Gravitational Spin-orbit Coupling Research Articles

Gravitational spin-orbit coupling through the third-subleading post-Newtonian order: Exploring spin-gauge flexibility

Gravitational spin-orbit coupling through the third-subleading post-Newtonian order: Exploring spin-gauge flexibility

N3LO gravitational spin-orbit coupling at order G4

In this paper we derive for the first time the N3LO gravitational spin-orbit coupling at order G4 in the post-Newtonian (PN) approximation within the effective field theory (EFT) of gravitating spinning objects. This represents the first computation in a spinning sector involving three-loop integration. We provide a comprehensive account of the topologies in the worldline picture for the computation at order G4. Our computation makes use of the publicly-available EFTofPNG code, which is extended using loop-integration techniques from particle amplitudes. We provide the results for each of the Feynman diagrams in this sector. The three-loop graphs in the worldline picture give rise to new features in the spinning sector, including divergent terms and logarithms from dimensional regularization, as well as transcendental numbers, all of which survive in the final result of the topologies at this order. This result enters at the 4.5PN order for maximally-rotating compact objects, and together with previous work in this line, paves the way for the completion of this PN accuracy.

Gravitational Spin-Orbit Coupling through Third-Subleading Post-Newtonian Order: From First-Order Self-Force to Arbitrary Mass Ratios.

Exploiting simple yet remarkable properties of relativistic gravitational scattering, we use first-order self-force (linear-in-mass-ratio) results to obtain arbitrary-mass-ratio results for the complete third-subleading post-Newtonian (4.5PN) corrections to the spin-orbit sector of spinning-binary conservative dynamics, for generic (bound or unbound) orbits and spin orientations. We thereby improve important ingredients of models of gravitational waves from spinning binaries, and we demonstrate the improvement in accuracy by comparing against aligned-spin numerical simulations of binary black holes.

Spectroscopic tests for short-range modifications of Newtonian and post-Newtonian potentials

There are theoretical frameworks, such as the large extra dimension models, which predict the strengthening of the gravitational field in short distances. Here we obtain new empiric constraints for deviations of standard gravity in the atomic length scale from analyses of recent and accurate data of hydrogen spectroscopy. The new bounds, extracted from transition, are compared with previous limits given by antiprotonic Helium spectroscopy. Independent constraints are also determined by investigating the effects of gravitational spin–orbit coupling on the atomic spectrum. We show that the analysis of the influence of that interaction, which is responsible for the spin precession phenomena, on the fine structure of the states can be employed as a test of a post-Newtonian potential in the atomic domain. The constraints obtained here from transition in hydrogen are tighter than previous bounds determined from measurements of the spin precession in an electron-nucleus scattering.

Gravitational spin-orbit coupling in binary systems at the second post-Minkowskian approximation

We compute the rotations, during a scattering encounter, of the spins of two gravitationally interacting particles at second-order in the gravitational constant (second post-Minkowskian order). Following a strategy introduced in Phys. Rev. D {\bf 96}, 104038 (2017), we transcribe our result into a correspondingly improved knowledge of the spin-orbit sector of the Effective One-Body (EOB) Hamiltonian description of the dynamics of spinning binary systems. We indicate ways of resumming our results for defining improved versions of spinning EOB codes which might help in providing a better analytical description of the dynamics of coalescing spinning binary black holes.

Planet formation in discs with inclined binary companions: can primordial spin–orbit misalignment be produced?

Many hot Jupiter (HJ) systems have been observed to have their stellar spin axis misaligned with the planet's orbital angular momentum axis. The origin of this spin-orbit misalignment and the formation mechanism of HJs remain poorly understood. A number of recent works have suggested that gravitational interactions between host stars, protoplanetary disks, and inclined binary companions may tilt the stellar spin axis with respect to the disk's angular angular momentum axis, producing planetary systems with misaligned orbits. These previous works considered idealized disk evolution models and neglected the gravitational influence of newly formed planets. In this paper, we explore how disk photoevaporation and planet formation and migration affect the inclination evolution of planet-star-disk-binary systems. We take into account planet-disk interactions and the gravitational spin-orbit coupling between the host star and the planet. We find that the rapid depletion of the inner disk via photoevaporation reduces the excitation of stellar obliquities. Depending on the formation and migration history of HJs, the spin-orbit coupling between the star and the planet may reduces and even completely suppress the excitation of stellar obliquities. Our work constrains the formation/migration history of HJs. On the other hand, planetary systems with "cold" Jupiters or close-in super-earths may experience excitation of stellar obliquities in the presence of distant inclined companions.

