Quadrupole moments of rapidly rotating compact objects in dilatonic Einstein-Gauss-Bonnet theory

We consider rapidly rotating black holes and neutron stars in dilatonic Einstein-Gauss-Bonnet (EGBd) theory and determine their quadrupole moments, which receive a contribution from the dilaton. The quadrupole moment of EGBd black holes can be considerably larger than the Kerr value. For neutron stars, the universality property of the $\widehat{I}$-$\widehat{Q}$ relation between the scaled moment of inertia and the scaled quadrupole moment appears to extend to EGBd theory.

Figure 1

(a) The scaled quadrupole moment $\widehat{Q}=QM/J^2$ is shown versus the scaled angular momentum $j=J/M^2$ for fixed values of the dimensionless horizon angular velocity ${\mathrm{\Omega }}_{\mathrm{H}}{\alpha }^{1/2}$. The shaded area represents the domain of existence of the EBGd black holes. (b) The scaled moment of inertia $\widehat{I}=J/({\mathrm{\Omega }}_{\mathrm{H}}{M}^3)$ is shown versus the scaled quadrupole moment $\widehat{Q}$ for fixed values of $j$. The dots indicate the corresponding values of the Kerr black holes. The dotted curve corresponds to the boundary of the domain of existence given by the critical solutions. The straight dotted lines represent the perturbative results of Ref. [12].

Figure 2

(a) The quadrupole moment $Q$ in units of $M_{\odot }·{\mathrm{km}}^2$ versus the angular velocity $\mathrm{\Omega }$ in Hz for fixed scaled angular momentum $j=0.4$, GB couplings $\alpha =0$, 1 and 2, the polytropic EOS DI-II [33] and the approximated FPS EOS [34]. (b) The scaled moment of inertia $\widehat{I}$ versus the scaled quadrupole moment $\widehat{Q}$ for the same set of solutions.