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Register a new userSpontaneously scalarized black holes in dynamical Chern-Simons gravity: dynamics and equilibrium solutions
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In the present paper, we construct spontaneously scalarized rotating black hole solutions in dynamical Chern-Simons (dCS) gravity by following the scalar field evolution in the decoupling limit. For the range of parameters where the Kerr black hole becomes unstable within dCS gravity the scalar field grows exponentially until it reaches an equilibrium configuration that is independent of the initial perturbation. Interestingly, the $mathbb{Z}_2$ symmetry of the scalar field is broken and a strong maximum around only one of the rotational axes can be observed. The black hole scalar charge is calculated for two coupling functions suggesting that the main observations would remain qualitatively correct even if one considers coupling functions/coupling parameters producing large deviations from the Kerr solution beyond the decoupling limit approximation.
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Spinning black holes in dynamical Einstein-Chern-Simons gravity are constructed by directly solving the field equations, without resorting to any perturbative expansion. This model is obtained by adding to the Einstein-Hilbert action a particular higher-curvature correction: the Pontryagin density, linearly coupled to a scalar field. The spinning black holes are stationary, axi-symmetric, asymptotically flat generalisations of the Kerr solution of Einsteins gravity, but they possess a non-trivial (odd-parity) scalar field. They are regular on and outside the horizon and satisfy a generalized Smarr relation. We discuss the deviations from Kerr at the level of the spin and mass distribution, the horizon angular velocity, the ergo-region and some basic properties of geodesic motion. For sufficiently small values of the Chern-Simons coupling our results match those previously obtained using a perturbative approach.
We produce the first numerical relativity binary black hole gravitational waveforms in a higher-curvature theory beyond general relativity. In particular, we study head-on collisions of binary black holes in order-reduced dynamical Chern-Simons gravity. This is a precursor to producing beyond-general-relativity waveforms for inspiraling binary black hole systems that are useful for gravitational wave detection. Head-on collisions are interesting in their own right, however, as they cleanly probe the quasi-normal mode spectrum of the final black hole. We thus compute the leading-order dynamical Chern-Simons modifications to the complex frequencies of the post-merger gravitational radiation. We consider equal-mass systems, with equal spins oriented along the axis of collision, resulting in remnant black holes with spin. We find modifications to the complex frequencies of the quasi-normal mode spectrum that behave as a power law with the spin of the remnant, and that are not degenerate with the frequencies associated with a Kerr black hole of any mass and spin. We discuss these results in the context of testing general relativity with gravitational wave observations.
We present a scheme for generating first-order metric perturbation initial data for an arbitrary background and source. We then apply this scheme to derive metric perturbations in order-reduced dynamical Chern-Simons gravity (dCS). In particular, we solve for metric perturbations on a black hole background that are sourced by a first-order dCS scalar field. This gives us the leading-order metric perturbation to the spacetime in dCS gravity. We then use these solutions to compute black hole shadows in the linearly perturbed spacetime by evolving null geodesics. We present a novel scheme to decompose the shape of the shadow into multipoles parametrized by the spin of the background black hole and the perturbation parameter $varepsilon^2$. We find that we can differentiate the presence of a pure Kerr spacetime from a spacetime with a dCS perturbation using the shadow, allowing in part for a null-hypothesis test of general relativity. We then consider these results in the context of the Event Horizon Telescope.
Dynamical Chern-Simons gravity has an interesting feature that the parity violating term exists, and the coupling is determined by a dynamical scalar field. When the spacetime has spherical symmetry, the parity violating term vanishes, and then the metric of the Schwarzschild spacetime with vanishing scalar field is an exact solution of dynamical Chern-Simons gravity. The effect of the Chern-Simons coupling appears in the study of perturbation around the Schwarzschild spacetime. Due to the parity violating term, the odd parity metric perturbation and the perturbed scalar field are coupled, and the perturbed field equations take the form of the coupled system of the Schrodinger equations. We prove linear mode stability for a generic massive scalar.
The detection of gravitational waves from compact binary mergers by the LIGO/Virgo collaboration has, for the first time, allowed us to test relativistic gravity in its strong, dynamical and nonlinear regime, thus opening a new arena to confront general relativity (and modifications thereof) against observations. We consider a theory which modifies general relativity by introducing a scalar field coupled to a parity-violating curvature term known as dynamical Chern-Simons gravity. In this theory, spinning black holes are different from their general relativistic counterparts and can thus serve as probes to this theory. We study linear gravito-scalar perturbations of black holes in dynamical Chern-Simons gravity at leading-order in spin and (i) obtain the perturbed field equations describing the evolution of the perturbed gravitational and scalar fields, (ii) numerically solve these equations by direct integration to calculate the quasinormal mode frequencies for the dominant and higher multipoles and tabulate them, (iii) find strong evidence that these rotating black holes are linearly stable, and (iv) present general fitting functions for different multipoles for gravitational and scalar quasinormal mode frequencies in terms of spin and Chern-Simons coupling parameter. Our results can be used to validate the ringdown of small-spin remnants of numerical relativity simulations of black hole binaries in dynamical Chern-Simons gravity and pave the way towards future tests of this theory with gravitational wave ringdown observations
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