We apply the point particle EFT approach to a compact star to systematically compute dynamical tidal love numbers for various non-rotating compact objects, extending the treatment of {arXiv:2307.10391[hep-th], arXiv:2407.08327 [gr-qc]}. We calculate the scattering amplitude in Black Hole Perturbation Theory(BPHT) for \textit{arbitrary} non-rotating compact stars using the Mano-Suzuki-Takasugi(MST) method with non zero surface reflectivity and match it with that obtained from point particle EFT order by order in the low frequency expansion. This sets up a systematic framework for extracting the static and dynamical tidal love numbers(TLNs) to any order in the multipole expansion. In this paper, we employ the technique to compute the Next-to-Next-to Leading Order TLN upto a universal constant and its Renormalization Group equation for non-viscous Neutron stars and Neutron stars admixed with Bosonic or Fermionic dark matter.
Dynamical Tidal Response of Non-rotating Black Holes: Connecting the MST Formalism and Worldline EFT
Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）；Graduate School of Science, The University of Tokyo（东京大学理学研究科）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study (UTIAS), The University of Tokyo（东京大学宇宙物质量子前沿研究中心（WPI），东京大学高等研究院，东京大学）；The Hakubi Center for Advanced Research, Kyoto University（京都大学博慧中心）；RIKEN iTHEMS（理化学研究所 iTHEMS）；Department of Physics, College of Humanities and Sciences, Nihon University（日本大学文理学部物理学系）；High Energy Physics Research Unit, Department of Physics, Faculty of Science, Chulalongkorn University（朱拉隆功大学理学院物理学系高能物理研究组）
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 illus…
In previous works, we obtained the leading, next-to-leading and next-to-next-to-leading (NNL) post-Newtonian (PN) corrections in the conservative tidal interactions between two compact non-spinning objects using a Lagrangian of effective field theory (EFT) in harmonic coordinates. In the present paper, we compute the corresponding NNL PN tidal effective Hamiltonian in ADM-like and isotropic coordinates, with contributions from mass quadrupole, current quadrupole and mass octupole tidal interactions, consistently included at that level. We also derive the NNL tidal Hamiltonian in Delaunay varia…
In this whitepaper, I describe modern applications of effective field theory (EFT) techniques to classical and quantum gravity, with relevance to problems in astrophysics and cosmology. As in applications of EFT to high-energy, nuclear, or condensed matter physics, the Wilsonian paradigm based on decoupling of short distance scales via renormalization group evolution remains a powerful organizing principle in the context of gravity. However, the presence of spacetime geometry brings in new elements ( non-trivial time-dependence, cosmological or black hole event horizons) which necessitate the …
Dynamical tidal Love numbers of black holes under generic perturbations: Connecting black hole perturbation theory with effective field theory
School of Physical Sciences, Indian Association for the Cultivation of Science（印度科学文化协会物理科学学院）；Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute)（引力物理学马普研究所（爱因斯坦研究所））；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础国际理论科学中心）；Institute for Theoretical Physics, Utrecht University（乌得勒支大学理论物理研究所）
We compute spin-orbit effects in the equations of motion, binding energy and energy loss of binary systems of compact objects at the next-to-leading order in the post-Newtonian (PN) approximation in the effective field theory (EFT) framework. We then use these quantities to compute the evolution of the orbital frequency and accumulated orbital phase including spin-orbit effects beyond the dominant order. To obtain the results presented in this paper, we make use of known ingredients in the EFT literature, such as the potential and the multipole moments with spin effects at next-to-leading orde…
We use the Effective Field Theory (EFT) framework to compute the mass quadrupole moment, the equation of motion, and the power loss of inspiralling compact binaries at the second order in the Post-Newtonian (PN) approximation. We present expressions for the stress-energy pseudo-tensor components of the binary system in higher PN orders. The 2PN correction to the mass quadrupole moment as well as to the acceleration computed in the linearized harmonic gauge presented here are the ingredients needed for the calculation of the next-to-next-to leading order radiation reaction force, which will be …
Universidade Federal do ABC（ABC联邦大学）；IFT - UNESP & ICTP - SAIFR（圣保罗州立大学物理研究所与ICTP-SAIFR）；CMCC, Universidade Federal do ABC（ABC联邦大学气候中心）；ITP, TU Wien（维也纳工业大学理论物理研究所）
Tidal deformability of a coalescing neutron star subjected to an external tidal field plays an important role in our probe for the structure and properties of compact stars. In particular, the tidal love number provides valuable information about the external gravitational field responsible for deforming the star. In this article, we compute the tidal love number of a particular class of anisotropic stars and analyze the impacts of anisotropy and compactness on the tidal love number.
