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Register a new userStability analysis of Schwarzschild black holes in dynamical Chern-Simons gravity
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Masashi Kimura
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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.
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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.
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