Gravitational spin-orbit coupling in binary systems, post-Minkowskian approximation, and effective one-body theory

A novel approach for extracting gauge-invariant information about spin-orbit coupling in gravitationally interacting binary systems is introduced. This approach is based on the "scattering holonomy", i.e. the integration (from the infinite past to the infinite future) of the differential spin evolution along the two worldlines of a binary system in hyperboliclike motion. We apply this approach to the computation, at the first post-Minkowskian approximation (i.e. first order in $G$ and all orders in $v/c$), of the values of the two gyrogravitomagnetic ratios describing spin-orbit coupling in the Effective One-Body formalism. These gyrogravitomagnetic ratios are found to tend to zero in the ultrarelativistic limit.

The effect of gravitational spin–orbit coupling on the circular photon orbit in the Schwarzschild geometry

The representation of the group SL(2, C) provides a six-component spinor equivalent to the electromagnetic field tensor. By means of the description, one can treat the photon field in curved spacetime via spin connection and the tetrad formalism, which is of great advantage to study the gravitational spin–orbit coupling of photons. Once the gravitational spin–orbit coupling is taken into account, the traditional radius of the circular photon orbit in the Schwarzschild geometry should be replaced with two different radiuses corresponding to the photons with the helicities of respectively. Owing to the splitting of energy levels induced by the spin–orbit coupling, photons (from Hawking radiations, say) escaping from a Schwarzschild black hole are partially polarized, provided that their initial velocities possess nonzero tangential components.

Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme

We implement the effective field theory for gravitating spinning objects in the post-Newtonian scheme at the next-to-next-to-leading order level to derive the gravitational spin-orbit interaction potential at the third and a half post-Newtonian order for rapidly rotating compact objects. From the next-to-next-to-leading order interaction potential, which we obtain here in a Lagrangian form for the first time, we derive straightforwardly the corresponding Hamiltonian. The spin-orbit sector constitutes the most elaborate spin dependent sector at each order, and accordingly we encounter a proliferation of the relevant Feynman diagrams, and a significant increase of the computational complexity. We present in detail the evaluation of the interaction potential, going over all contributing Feynman diagrams. The computation is carried out in terms of the ``nonrelativistic gravitational'' fields, which are advantageous also in spin dependent sectors, together with the various gauge choices included in the effective field theory for gravitating spinning objects, which also optimize the calculation. In addition, we automatize the effective field theory computations, and carry out the automated computations in parallel. Such automated effective field theory computations would be most useful to obtain higher order post-Newtonian corrections. We compare our Hamiltonian to the ADM Hamiltonian, and arrive at a complete agreement between the ADM and effective field theory results. Finally, we provide Hamiltonians in the center of mass frame, and complete gauge invariant relations among the binding energy, angular momentum, and orbital frequency of an inspiralling binary with generic compact spinning components to third and a half post-Newtonian order. The derivation presented here is essential to obtain further higher order post-Newtonian corrections, and to reach the accuracy level required for the successful detection of gravitational radiation.

Study of Gravitomagnetic Clock Effect Due To Gravitational Spin-Orbit Coupling

In this paper, we consider a possible gravitational spin-orbit coupling. It is shown that in presence of such a coupling there would appear a clock effect very similar to the gravitomagnetic clock effect. The new clock effect is found to be topological. According to this effect, two counter orbiting spinning test particles placed on two identical circular equatorial orbits around a central massive body would take different times to complete a full revolution. In this paper, we calculate the period difference using the gravitational spin- orbit coupling term as given by the expression found by Barker and O'Connel.

Nonrelativistic limit of the Dirac-Schwarzschild Hamiltonian: GravitationalZitterbewegungand gravitational spin-orbit coupling

We investigate the nonrelativistic limit of the gravitationally coupled Dirac equation via a Foldy-Wouthuysen transformation. The relativistic correction terms have immediate and obvious physical interpretations in terms of a gravitational Zitterbewegung and a gravitational spin-orbit coupling. We find no direct coupling of the spin vector to the gravitational force, which would otherwise violate parity. The particle-antiparticle symmetry described recently by one of us [Jentschura, Phys. Rev. A 87, 032101 (2013)] is verified on the level of the perturbative corrections accessed by the Foldy-Wouthuysen transformation. The gravitational corrections to the electromagnetic transition current are calculated.

