[abridged] Chern-Simons (CS) modified gravity is a 4D effective theory that descends both from string theory and loop quantum gravity, and that corrects the Einstein-Hilbert action by adding the product of a scalar field and the parity-violating, Pontryagin density. In this theory, the gravitational field of spinning black holes is described by a modified Kerr geometry whose multipole moments deviate from the Kerr ones only at the fourth multipole, l = 4. We investigate possible signatures of this theory in the gravitational wave emission produced in the inspiral of stellar compact objects into massive black holes, both for intermediate- and extreme-mass ratios. We use the semi-relativistic approximation, where the trajectories are geodesics of the massive black hole geometry and the gravitational waveforms are obtained from a multipolar decomposition of the radiative field. The main CS corrections to the waveforms arise from modifications to the geodesic trajectories, due to changes to the massive black hole geometry, and manifest themselves as an accumulating dephasing relative to the general relativistic case. We also explore the propagation and the stress-energy tensor of gravitational waves in this theory. We find that, although this tensor has the same form as in General Relativity, the energy and angular momentum balance laws are indeed modified through the stress-energy tensor of the CS scalar field. These balance laws could be used to describe the inspiral through adiabatic changes in the orbital parameters, which in turn would enhance the dephasing effect. Gravitational-wave observations of intermediate- or extreme-mass ratio inspirals with advanced ground detectors or with LISA could use such dephasing to test the dynamical theory to unprecedented levels.
Deep Dive into Extreme- and Intermediate-Mass Ratio Inspirals in Dynamical Chern-Simons Modified Gravity.
[abridged] Chern-Simons (CS) modified gravity is a 4D effective theory that descends both from string theory and loop quantum gravity, and that corrects the Einstein-Hilbert action by adding the product of a scalar field and the parity-violating, Pontryagin density. In this theory, the gravitational field of spinning black holes is described by a modified Kerr geometry whose multipole moments deviate from the Kerr ones only at the fourth multipole, l = 4. We investigate possible signatures of this theory in the gravitational wave emission produced in the inspiral of stellar compact objects into massive black holes, both for intermediate- and extreme-mass ratios. We use the semi-relativistic approximation, where the trajectories are geodesics of the massive black hole geometry and the gravitational waveforms are obtained from a multipolar decomposition of the radiative field. The main CS corrections to the waveforms arise from modifications to the geodesic trajectories, due to changes t
The experimental verification of symmetry breaking is one of the most powerful tools to understand in which direction to extend the current canon toward more fundamental physical theories. For example, the experimental confirmation of the violation of charge conjugation, parity transformation and time-reversal symmetries in elementary particle interactions forced the improvement of the quantum field theory of particles into what is today the standard model. Similarly, violation of symmetries in gravitational interactions can push toward generalizations of General Relativity (GR) by providing the first experimental evidence of high-energy extensions.
Gravitational parity violation can be tuned by the inclusion of a Pontryagin term in the Einstein-Hilbert action, which defines an effective, four-dimensional gravitational theory: Chern-Simons (CS) modified gravity [1]. In fact, the inclusion of such a term in the action is inescapable in four-dimensional compactifications of perturbative string theory (i.e. Type I, IIb, Heterotic, etc.) due to the Green-Schwarz anomaly-canceling mechanism [2]. This fact can also be extended to the nonperturbative sector in the presence of Ramond-Ramond scalars (D-instanton charges) due to duality symmetries [3]. Such a term also arises naturally in loop quan-tum gravity when the Barbero-Immirzi parameter is promoted to a scalar field coupled to the Nieh-Yan invariant [4,5].
The action of Dynamical CS Modified Gravity (DC-SMG) consists of the Einstein-Hilbert term plus the product of a scalar field and the Pontryagin density (the contraction of the Riemann curvature tensor with its dual), plus the action for this scalar field and/or other matter fields. The correction proportional to the Pontryagin density modifies the field equations for the metric components by adding two extra terms to the Einstein equations: the so-called C-tensor and an stress-energy tensor for the scalar field. The C-tensor depends on derivatives of the CS scalar and the contraction of the Levi-Civita tensor with covariant derivatives of the Ricci tensor and the dual Riemann tensor. In addition, the variation of the action with respect to the CS scalar field leads to an equation of motion for this field, which is sourced by the Pontryagin density.
The CS gravitational modification has been investigated mostly in the non-dynamical framework, in which the scalar field is non-dynamical (there is no kinetic term for it in the action), and hence it is assumed to be an a priori prescribed spacetime function. Such studies include an analysis of exact solutions [1,6], approximate solutions [1,7,8,9,10,11], matter interac-tions [12,13], cosmology [3,14,15,16], and astrophysical tests [17,18,19]. Non-dynamical CS modified gravity has been shown to be theoretically problematic in relation to Schwarzschild black hole perturbation theory [20], the existence of stationary and axisymmetric solutions [21], and the uniqueness of solutions of the theory [22].
The detailed study of the dynamical formulation of CS modified gravity has only recently begun. This paper is the second in a series that deals with the details of the dynamics of CS modified, spinning black holes. In the first paper [22], henceforth Paper I, an approximate solution was found for a spinning black hole, using the slow-rotation approximation and a small-coupling approximation. The first type of approximation restricts attention to black holes with small angular momentum per unit mass, while the second one allows one to search for small CS deformations of known GR solutions. The new solution corresponds to a deformation of the Kerr metric whose deviations fall off with a high power of the distance to the black hole.
In this paper, we concentrate on the study of intermediate and extreme-mass ratio inspirals (IMRIs and EMRIs respectively) in the context of DCSMG. Such systems consist of a small compact object (SCO) (with masses in the range 1 -30 M ⊙ ) orbiting around a (spinning) massive black hole (MBH), (with masses in the range 10 4 -10 7 M ⊙ ) in the case of EMRIs, and an intermediate-mass black hole (IMBH) (with masses in the range 10 2 -10 4 M ⊙ ; see [23] for a review on the evidence of the existence of IMBHs) in the case of IMRIs. Another IMRI possibility would be that of an IMBH falling into a MBH, a system with obviously also an intermediate mass ratio (see [24] and references therein). The mass ratios involved are then in the range (10 -2 -10 -4 ) for IMRIs and (10 -4 -10 -7 ) for EMRIs.
EMRIs (and IMRIs involving a IMBH-MBH binary) are important sources of gravitational waves (GWs) for future space detectors [25] as the Laser Interferometer Space Antenna (LISA) [26,27,28,29,30], whereas IMRIs are important sources for second generation ground based detectors (see [31,32]), such as Advanced LIGO [33] and Advanced VIRGO [34], and for future planned third generation detectors as the Einstein Telescope [35]. Both IMRIs and EMRIs are high-pre
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