Abstract
We study the dynamical Chern-Simons gravity as an effective quantum field theory, and discuss a broad range of its parameter space where the theory is valid. Within that validity range, we show that slowly rotating black holes acquire novel geometric structures due to the gravitational dynamical Chern-Simons term. In particular, the rotating black-hole solutions get endowed with two caplike domains, emanating from the north and south poles in the standard Boyer-Lindquist coordinates. The domains extend out to a distance that is approximately a few percent of the black hole's size. The caplike domains have an unusual equation of state, pointing to nonstandard dynamics within the caps. In particular, the focusing condition for geodesics is violated in those domains. This in turn implies that the Hawking-Penrose singularity theorem cannot be straightforwardly applied to hypothetical probe matter placed within the Chern-Simons caps.
Highlights
AND OUTLINEDynamical Chern-Simons gravity [1,2] modifies the Einstein-Hilbert action with the addition of a parityviolating Chern-Simons form coupled to a derivative of a pseudoscalar field. dCS gravity is not an arbitrary extension of general relativity (GR), but rather has physical roots in particle physics [3] and string theory [4,5,6]. dCS gravity naturally emerges as an anomaly-canceling term through the Green-Schwarz mechanism [7]
We study the dynamical Chern-Simons gravity as an effective quantum field theory, and discuss a broad range of its parameter space where the theory is valid
We show that slowly rotating black holes acquire novel geometric structures due to the gravitational dynamical Chern-Simons term
Summary
Dynamical Chern-Simons (dCS) gravity [1,2] modifies the Einstein-Hilbert action with the addition of a parityviolating Chern-Simons form coupled to a derivative of a pseudoscalar field. dCS gravity is not an arbitrary extension of general relativity (GR), but rather has physical roots in particle physics [3] and string theory [4,5,6]. dCS gravity naturally emerges as an anomaly-canceling term through the Green-Schwarz mechanism [7]. General relativity is not a renormalizable theory, and the action in Eq (1) could only be part of an effective field theory that contains an infinite number of higher curvature terms, proportional to R2, R3, and so on, and their derivatives, supprespseffidffiffiffiffibffi y the respective powers of the Planck mass, MP 1⁄4 1= GN. CHERN-SIMONS CAPS FOR ROTATING BLACK HOLES pffiffiffiffiffiffiffiffiffi modulus of the scalar, ρ 1⁄4 ΣþΣ, acquire their masses due to the vacuum expectation value hΣi 1⁄4 μ These masses are proportional to the respective coupling constants and the energy scale μ. Quantum corrections will not generate a nonzero mass and potential for σ because of the shift symmetry, σ → σ þ const This symmetry is expected to be broken by nonperturbative quantum gravity effects and the pseudoscalar field would acquire a mass [24]. The latter is much higher than the scale of 10−2 eV, up to which precision gravity measurements have so far probed deviations from conventional gravity
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