Within the framework of the effective field theory approach to the post-Newtonian approximation to General Relativity, we report the so far missing G^3 and G^4 sectors of the conservative two body dynamics at fourth perturbative order for non-spinning compact objects. Following the standard procedure, the exchange of gravitational interaction is integrated out to obtain a systematic expansion in terms of Feynman graphs. Building on this result and on previously obtained ones, we are able to write the local-in-time regularized Lagrangian at fourth post-Newtonian order, which is in agreement wit…
Using the Effective Field Theory approach together with the Boundary-to-Bound map, we compute the next-to-leading order (NLO) Post-Minkowskian (PM) tidal effects in the conservative dynamics of compact binary systems. We derive the mass and current quadrupole and, for the first time, octupole corrections to the binding energy for circular orbits at ${\cal O}(G^3)$. Our results are consistent with the test-body limit as well as the existent Post-Newtonian literature. We also reconstruct a Hamiltonian incorporating tidal effects to NLO in the PM expansion and find complete agreement with the rec…
We use an effective field theory (EFT) approach to calculate the next to leading order (NLO) gravitational spin-orbit interaction between two spinning compact objects. The NLO spin-orbit interaction provides the most computationally complex sector of the NLO spin effects, previously derived within the EFT approach. In particular, it requires the inclusion of non-stationary cubic self-gravitational interaction, as well as the implementation of a spin supplementary condition (SSC) at higher orders. The EFT calculation is carried out in terms of the non-relativistic gravitational field parametriz…
We provide a compact and unified treatment of power spectrum observables for the effective field theory (EFT) of inflation with the complete set of operators that lead to second-order equations of motion in metric perturbations in both space and time derivatives, including Horndeski and GLPV theories. We relate the EFT operators in ADM form to the four additional free functions of time in the scalar and tensor equations. Using the generalized slow roll formalism, we show that each power spectrum can be described by an integral over a single source that is a function of its respective sound hor…
We use the recently proposed Kaluza-Klein (KK) reduction over the time dimension, within an effective field theory (EFT) approach, to calculate the next to leading order (NLO) gravitational spin1-spin2 interaction between two spinning compact objects. It is shown here that to NLO in the spin1-spin2 interaction, the reduced KK action within the stationary approximation is sufficient to describe the gravitational interaction, and that it simplifies calculation substantially. We also find here that the gravito-magnetic vector field defined within the KK decomposition of the metric mostly dominate…
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 w…
We generalize the worldline EFT formalism developed in [4-9] to calculate the non-conservative tidal effects on spinning black holes in a long wavelength approximation that is valid to all orders in the magnitude of the spin. We present results for the rate of change of mass and angular momentum in a background field and find agreement with previous calculations obtained by different techniques. We also present new results for both the non-conservative equations of motion and power loss/gain for a binary inspiral, which start at 5PN and 2.5PN order respectively and manifest the Penrose process…
We present an Effective Field Theory (EFT) formalism which describes the dynamics of non-relativistic extended objects coupled to gravity. The formalism is relevant to understanding the gravitational radiation power spectra emitted by binary star systems, an important class of candidate signals for gravitational wave observatories such as LIGO or VIRGO. The EFT allows for a clean separation of the three relevant scales: r_s, the size of the compact objects, r the orbital radius and r/v, the wavelength of the physical radiation (where the velocity v is the expansion parameter). In the EFT radia…
We examine the tidal deformation of a nonrotating compact body (material body or black hole) in general relativity. The body's exterior metric is calculated in a simultaneous expansion in powers of the ratio between the distance to the body and three distinct length scales: the radius of curvature of the external spacetime in which the body is inserted, the scale of spatial inhomogeneity of the curvature, and the scale of temporal variation. The metric is valid in the body's immediate neighborhood, which excludes the external matter responsible for the tidal environment. The body's tidal respo…
