Greybody factor for massive fermion emitted by a black hole in de Rham-Gabadadze-Tolley massive gravity theory

The greybody factor of the massive Dirac field around the black hole in the dRGT massive gravity theory is investigated using the rigorous bound and the WKB approximation methods. In both methods, the greybody factor significantly depends on the shape of the potential. If the potential is smaller, there is more probability for the Dirac field to transmit through the black hole, therefore, the greybody factor is higher. Moreover, there exists a critical mass of the Dirac field such that the greybody factor is maximum. By comparing the results from these two methods, we argue that it is useful to use the rigorous bound method for the low potential cases, while using the WKB approximation method for the high potential cases.

Figure 1

This figure shows the horizon structure of the dS solution for parameters ${\alpha }_g=\tilde{M}=1$, $c_2=\frac{-0.2}{3}$.

Figure 2

The left panel shows the potential for Sch, Sch-dS, and dRGT black holes with ${\alpha }_g=M=1$, $c_2=-1/300$, ${\beta }_m=0.755$, and $l=0$. The right panel shows the corresponding greybody factor bound.

Figure 3

The left panel shows the potential for dRGT black holes with ${\alpha }_g=M=1$, $c_2=-2/300$ and $l=1$. The right panel shows the corresponding greybody factor bound.

Figure 4

The left panel shows the potential for dRGT black holes with ${\alpha }_g=M=1$, ${\beta }_m=0.6$, and $l=1$. The right panel shows the corresponding greybody factor bound.

Figure 5

The left panel shows the potential for dRGT black holes with ${\alpha }_g=M=1$, $c_2=-2/300$ and ${\beta }_m=0.5$. The right panel shows the corresponding greybody factor bound.

Figure 6

The greybody factor bound is evaluated using the full expression (solid line) and approximated expression (dashed line) with ${\alpha }_g=M=1$, ${\beta }_m=0.8$, $c_2=-0.1/3$.

Figure 7

The greybody factor bound is evaluated using the full expression (solid-blue line) and approximated expression (dashed-black line) with ${\alpha }_g=M=1$, ${\beta }_m=0.8$, $c_2=-0.1/3$, $\omega =1$.

Figure 8

The greybody factor bound is evaluated using the full expression (solid blue line) and approximated expression (dashed black line) with ${\alpha }_g=M=1$, ${\beta }_m=0.8$, $c_2=-0.1/3$, $\omega =1$.

Figure 9

The greybody factor bound (left panel) and the potential with various value of $\mu =m/\lambda$ where ${\alpha }_g=M=1$, ${\beta }_m=0.8$, $c_2=-0.1/3$.

Figure 10

The greybody factor for massless Dirac particle with ${\beta }_m=0.5$, $c_2=-2/300$ and change $l$.

Figure 11

The greybody factor for massless Dirac particle corresponding to the effective potential in Fig. 3 and Fig. 4.

Figure 12

The greybody factor and the effective potential for massive Dirac particle with ${\beta }_m=0.5$, $c_2=-2/300$, and $l=5$.

Figure 13

The greybody factor and the effective potential for massive Dirac particle with ${\beta }_m=0.5$, $c_2=-3/300$, and $l=5$.

Figure 14

The greybody factor and the effective potential for massive Dirac particle with ${\beta }_m=0.7$, $c_2=-2/300$, and $l=5$.

Figure 15

The greybody factors and the effective potentials for massive Dirac particle in Schwarzschild and Schwarzschild-dS spacetimes.

Figure 16

Example of efficient areas for greybody factors with the parameters ${\beta }_m=0.7$, $c_2=-2/300$, $l=5$, and $\mu =0.03$, 0.05, 0.1, 0.2.