by Binétruy, Pierre and Bohé, Alejandro and Caprini, Chiara and Dufaux, Jean-François
46 pages, 12 figures

We review the main cosmological backgrounds of gravitational waves accessible to detectors in space sensitive to the range $latex 10^{-4}$ to $latex 10^{-1}$ Hz, with a special emphasis on those backgrounds due to phase transitions or networks of cosmic strings. We apply this to identify the scientific potential of the NGO/eLISA mission of ESA, regarding the detectability of such cosmological backgrounds.

by Alsing, Justin and Berti, Emanuele and Will, Clifford and Zaglauer, Helmut
19 pages, 2 figures, 2 tables

We derive the equations of motion, the periastron shift, and the gravitational radiation damping for quasicircular compact binaries in a massive variant of the Brans-Dicke theory of gravity. We also study the Shapiro time delay and the Nordtvedt effect in this theory. By comparing with recent observational data, we put bounds on the two parameters of the theory: the Brans-Dicke coupling parameter \omega_{BD} and the scalar mass m_s. We find that the most stringent bounds come from Cassini measurements of the Shapiro time delay in the Solar System, that yield a lower bound \omega_{BD}>40000 for scalar masses m_s1000 for m_s1250 for m_s<10^{-20} eV. A first estimate suggests that bounds comparable to the Shapiro time delay may come from observations of radiation damping in the eccentric white dwarf-neutron star binary PSR J1141-6545, but a quantitative prediction requires the extension of our work to eccentric orbits.

by Chen, Songbai and Jing, Jiliang
13 pages, 5 figures. References added, Expanded discussion of the marginally stable orbit and its consequence. arXiv admin note: substantial text overlap with arXiv:1106.5183

We study the accretion process in the thin disk around a rotating non-Kerr black hole with a deformed parameter and an unbound rotation parameter. Our results show that the presence of the deformed parameter $latex \epsilon$ modifies the standard properties of the disk. For the case in which the black hole is more oblate than a Kerr black hole, the larger deviation leads to the smaller energy flux, the lower radiation temperature and the fainter spectra luminosity in the disk. For the black hole with positive deformed parameter, we find that the effect of the deformed parameter on the disk becomes more complicated. It depends not only on the rotation direction of the black hole and the orbit particles, but also on the sign of the difference between the deformed parameter $latex \epsilon$ and a certain critical value $latex \epsilon_{c}$. These significant features in the mass accretion process may provide a possibility to test gravity in the strong field regime in future astronomical observations.

by Yagi, Kent and Stein, Leo C. and Yunes, Nicolas and Tanaka, Takahiro
26 pages, 3 figures, 2 tables; submitted to PRD

We consider a general class of quantum gravity-inspired, modified gravity theories, where the Einstein-Hilbert action is extended through the addition of all terms quadratic in the curvature tensor coupled to scalar fields with standard kinetic energy. This class of theories includes Einstein-Dilaton-Gauss-Bonnet and Chern-Simons modified gravity as special cases. We analytically derive and solve the coupled field equations in the post-Newtonian approximation, assuming a comparable-mass, spinning black hole binary source in a quasi-circular, weak-field/slow-motion orbit. We find that a naive subtraction of divergent piece associated with the point-particle approximation is ill-suited to represent compact objects in these theories. Instead, we model them by appropriate effective sources built so that known strong-field solutions are reproduced in the far-field limit. In doing so, we prove that black holes in Einstein-Dilaton-Gauss-Bonnet and Chern-Simons theory can have hair, while neutron stars have no scalar monopole charge, in diametrical opposition to results in scalar-tensor theories. We then employ techniques similar to the direct integration of the relaxed Einstein equations to obtain analytic expressions for the scalar field, metric perturbation, and the associated gravitational wave luminosity measured at infinity. We find that scalar field emission mainly dominates the energy flux budget, sourcing electric-type (even-parity) dipole scalar radiation and magnetic-type (odd-parity) quadrupole scalar radiation, correcting the General Relativistic prediction at relative -1PN and 2PN orders. Such modifications lead to corrections in the emitted gravitational waves that can be mapped to the parameterized post-Einsteinian framework. Such modifications could be strongly constrained with gravitational wave observations.