One of the macroscopically measurable effects of gravity is the tidal deformability of astrophysical objects, which can be quantified by their tidal Love numbers. For planets and stars, these numbers measure the resistance of their material against the tidal forces, and the resulting contribution to their gravitational multipole moments. According to general relativity, nonrotating deformed black holes, instead, show no addition to their gravitational multipole moments, and all of their Love numbers are zero. In this paper we explore different configurations of nonrotating compact and ultracom…
In this series we construct an effective field theory (EFT) in curved spacetime to study gravitational radiation and backreaction effects. We begin in this paper with a derivation of the self-force on a compact object moving in the background spacetime of a supermassive black hole. The EFT approach utilizes the disparity between two length scales, which in this problem are the size of the compact object and the radius of curvature of the background spacetime, to treat the orbital dynamics of the compact object, described as an effective point particle, separately from its tidal deformations. U…
During the early phase of in-spiral of a binary system, the tidal heating of a compact object due to its companion plays a significant role in the determination of the orbital evolution of the binary. The phenomenon depends crucially on the `hairs', as well as on the nature of the compact object. It turns out that the presence of extra dimension affects both these properties, by incorporating an extra tidal charge for braneworld black holes and also by introducing quantum effects, leading to possible existence of exotic compact objects. It turns out that the phasing information from tidal heat…
As a first step in the computation of the orbital phase evolution of spinless compact binaries including tidal effects up to the next-to-next-to-leading (NNL) order, we obtain the equations of motion of those systems and the associated conserved integrals in harmonic coordinates. The internal structure and finite size effects of the compact objects are described by means of an effective Fokker-type action. Our results, complete to the NNL order, correspond to the second-post-Newtonian (2PN) approximation beyond the leading tidal effect itself, already occurring at the 5PN order. They are param…
Using the gravitational potential and source multipole moments bilinear in the spins, first computed to next-to-leading order (NLO) in the post-Newtonian (PN) expansion within the effective field theory (EFT) framework, we complete here the derivation of the dynamical invariants and flux-balance equations, including energy and angular momentum. We use these results to calculate spin-spin effects in the orbital frequency and accumulated phase to NLO for circular orbits. We also derive the linear momentum and center-of-mass fluxes and associated kick-velocity, to the highest relevant PN order. W…
Tidal deformations of general-relativistic multifluid compact stars
Institute of Astronomy and Astrophysics, Université Libre de Bruxelles（布鲁塞尔自由大学天体物理与天文学研究所）；Brussels Laboratory of the Universe（布鲁塞尔宇宙实验室）；Leuven Gravity Institute, KU Leuven（荷语鲁汶大学引力研究所）
The late part of the gravitational wave signal of binary neutron star inspirals can in principle yield crucial information on the nuclear equation of state via its dependence on relativistic tidal parameters. In the hope of analytically describing the gravitational wave phasing during the late inspiral (essentially up to contact) we propose an extension of the effective one body (EOB) formalism which includes tidal effects. We compare the prediction of this tidal-EOB formalism to recently computed nonconformally flat quasi-equilibrium circular sequences of binary neutron star systems. Our anal…
The effect of energy absorption during the binary evolution of Exotic-compact-objects (ECOs) is extensively studied. We review the underlying mechanism that provides the energy dissipation in material objects - tidal friction. We show that unlike typical astrophysical objects, where absorption due to viscosity is negligible, in ECOs, absorption could potentially mimic the analogous effect of black-holes (BHs) - tidal heating. We stand for their differences and similarities in the context of energy dissipation during the inspiral. Inspired by the membrane paradigm and recent studies, we demonst…
In this paper we construct an effective field theory (EFT) that describes long wavelength gravitational radiation from compact systems. To leading order, this EFT consists of the multipole expansion, which we describe in terms of a diffeomorphism invariant point particle Lagrangian. The EFT also systematically captures "post-Minkowskian" corrections to the multipole expansion due to non-linear terms in general relativity. Specifically, we compute long distance corrections from the coupling of the (mass) monopole moment to the quadrupole moment, including up to two mass insertions. Along the wa…
