Isolated and binary neutron stars in dynamical Chern-Simons gravity

Abstract

In Ref.[1], the Chern-Simons correction to the osculating orbital elements due to the dipole-dipole interaction for the scalar field was derived in Eq. (130) by integrating out the interaction Lagrangian, which was taken to be the kinetic term for the scalar field [Eq. (122) in [1]], using the scalar field solution. However, such kinetic term only leads to the left-hand side of the evolution equation for the scalar field, i.e.where J is the effective source term of the scalar field equation [2]. In order to obtain the correct interaction Lagrangian, one also needs to include the source term (L source ) that reproduces the right-hand side of the above evolution equation. The Lagrangian density for such an additional term is given by −ϑJ. Therefore, Eq. (126) needs to be changed towhere L source,int is the interaction part of the source term Lagrangian density. Notice that, by accounting for such additional term, the sign of the interaction Lagrangian now flips. This means that the sign in Eqs. (127), (129) and (130) needs to be reversed. The results in Sec. IX B are unaffected since we have neglected contribution from the dipole-dipole interaction because the spin of the secondary pulsar in the double binary pulsar is much smaller than that of the primary. We also report errors in App. B of [1]. In this appendix, we calculated dissipative corrections to the energy and angular momentum energy flux emitted from neutron star binaries based on calculations in [2]. However, some terms in the perturbed scalar and metric field equations were not properly accounted for in [2]. Taking these terms into account, we found that corrections to the gravitational energy and angular momentum flux due to metric perturbations enter at third post-Newtonian order relative to general relativity, which is of 1 post-Newtonian order higher than the effect due to the scalar field. Therefore, Apps. B.1.b and B.2.b in [1] are now irrelevant. We discuss this in more detail in [3].On the other hand, the scalar energy flux in App. B.1.a is affected as follows. First, the far-zone solution for the scalar field in Eq. (B3) becomesThen, the scalar energy flux in Eqs. (B5) and (B6) becomesrespectively. Finally, Eq. (B8) is corrected to T. Tanaka, Phys. Rev., D85, 064022 (2012), arXiv:1110.5950 [gr-qc].[3] K. Yagi, L. C. Stein, N. Yunes, and T. Tanaka, Phys. Rev., D93, 029902 (2016D93, 029902 ( ), arXiv:1110. We study isolated and binary neutron stars in dynamical Chern-Simons gravity. This theory modifies the Einstein-Hilbert action through the introduction of a dynamical scalar field coupled to the Pontryagin density. We here treat this theory as an effective model, working to leading order in the Chern-Simons coupling. We first construct isolated neutron star solutions in the slow-rotation expansion to quadratic order in spin. We find that isolated neutron stars acquire a scalar dipole charge that corrects its spin angular momentum to linear order in spin and corrects its mass and quadrupole moment to quadratic order in spin, as measured by ...

Extreme gravity tests with gravitational waves from compact binary coalescences: (I) inspiral–merger

“…Just as in the case of EdGB gravity, the calculation of (monopole) scalar charges (or sensitivities) is also crucial here to understand the emission of scalar radiation. The asymptotic behavior of the scalar field at spatial infinity has revealed that black holes have a rather large scalar charge [19,100], while the scalar charge of neutron stars is greatly suppressed [23,107]; the derivation of the latter result follows closely the explanation in EdGB gravity presented in the previous section. As in the EdGB case, this means that stars have a tiny scalar field, but this grows upon gravitational collapse, until the charge asymptotes that of isolated black holes.…”

Numerical binary black hole mergers in dynamical Chern-Simons gravity: Scalar field

“…All of the results that we present will be given in terms of powers of the dimensionless coupling ( /GM ). We will also compare to known post-Newtonian results [24], that were presented in terms of α YSYT…”

The Confrontation between General Relativity and Experiment

“…The PPN parameters for a non-dynamical version of the theory with α = κ and β = 0 are identical to those of GR; however, there is an additional, parity-even potential in the g 0 i component of the metric that does not appear in the standard PPN framework, given by Unfortunately, the non-dynamical version has been shown to be unstable [137], while the dynamical version is sufficiently complex that its observable consequences have been analyzed for only special situations [6, 444]. Alexander and Yunes [5] give a thorough review of Chern-Simons gravity.…”