The planetary spin and rotation period: a modern approach

Using a new approach, we have obtained a formula for calculating the rotation period and radius of planets. In the ordinary gravitomagnetism the gravitational spin (S) orbit (L) coupling, \(\vec{L}\cdot\vec{S}\propto L^{2}\), while our model predicts that \(\vec{L}\cdot\vec{S}\propto\frac{m}{M}L^{2}\), where M and m are the central and orbiting masses, respectively. Hence, planets during their evolution exchange L and S until they reach a final stability at which MS∝mL, or \(S\propto\frac{m^{2}}{v}\), where v is the orbital velocity of the planet. Rotational properties of our planetary system and exoplanets are in agreement with our predictions. The radius (R) and rotational period (D) of tidally locked planet at a distance a from its star, are related by, \(D^{2}\propto\sqrt{\frac{M}{m^{3}}}R^{3}\) and that \(R\propto\sqrt{\frac {m}{M}}a\).

Periastron precession due to gravitational spin–orbit coupling

In this paper, we consider gravitational spin–orbit coupling of the spin of a spinning test particle with its own orbital angular momentum. It is shown that in the presence of such a coupling, the periastron of the spinning particle would shift in much the same way that the periastron of a non-spinning particle in the field of a Kerr black hole shifts. We obtain, in this paper, an expression for the periastron shift.

Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach

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 parametrization, making the calculation more efficient with no need to rely on automated computations, and illustrating the coupling hierarchy of the different gravitational field components to the spin and mass sources. Finally, we show explicitly how to relate the EFT derived spin results to the canonical results obtained with the ADM Hamiltonian formalism. This is done using non-canonical transformations, required due to the implementation of covariant SSC, as well as canonical transformations at the level of the Hamiltonian, with no need to resort to the equations of motion or the Dirac brackets.

ADM canonical formalism for gravitating spinning objects

In general relativity, systems of spinning classical particles are implemented into the canonical formalism of Arnowitt, Deser, and Misner [R. Arnowitt, S. Deser, and C. W. Misner, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962), p. 227; arXiv:gr-qc/0405109]. The implementation is made with the aid of a symmetric stress-energy tensor and not a 4-dimensional covariant action functional. The formalism is valid to terms linear in the single spin variables and up to and including the next-to-leading order approximation in the gravitational spin-interaction part. The field-source terms for the spinning particles occurring in the Hamiltonian are obtained from their expressions in Minkowski space with canonical variables through 3-dimensional covariant generalizations as well as from a suitable shift of projections of the curved spacetime stress-energy tensor originally given within covariant spin supplementary conditions. The applied coordinate conditions are the generalized isotropic ones introduced by Arnowitt, Deser, and Misner. As applications, the Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling, recently obtained by Damour, Jaranowski, and Sch\"afer [Phys. Rev. D 77, 064032 (2008)], is rederived and the derivation of the next-to-leading order gravitational spin(1)-spin(2) Hamiltonian, shown for the first time in [J. Steinhoff, S. Hergt, and G. Sch\"afer, Phys. Rev. D 77, 081501(R) (2008)], is presented.

Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling

A Hamiltonian formulation is given for the gravitational dynamics of two spinning compact bodies to next-to-leading order ($G/{c}^{4}$ and ${G}^{2}/{c}^{4}$) in the spin-orbit interaction. We use a novel approach (valid to linear order in the spins) which starts from the second-post-Newtonian metric (in Arnowitt-Deser-Misner coordinates) generated by two spinless bodies and computes the next-to-leading order precession, in this metric, of suitably redefined ``constant-magnitude'' 3-dimensional spin vectors ${\mathbf{S}}_{1}$, ${\mathbf{S}}_{2}$. We prove the Poincar\'e invariance of our Hamiltonian by explicitly constructing 10 phase-space generators realizing the Poincar\'e algebra. A remarkable feature of our approach is that it allows one to derive the orbital equations of motion of spinning binaries to next-to-leading order in spin-orbit coupling without having to solve Einstein's field equations with a spin-dependent stress tensor. We show that our Hamiltonian (orbital and spin) dynamics is equivalent to the dynamics recently obtained by Faye, Blanchet, and Buonanno, by solving Einstein's equations in harmonic coordinates.

Clock effect due to gravitational spin–orbit coupling

In this Letter, we consider a possible gravitational spin–orbit coupling. It is shown that in presence of such a coupling there would appear a clock effect very similar to the gravitomagnetic clock effect. The new clock effect is found to be topological. According to this effect, two counter-orbiting spinning test particles placed on two identical, circular equatorial orbits around a central massive body would take different times to complete a full revolution. We obtain, in this Letter, a qualitative expression for the period difference.

