figure 9

Grey-body factor of the Kerr-Newman black hole (left panel: $a=0.5$, $Q=0.1$; right panel: $a=0.5$, $Q=0.5$) in the magnetic field $B=2/3$ due to massless charged particles ($e=3/20$, $l=1$). From left to right: $m=-1$ negative charge particles, $m=-1$ positive charge particles, $m=0$ positive charge particles, $m=0$ negative charge particles, $m=1$ positive charge particles, $m=1$ negative charge particles. For the extremal black hole $m=0$, grey-body factors for the particles and antiparticles are the same (black line).

Figure 10

Energy emission rate of the Kerr-Newman black hole (left panels: $a=0.5$, $Q=0.1$, right panels: $a=0.5$, $Q=0.5$) without the magnetic field (top panels) and with the magnetic field $B=2/3$ (bottom panels) due to massless charged particles ($e=3/20$). The top (red) and bottom (blue) lines correspond, respectively, to the same and the opposite signs of the charges of the black hole and the emitted particles.

Figure 11

Angular momentum emission rate of the Kerr-Newman black hole (left panels: $a=0.5$, $Q=0.1$; right panels: $a=0.5$, $Q=0.5$) without the magnetic field (top panels) and with the magnetic field $B=2/3$ (bottom panels) due to massless charged particles ($e=3/20$). The top (red) and bottom (blue) lines correspond, respectively, to the same and the opposite signs of the charges of the black hole and the emitted particles.

Figure 12

Charge emission rate of the Kerr-Newman black hole (left panels: $a=0.5$, $Q=0.1$; right panels: $a=0.5$, $Q=0.5$) without the magnetic field (top panels) and with the magnetic field $B=2/3$ (bottom panels) due to massless charged particles ($e=3/20$).