Black hole merger estimates in Einstein-Maxwell and Einstein-Maxwell-dilaton gravity

The recent birth of gravitational wave astronomy invites a new generation of precision tests of general relativity. Signatures of black hole (BH) mergers must be systematically explored in a wide spectrum of modified gravity theories. Here, we turn to one such theory in which the initial value problem for BH mergers is well posed, the Einstein-Maxwell-dilaton system. We present conservative estimates for the merger parameters (final spins, quasinormal modes) based on techniques that have worked well for ordinary gravity mergers and utilize information extracted from test particle motion in the final BH metric. The computation is developed in parallel for the modified gravity BHs (we specifically focus on the Kaluza-Klein value of the dilaton coupling, for which analytic BH solutions are known) and ordinary Kerr-Newman BHs. We comment on the possibility of obtaining final BHs with spins consistent with current observations.

Figure 1

The final spin $|A_f/M|$ vs $Q/M$. The filled area illustrates possible values of $A_f/M$, while the blue line represents the extremal value of $|A_f/M|$. The final spin decreases as $Q/M$ increases.

Figure 2

The final spin $A_f/M$ vs $\nu$ for $\chi =0$.

Figure 3

The final spin $A_f/M$ vs $\nu$ for $\chi =0.4$.

Figure 4

The final spin $A_f/M$ plotted against varying $\nu$ and $Q/M$ for the case $\chi =0.98$.

Figure 5

ISCO radius $r_{\mathrm{ISCO}}/M$ vs $e$ for $A=0.5M$.

Figure 6

Angular momentum per mass $l(r_{\mathrm{ISCO}})/M$ vs $e$ for $A=0.5M$.

Figure 7

The final spin $A_f/M$ vs $\nu$ for $\chi =0$, and $Q=0.4M$.

Figure 8

The final spin $A_f/M$ vs $\nu$ for $\chi =0$, and $Q=M$.

Figure 9

The final spin $A_f/M$ vs $\nu$ for $\chi =0.4$, and $Q=0.8M$.

Figure 10

${\mathrm{\Omega }}_c$ and $\lambda$ vs the charge ratio $Q_2/Q_1$ for different $Q$ (KK BHs of equal masses with zero initial spins).

Figure 11

${\mathrm{\Omega }}_c$ and $\lambda$ vs the total charge $Q$ (KK BHs of equal masses with zero initial spins).

Figure 12

ISCO radius $r_{\mathrm{ISCO}}/M$ vs $e$ for $a=0.5M$ for Kerr-Newman BHs.

Figure 13

Angular momentum per mass $l(r_{\mathrm{ISCO}})/M$ vs $e$ for $a=0.5M$ for Kerr-Newman BHs.

Figure 14

Kerr-Newman: The final spin $A_f/M$ vs $\nu$ for $Q=0.4M$, and $\chi =0$.

Figure 15

Kerr-Newman: The final spin $A_f/M$ vs $\nu$ for $Q=0.4M$, and $\chi =0.4$.

Figure 16

Kerr-Newman: ${\mathrm{\Omega }}_c$ and $\lambda$ vs the charge ratio for various values of the total charge, in the equal-mass case and zero initial spins.

Figure 17

Kerr-Newman: ${\mathrm{\Omega }}_c$ and $\lambda$ vs the total charge, in the equal-mass case and zero initial spins.

Figure 18

$A_f/M$ vs $Q_2/Q_1$ for Kaluza-Klein (left) and Kerr-Newman (right) BHs.

Figure 19

Difference of $A_f/M$ between Kaluza-Klein and Kerr-Newman BHs vs $Q_2/Q_1$

Figure 20

$A_f/M$ vs $Q/M$ (solid line) KN BHs, (dashed line) KK BHs, in the equal-charge case. (The value for Kerr BHs is indicated for reference).

Figure 21

$A_f/M$ vs $Q/M$ (solid lines) KN BHs, (dashed line) KK BHs, for various charge ratios. (The value for the Kerr BH is indicated for reference).

Figure 22

$\chi$ vs $Q/M$ that produce $A_f/M=0.66$. (solid lines) KN BHs, (dashed line) KK BHs, for various charge ratios.

Figure 23

Fundamental frequencies of QNMs: (solid lines) KN BHs, (dashed line) KK BHs, for various charge ratios.

Figure 24

Fundamental frequencies of QNMs: (solid lines) KN BHs, (dashed line) KK BHs, for various total charges compatible with final spin of 0.66