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Register a new userGravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory
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Added by
Massimiliano Maria Riva
Publication date
2021
fields
Physics
and research's language is
English
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We study the gravitational radiation emitted during the scattering of two spinless bodies in the post-Minkowskian Effective Field Theory approach. We derive the conserved stress-energy tensor linearly coupled to gravity and the classical probability amplitude of graviton emission at leading and next-to-leading order in the Newtons constant $G$. The amplitude can be expressed in compact form as one-dimensional integrals over a Feynman parameter involving Bessel functions. We use it to recover the leading-order radiated angular momentum expression. Upon expanding it in the relative velocity between the two bodies $v$, we compute the total four-momentum radiated into gravitational waves at leading-order in $G$ and up to an order $v^8$, finding agreement with what was recently computed using scattering amplitude methods. Our results also allow us to investigate the zero frequency limit of the emitted energy spectrum.
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Using the recently established formalism of a worldline quantum field theory (WQFT) description of the classical scattering of two spinless black holes, we compute the far-field time-domain waveform of the gravitational waves produced in the encounter at leading order in the post-Minkowskian (weak field, but generic velocity) expansion. We reproduce previous results of Kovacs and Thorne in a highly economic way. Then using the waveform we extract the leading-order total radiated angular momentum and energy (including differential results). Our work may enable crucial improvements of gravitational-wave predictions in the regime of large relative velocities.
Effective field theories describing gravity coupled to matter are investigated, allowing for operators of arbitrary mass dimension. Terms violating local Lorentz and diffeomorphism invariance while preserving internal gauge symmetries are included. The theoretical framework for violations of local Lorentz and diffeomorphism invariance and associated conceptual issues are discussed, including transformations in curved and approximately flat spacetimes, the treatment of various types of backgrounds, the implications of symmetry breaking, and the no-go constraints for explicit violation in Riemann geometry. Techniques are presented for the construction of effective operators, and the possible terms in the gravity, gauge, fermion, and scalar sectors are classified and enumerated. Explicit expressions are obtained for terms containing operators of mass dimension six or less in the effective action for General Relativity coupled to the Standard Model of particle physics. Special cases considered include Einstein-Maxwell effective field theories and the limit with only scalar coupling constants.
Advanced methods for computing perturbative, quantum-gravitational scattering amplitudes show great promise for improving our knowledge of classical gravitational dynamics. This is especially true in the weak-field and arbitrary-speed (post-Minkowskian, PM) regime, where the conservative dynamics at 3PM order has been recently determined for the first time, via an amplitude calculation. Such PM results are most relevantly applicable to relativistic scattering (unbound orbits), while bound/inspiraling binary systems, the most frequent sources of gravitational waves for the LIGO and Virgo detectors, are most suitably modeled by the weak-field and slow-motion (post-Newtonian, PN) approximation. Nonetheless, it has been suggested that PM results can independently lead to improved modeling of bound binary dynamics, especially when taken as inputs for effective-one-body (EOB) models of inspiraling binaries. Here, we initiate a quantitative study of this possibility, by comparing PM, EOB and PN predictions for the binding energy of a two-body system on a quasi-circular inspiraling orbit against results of numerical relativity (NR) simulations. The binding energy is one of the two central ingredients (the other being the gravitational-wave energy flux) that enters the computation of gravitational waveforms employed by LIGO and Virgo detectors, and for (quasi-)circular orbits it provides an accurate diagnostic of the conservative sector of a model. We find that, whereas 3PM results do improve the agreement with NR with respect to 2PM (especially when used in the EOB framework), it is crucial to push PM calculations at higher orders if one wants to achieve better performances than current waveform models used for LIGO/Virgo data analysis.
We develop an Effective Field Theory (EFT) formalism to solve for the conservative dynamics of binary systems in gravity via Post-Minkowskian (PM) scattering data. Our framework combines a systematic EFT approach to compute the deflection angle in the PM expansion, together with the Boundary-to-Bound (B2B) dictionary introduced in [1910.03008, 1911.09130]. Due to the nature of scattering processes, a remarkable reduction of complexity occurs both in the number of Feynman diagrams and type of integrals, compared to a direct EFT computation of the potential in a PM scheme. We provide two illustrative examples. Firstly, we compute all the conservative gravitational observables for bound orbits to 2PM, which follow from only one topology beyond leading order. The results agree with those in [1910.03008, 1911.09130], obtained through the impetus formula applied to the classical limit of the one loop amplitude in Cheung et al. [1808.02489]. For the sake of comparison we reconstruct the conservative Hamiltonian to 2PM order, which is equivalent to the one derived in [1808.02489] from a matching calculation. Secondly, we compute the scattering angle due to tidal effects from the electric- and magnetic-type Love numbers at leading PM order. Using the B2B dictionary we then obtain the tidal contribution to the periastron advance. We also construct a Hamiltonian including tidal effects at leading PM order. Although relying on (relativistic) Feynman diagrams, the EFT formalism developed here does not involve taking the classical limit of a quantum amplitude, neither integrals with internal massive fields, nor additional matching calculations, nor spurious (super-classical) infrared singularities. By construction, the EFT approach can be automatized to all PM orders.
Theories of scalars and gravity, with non-minimal interactions, $sim (M_P^2 +F(phi) )R +L(phi)$, have graviton exchange induced contact terms. These terms arise in single particle reducible diagrams with vertices $propto q^2$ that cancel the Feynman propagator denominator $1/q^2$ and are familiar in various other physical contexts. In gravity these lead to additional terms in the action such as $sim F(phi) T_mu^mu(phi)/M_P^2$ and $F(phi)partial^2 F(phi)/M_P^2$. The contact terms are equivalent to induced operators obtained by a Weyl transformation that removes the non-minimal interactions, leaving a minimal Einstein-Hilbert gravitational action. This demonstrates explicitly the equivalence of different representations of the action under Weyl transformations, both classically and quantum mechanically. To avoid such hidden contact terms one is compelled to go to the minimal Einstein-Hilbert representation.
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