(Abridged) It is well known that the tidal deformability of a compact star carries important information about the interior equation-of-state (EOS) of the star. The first gravitational-wave event GW170817 from a binary compact star merger observed by the LIGO/VIRGO detectors have already put limits on the tidal deformability and provided constraints on the ultra-high nuclear density EOS. In view of this ground breaking discovery, we revisit and extend our previous work [Phys. Rev. D 95, 101302(R) (2017)] which found that taking the effect of elasticity into account in the calculation of the ti…
The tidal deformability of compact objects by a companion has a detectable imprint in the gravitational waves emitted by a binary system. This effect is governed by the so-called tidal Love numbers. For a particular theory of gravity, these depend solely on the object internal structure and they vanish for black holes in general relativity. A measurement compatible with nonzero tidal Love numbers could thus provide evidence of new physics in the strong-field regime. However, in realistic astrophysical scenarios, compact objects are surrounded by a nonvacuum environment. In this work, we study …
We use the post-Newtonian-Affine model to assess the validity of the adiabatic approximation in modeling tidal effects in the phase evolution of compact binary systems. We compute the dynamical evolution of the tidal tensor, which we estimate at the 2 PN order, and of the quadrupole tensor, finding that their ratio, i.e. the tidal deformability, increases in the last phases of the inspiral. We derive the gravitational wave phase corrections due to this phenomenon and quantify how they affect gravitational wave detectability.
We study the tidal deformability of bare quark stars and hybrid compact stars composed of a quark matter core in general relativity, assuming that the deconfined quark matter exists in a crystalline color superconducting phase. We find that taking the elastic property of crystalline quark matter into account in the calculation of the tidal deformability can break the universal I-Love relation discovered for fluid compact stars, which connects the moment of inertia and tidal deformability. Our result suggests that measurements of the moment of inertia and tidal deformability can in principle be…
We develop a semi-analytical approach, based on the post-Newtonian expansion and on the affine approximation, to model the tidal deformation of neutron stars in the coalescence of black hole-neutron star or neutron star-neutron star binaries. Our equations describe, in a unified framework, both the system orbital evolution, and the neutron star deformations. These are driven by the tidal tensor, which we expand at 1/c^3 post-Newtonian order, including spin terms. We test the theoretical framework by simulating black hole-neutron star coalescence up to the onset of mass shedding, which we deter…
We extend the gravitational self-force approach to encompass `self-interaction' tidal effects for a compact body of mass $μ$ on a quasi-circular orbit around a black hole of mass $M \gg μ$. Specifically, we define and calculate at $O(μ)$ (conservative) shifts in the eigenvalues of the electric- and magnetic-type tidal tensors, and a (dissipative) shift in a scalar product between their eigenbases. This approach yields four gauge-invariant functions, from which one may construct other tidal quantities such as the curvature scalars and the speciality index. First, we analyze the general case of …
General relativistic effects in the spacetime around the massive astrophysical objects can be captured using a spinning test gyro orbiting around the object in a circular geodesic. This article discusses how the tidal disruption due to a companion object affects the precession frequency of a spinning gyro orbiting around a compact astrophysical object. The precession frequency is studied in a region of space around the central object using a perturbative approach. In this study, the central object is either a neutron star or a white dwarf. The gyro is any planetary or asteroid-like object orbi…
We compute the spin-tidal couplings that affect the dynamics of two orbiting bodies at the leading order in the post-Newtonian (PN) framework and to linear order in the spin. These corrections belong to two classes: (i) terms arising from the coupling between the ordinary tidal terms and the point-particle terms, which depend on the standard tidal Love numbers of order $l$ and affect the gravitational-wave (GW) phase at $(2l+5/2)$PN order and (ii) terms depending on the rotational tidal Love numbers, recently introduced in previous work, that affect the GW phase at $(2l+1/2+δ_{2l})$PN order. F…
The deformability of a compact object induced by a perturbing tidal field is encoded in the tidal Love numbers, which depend sensibly on the object's internal structure. These numbers are known only for static, spherically-symmetric objects. As a first step to compute the tidal Love numbers of a spinning compact star, here we extend powerful perturbative techniques to compute the exterior geometry of a spinning object distorted by an axisymmetric tidal field to second order in the angular momentum. The spin of the object introduces couplings between electric and magnetic deformations and new c…