by Mirshekari, Saeed and Yunes, Nicolas and Will, Clifford M.
11 pages, 3 figures, 2 tables. Submitted to Phys. Rev. D

Modified gravity theories generically predict a violation of Lorentz invariance, which may lead to a modified dispersion relation for propagating modes of gravitational waves. We construct a parametrized dispersion relation that can reproduce a range of known Lorentz-violating predictions and investigate their impact on the propagation of gravitational waves. A modified dispersion relation forces different wavelengths of the gravitational wave train to travel at slightly different velocities, leading to a modified phase evolution observed at a gravitational-wave detector. We show how such corrections map to the waveform observable and to the parametrized post-Einsteinian framework, proposed to model a range of deviations from General Relativity. Given a gravitational-wave detection, the lack of evidence for such corrections could then be used to place a constraint on Lorentz violation. The constraints we obtain are tightest for dispersion relations that scale with small power of the graviton’s momentum and deteriorate for a steeper scaling.

by Harada, Tomohiro and Kimura, Masashi
17 pages, no figure

An inspiralling object of mass $latex \mu$ around a Kerr black hole of mass $latex M (\gg \mu)$ experiences a continuous transition near the innermost stable circular orbit from adiabatic inspiral to plunge into the horizon as gravitational radiation extracts its energy and angular momentum. We investigate the collision of such an object with a generic counterpart around a Kerr black hole. We find that the angular momentum of the object is fine-tuned through gravitational radiation and that the high-velocity collision of the object with a generic counterpart naturally occurs around a nearly maximally rotating black hole. We also find that the centre-of-mass energy can be far beyond the Planck energy for dark matter particles colliding around a stellar mass black hole and as high as $latex 10^{58}$ erg for stellar mass compact objects colliding around a supermassive black hole, where the present transition formalism is well justified. Therefore, rapidly rotating black holes can accelerate objects inspiralling around them to energy high enough to be of great physical interest.

by Levi, Michele
24 pages, revtex4-1, 5 figures

We calculate the next-to-next-to-leading order (NNLO) spin1-spin2 dynamics of a compact binary evaluated at fourth post-Newtonian (PN) order. We use an effective field theory (EFT) approach, and first demonstrate here the ability of the EFT approach to go at NNLO in the PN corrections of spin effects. The NNLO spin1-spin2 interaction sector includes contributions from diagrams, which are not pure spin1-spin2 diagrams, as they arise from other sectors. These diagrams contribute through the leading order spin accelerations and precessions, that should be first taken into account here. The EFT calculation is carried out in terms of the nonrelativistic gravitational (NRG) fields. The fact that the spin is derivative-coupled adds significantly to the complexity of computations. In particular, for the irreducible two-loop diagrams, which are the most complicated in this sector, irreducible two-loop tensor integrals up to order 4 are encountered. Moreover, not all of the benefits of the NRG fields apply to spin interactions, as all possible diagram topologies are realized at each order of G included. Still, the NRG fields remain advantageous, and thus there was no use of automated computations in this work. Our final result can be reduced, and a NNLO spin1-spin2 Hamiltonian can be derived from it.

by Hartung, Johannes and Steinhoff, Jan
7 pages, submitted to AdP

We present the next-to-next-to-leading order post-Newtonian (PN) spin(1)-spin(2) Hamiltonian for two self-gravitating spinning compact objects. If both objects are rapidly rotating, then the corresponding interaction is comparable in strength to a 4PN effect. The Hamiltonian is checked via the global Poincare algebra with the center-of-mass vector uniquely determined by an ansatz.

by Galley, Chad R.
For Part 1 of this series, see arXiv:1012.4488. 20 pages, 7 figures