Gravitational spin–orbit coupling and the equivalence principle

The nonrelativistic Hamiltonian for a Dirac particle in the Schwarzschild space is compared with that in the frame with a constant acceleration a . The spin–orbit coupling − s ·( a × p )/(2mc 2) , in the accelerated frame, turns out to be the Thomas precession. But in the Schwarzschild Hamiltonian, in addition to the Thomas precession, there exists a gravitational spin–orbit coupling which seems to violate the Einstein's equivalence principle.

Systems of Self-Gravitating Particles in General Relativity and the Concept of an Equation of State

A method of self-consistent fields is used to study the equilibrium configurations of a system of self-gravitating scalar bosons or spin-\textonehalf{} fermions in the ground state without using the traditional perfect-fluid approximation or equation of state. The many-particle system is described by a second-quantized free field, which in the boson case satisfies the Klein-Gordon equation in general relativity, ${\ensuremath{\nabla}}_{\ensuremath{\alpha}}{\ensuremath{\nabla}}^{\ensuremath{\alpha}}\ensuremath{\varphi}={\ensuremath{\mu}}^{2}\ensuremath{\varphi}$, and in the fermion case the Dirac equation in general relativity ${\ensuremath{\gamma}}^{\ensuremath{\alpha}}{\ensuremath{\nabla}}_{\ensuremath{\alpha}}\ensuremath{\psi}=\ensuremath{\mu}\ensuremath{\psi}$ (where $\ensuremath{\mu}=\frac{\mathrm{mc}}{\ensuremath{\hbar}}$). The coefficients of the metric ${g}_{\ensuremath{\alpha}\ensuremath{\beta}}$ are determined by the Einstein equations with a source term given by the mean value $〈\ensuremath{\varphi}|{T}_{\ensuremath{\mu}\ensuremath{\nu}}|\ensuremath{\varphi}〉$ of the energy-momentum tensor operator constructed from the scalar or the spinor field. The state vector $〈\ensuremath{\varphi}|$ corresponds to the ground state of the system of many particles. In both cases, for completeness, a nonrelativistic Newtonian approximation is developed, and the corrections due to special and general relativity explicitly are pointed out. For $N$ bosons, both in the region of validity of the Newtonian treatment (density from ${10}^{\ensuremath{-}80}$ to ${10}^{54}$ g ${\mathrm{cm}}^{\ensuremath{-}3}$, and number of particles from 10 to ${10}^{40}$) as well as in the relativistic region (density \ensuremath{\sim}${10}^{54}$ g ${\mathrm{cm}}^{\ensuremath{-}3}$, number of particles \ensuremath{\sim}${10}^{40}$), we obtain results completely different from those of a traditional fluid analysis. The energy-momentum tensor is anisotropic. A critical mass is found for a system of $N\ensuremath{\sim}{[\frac{(\mathrm{Planck}\mathrm{mass})}{m}]}^{2}\ensuremath{\sim}{10}^{40}$ (for $m\ensuremath{\sim}{10}^{\ensuremath{-}25}$ g) self-gravitating bosons in the ground state, above which mass gravitational collapse occurs. For $N$ fermions, the binding energy of typical particles is ${G}^{2}{m}^{5}{N}^{\frac{4}{3}}{\ensuremath{\hbar}}^{\ensuremath{-}2}$ and reaches a value $\ensuremath{\sim}{\mathrm{mc}}^{2}$ for $N\ensuremath{\sim}{N}_{\mathrm{crit}}\ensuremath{\sim}{[\frac{(\mathrm{Planck}\mathrm{mass})}{m}]}^{3}\ensuremath{\sim}{10}^{57}$ (for $m\ensuremath{\sim}{10}^{\ensuremath{-}24}$ g, implying mass \ensuremath{\sim}${10}^{33}$ g, radius \ensuremath{\sim}${10}^{6}$ cm, density \ensuremath{\sim}${10}^{15}$ g/${\mathrm{cm}}^{3}$). For densities of this order of magnitude and greater, we have given the full self-consistent relativistic treatment. It shows that the concept of an equation of state makes sense only up to ${10}^{42}$ g/${\mathrm{cm}}^{3}$, and it confirms the Oppenheimer-Volkoff treatment in extremely good approximation. There exists a gravitational spin-orbit coupling, but its magnitude is generally negligible. The problem of an elementary scalar particle held together only by its gravitational field is meaningless in this context.