Quasinormal ringing of black holes in Einstein-aether theory

The gravitational consequence of local Lorentz violation (LV) should show itself in derivation of the characteristic quasinormal ringing of black hole mergers from their general relativity case. In this paper, we study quasinormal modes (QNMs) of the scalar and electromagnetic field perturbations to Einstein-aether black holes. We find that quasinormal ringing of the first kind aether black hole is similar to that of another Lorentz violation model—the QED-extension limit of standard model extension. These similarities between completely different backgrounds may imply that LV in gravity sector and LV in matter sector have some connections between themselves: damping quasinormal ringing of black holes more rapidly and prolonging its oscillation period. By compared to Schwarzschild black hole, both the first and the second kind aether black holes have larger damping rate and smaller real oscillation frequency of QNMs. And the differences are from 0.7 percent to 35 percents, those could be detected by new generation of gravitational antennas.

Figure 1

The left both figures are the effective potential of scalar field perturbations $V_s$ near the first kind aether black hole ($M=1$) with different coefficients $c_{13}$. The third figure is for the electromagnetic field perturbations $V_e$.

Figure 2

The left both figures are the effective potential of scalar field perturbations $V_s$ near the second kind aether black hole ($M=1$) with different coefficients $c_{13}$ and fixed coefficient $c_{14}=0.2$. The third figure is for the electromagnetic field perturbations $V_e$.

Figure 3

The relationship between the real and imaginary parts of quasinormal frequencies of the scalar field in the background of the first kind aether black hole with the decreasing of $c_{13}$.

Figure 4

The real (left) and imaginary (right) parts of quasinormal frequencies of the scalar field in the background of the first kind aether black hole with different $c_{13}$.

Figure 5

The real (left) and imaginary (right) parts of quasinormal frequencies of the scalar field in the background of the first kind aether black hole with different $c_{13}$.

Figure 6

The relationship between the real and imaginary parts of quasinormal frequencies of the electromagnetic field in the background of the first kind aether black hole with the decreasing of $c_{13}$.

Figure 7

The relationship between the real and imaginary parts of quasinormal frequencies of the scalar field in the background of the second kind aether black hole with the decreasing of $c_{13}$.

Figure 8

The real (left) and imaginary (right) parts of quasinormal frequencies of the scalar field in the background of the second kind aether black hole with different $c_{13}$.

Figure 9

The relationship between the real and imaginary parts of quasinormal frequencies of the electromagnetic field in the background of the second kind aether black hole with the decreasing of $c_{13}$.