The motion of a small compact object (SCO) in a background spacetime is investigated further in a class of model nonlinear scalar field theories having a perturbative structure analogous to the General Relativistic description of extreme mass ratio inspirals (EMRIs). We derive regular expressions for the scalar perturbations generated by the SCO’s motion valid through third order in $latex \epsilon$, the size of the SCO to the background curvature length scale. Our expressions are compared to those calculated through second order in $latex \epsilon$ by Rosenthal in [E. Rosenthal, CQG 22, S859 (2005)] and found to agree but our procedure for regularizing the scalar perturbations is considerably simpler. Following the Detweiler-Whiting (DW) scheme, we use our regular expressions for the field and derive the regular self-force corrections through third order. We find agreement with our previous derivation based on a variational principle of an effective action for the worldline associated with the SCO thus demonstrating the internal consistency of our formalism. This also explicitly demonstrates that the DW decomposition of Green’s functions is a valid and practical method of self force computation at higher orders in perturbation theory and, as we show in an appendix, at all orders in perturbation theory. Finally, we identify a master source from which all other physically relevant quantities are derivable. Knowing the master source perturbatively allows one to construct the waveform measured by an observer, the regular part of the field on the worldline, the regular part of the self force, and orbital quantities such as shifts of the innermost stable circular orbit, etc. The existence of a master source together with the regularization methods implemented in this series should be indispensable for derivations of higher-order gravitational self force corrections.

by Pani, Paolo and Cardoso, Vitor and Gualtieri, Leonardo
RevTex4, 18 pages, 7 figures, 1 table

Dynamical Chern-Simons gravity is an interesting extension of General Relativity, which finds its way in many different contexts, including string theory, cosmological settings and loop quantum gravity. In this theory, the gravitational field is coupled to a scalar field by a parity-violating term, which gives rise to characteristic signatures. Here we investigate how Chern-Simons gravity would affect the quasi-circular inspiralling of a small, stellar-mass object into a large non-rotating supermassive black hole, and the accompanying emission of gravitational and scalar waves. We find the relevant equations describing the perturbation induced by the small object, and we solve them through the use of Green’s function techniques. Our results show that for a wide range of coupling parameters, the Chern-Simons coupling gives rise to an increase in total energy flux, which translates into a fewer number of gravitational-wave cycles over a certain bandwidth. For space-based gravitational-wave detectors such as LISA, this effect can be used to constrain the coupling parameter effectively.

by Will, Clifford M.
9 pages, 2 figures, submitted to Proceedings of the National Academy of Sciences (US)

The post-Newtonian approximation is a method for solving Einstein’s field equations for physical systems in which motions are slow compared to the speed of light and where gravitational fields are weak. Yet it has proven to be remarkably effective in describing certain strong-field, fast-motion systems, including binary pulsars containing dense neutron stars and binary black hole systems inspiraling toward a final merger. The reasons for this effectiveness are largely unknown. When carried to high orders in the post-Newtonian sequence, predictions for the gravitational-wave signal from inspiraling compact binaries will play a key role in gravitational-wave detection by laser-interferometric observatories.

by Harada, Tomohiro and Kimura, Masashi
21 pages, 3 figures, submitted to PRD

We obtain an explicit expression for the center-of-mass (CM) energy of two colliding general geodesic massive and massless particles at any spacetime point around a Kerr black hole. Applying this, we show that the CM energy can be arbitrarily high only in the limit to the horizon and then derive a formula for the CM energy of two general geodesic particles colliding near the horizon in terms of the conserved quantities of each particle and the polar angle. We present the necessary and sufficient condition for the CM energy to be arbitrarily high in terms of the conserved quantities of each particle. To have an arbitrarily high CM energy, the angular momentum of either of the two particles must be fine-tuned to the critical value $latex L_{i}=\Omega_{H}^{-1}E_{i}$, where $latex \Omega_{H}$ is the angular velocity of the horizon and $latex E_{i}$ and $latex L_{i}$ are the energy and angular momentum of particle $latex i$ ($latex =1,2$), respectively. We show that, in the direct collision scenario, the collision with an arbitrarily high CM energy can occur near the horizon of maximally rotating black holes not only at the equator but also on a belt centered at the equator. If the critical particle is massless, this belt lies between latitudes $latex \pm acos(\sqrt{3}-1)\simeq \pm 42.94^{\circ}$. If the critical particle is massive, the highest absolute value of the latitude depends on the specific energy of the critical particle but rises up to the same value as the specific energy is increased to infinity. This is also true in the scenario through the collision of a last stable orbit particle.

by Cen, Renyue
6 pages, no figure, submitted to the Astrophysical Journal Letters

If a supermassive black hole has some material orbiting around it at close to its innermost stable circular orbit (ISCO), then, when it plunges into a second supermassive black hole, the orbiting material has a velocity dispersion of order of speed of light about the orbital velocity of its host black hole. It becomes plausible that some of the orbiting material will be “catapulted” to the negative-energy ergosphere orbits of the second black hole at the plunge. This may provide an astrophysically plausible way to extract energy from the black hole, originally suggested by Penrose.

by Sopuerta, Carlos F. and Yunes, Nicolas
10 pages, 2 figures, Springer Verlag LaTeX style. To appear in the proceedings of Cosmology, the Quantum Vacuum, and Zeta Functions: A workshop with a celebration of Emilio Elizalde’s sixtieth birthday, Bellaterra, Barcelona, Spain, 8-10 Mar 2010. Eds. S. D. Odintsov, D. Saez-Gomez, and S. Xambo

The emergent area of gravitational wave astronomy promises to provide revolutionary discoveries in the areas of astrophysics, cosmology, and fundamental physics. One of the most exciting possibilities is to use gravitational-wave observations to test alternative theories of gravity. In this contribution we describe how to use observations of extreme-mass-ratio inspirals by the future Laser Interferometer Space Antenna to test a particular class of theories: Chern-Simons modified gravity.

by Garfinkle, David and Pretorius, Frans and Yunes, Nicolas
4 pages, no figures, submitted to Rapid Communications

We perform a linear stability analysis of dynamical Chern-Simons modified gravity in the geometric optics approximation and find that it is linearly stable on the backgrounds considered. Our analysis also reveals that gravitational waves in the modified theory travel at the speed of light in Minkowski spacetime. However, on a Schwarzschild background the characteristic speed of propagation along a given direction splits into two modes, one subluminal and one superluminal. The width of the splitting depends on the azimuthal components of the propagation vector, is linearly proportional to the mass of the black hole, and decreases with the third inverse power of the distance from the black hole. Radial propagation is unaffected, implying that as probed by gravitational waves the location of the event horizon of the spacetime is unaltered. The analysis further reveals that when a high frequency, pure gravitational wave is scattered from a black hole, a scalar wave of comparable amplitude is excited, and vice-versa.

by Porto, Rafael A.
25 pages, 4 figures, revtex4

Using effective field theory (EFT) techniques we calculate the next-to-leading order (NLO) spin-orbit contributions to the gravitational potential of inspiralling compact binaries. We use the covariant spin supplementarity condition (SSC), and explicitly prove the equivalence with previous results by Faye et al. in arXiv:gr-qc/0605139. We also show that the direct application of the Newton-Wigner SSC at the level of the action leads to the correct dynamics using a canonical (Dirac) algebra. This paper then completes the calculation of the necessary spin dynamics within the EFT formalism that will be used in a separate paper to compute the spin contributions to the energy flux and phase evolution to NLO.

by Molina, C. and Pani, Paolo and Cardoso, Vitor and Gualtieri, Leonardo
RevTex4, 12 pages, 8 figures, 3 Tables

Dynamical Chern-Simons gravity is an extension of General Relativity in which the gravitational field is coupled to a scalar field through a parity-violating Chern-Simons term. In this framework, we study perturbations of spherically symmetric black hole spacetimes, assuming that the background scalar field vanishes. Our results suggest that these spacetimes are stable, and small perturbations die away as a ringdown. However, in contrast to standard General Relativity, the gravitational waveforms are also driven by the scalar field. Thus, the gravitational oscillation modes of black holes carry imprints of the coupling to the scalar field. This is a smoking gun for Chern-Simons theory and could be tested with gravitational-wave detectors, such as LIGO or LISA. For negative values of the coupling constant, ghosts are known to arise, and we explicitly verify their appearance numerically. Our results are validated using both time evolution and frequency domain methods.

by Sopuerta, Carlos F. and Yunes, Nicolas
3 pages. To appear in Proceedings of the Twelfth Marcel Grossmann Meeting on General Relativity, edited by Thibault Damour, Robert T Jantzen and Remo Ruffini, World Scientific, Singapore, 2010

The inspiral of stellar compact objects into massive black holes, usually known as extreme-mass-ratio inspirals (EMRIs), is one of the most important sources of gravitational-waves for the future Laser Interferometer Space Antenna (LISA). Intermediate-mass-ratio inspirals (IMRIs are also of interest to advance ground-based gravitational-wave observatories. We discuss here how modifications to the gravitational interaction can affect the signals emitted by these systems and their detectability by LISA. We concentrate in particular on Chern-Simons modified gravity, a theory that emerges in different quantum gravitational approaches.

by Spallicci, A. and Aoudia, S.
To be published on 21 Rencontres de Blois: Windows on the Universe, http://confs.obspm.fr/Blois2009/, 4 pages 1 figure

Through detection by low gravitational wave space interferometers, the capture of stars by supermassive black holes will constitute a giant step forward in the understanding of gravitation in strong field. The impact of the perturbations on the motion of the star is computed via the tail, the back-scattered part of the perturbations, or via a radiative Green function. In the former approach, the self-force acts upon the background geodesic, while in the latter, the geodesic is conceived in the total (background plus perturbations) field. Regularisations (mode-sum and Riemann-Hurwitz $latex \zeta$ function) intervene to cancel divergencies coming from the infinitesimal size of the particle. The non-adiabatic trajectories require the most sophisticated techniques for studying the evolution of the motion, like the self-consistent approach.

by Yunes, Nicolas and Pretorius, Frans
25 pages, submitted to Phys. Rev. D

We consider the concept of fundamental bias in gravitational wave astrophysics as the assumption that general relativity is the correct theory of gravity during the entire wave-generation and propagation regime. Such an assumption is valid in the weak-field, as verified by precision experiments and observations, but it need not hold in the dynamical strong-field regime where tests are lacking. Fundamental bias can cause systematic errors in the detection and parameter estimation of signals, which can lead to a mischaracterization of the universe through incorrect inferences about source event rates and populations. We propose a remedy through the introduction of the parameterized post-Einsteinian framework, which consists of the enhancement of waveform templates via the inclusion of post-Einsteinian parameters. These parameters would ostensibly be designed to interpolate between templates constructed in general relativity and well-motivated alternative theories of gravity, and also include extrapolations that follow sound theoretical principles, such as consistency with conservation laws and symmetries. As an example, we construct parameterized post-Einsteinian templates for the binary coalescence of equal-mass, non-spinning compact objects in a quasi-circular inspiral. The parametrized post-Einsteinian framework should allow matched filtered data to select a specific set of post-Einsteinian parameters without a priori assuming the validity of the former, thus either verifying general relativity or pointing to possible dynamical strong-field deviations.

by Capozziello, S. and De Laurentis, M. and Forte, L. and Garufi, F. and Milano, L.
14 pages, 7 figures

Gravitational waveforms and production could be considerably affected by gravitomagnetic corrections considered in relativistic theory of orbits. Beside the standard periastron effect of General Relativity, new nutation effects come out when c^{-3} corrections are taken into account. Such corrections emerge as soon as matter-current densities and vector gravitational potentials cannot be discarded into dynamics. We study the gravitational waves emitted through the capture, in the gravitational field of massive binary systems (e.g. a very massive black hole on which a stellar object is inspiralling) via the quadrupole approximation, considering precession and nutation effects. We present a numerical study to obtain the gravitational wave luminosity, the total energy output and the gravitational radiation amplitude. From a crude estimate of the expected number of events towards peculiar targets (e.g. globular clusters) and in particular, the rate of events per year for dense stellar clusters at the Galactic Center (SgrA*), we conclude that this type of capture could give signatures to be revealed by interferometric GW antennas, in particular by the forthcoming laser interferometer space antenna LISA.

by Levin, Janna
7 pages

A spinning black hole with a much smaller black hole companion forms a fundamental gravitational system, like a colossal classical analog to an atom. In an appealing if imperfect analogy to atomic physics, this gravitational atom can be understood through a discrete spectrum of periodic orbits. Through a correspondence between the set of periodic orbits and the set of rational numbers, we are able to construct periodic tables of orbits and energy level diagrams of the accessible states around black holes. We also present a closed form expression for the rational q, thereby quantifying zoom-whirl behavior in terms of spin, energy, and angular momentum. The black hole atom is not just a theoretical construct, but corresponds to extant astrophysical systems detectable by future gravitational wave observatories.