Expanding on the recent derivation of tidal actions for scalar particles, we present here the action for a tidally deformed spin-$1/2$ particle. Focusing on operators containing two powers of the Weyl tensor, we combine the Hilbert series with an on-shell amplitude basis to construct the tidal action. With the tidal action in hand, we compute the leading-post-Minkowskian tidal contributions to the spin-1/2 -- spin-1/2 amplitude, arising at $\mathcal{O}(G^{2})$. Our amplitudes provide evidence that the observed long range spin-universality for the scattering of two point particles extends to the scattering of tidally deformed objects. From the scattering amplitude we find the conservative two-body Hamiltonian, linear and angular impulses, eikonal phase, spin kick, and aligned-spin scattering angle. We present analogous results in the electromagnetic case along the way.
Recent study shows that the magnetic reconnection can serve as an efficient mechanism to extract energy from rapidly spinning black holes. In this paper, we consider the effects of the tidal charge on the energy extraction via the magnetic reconnection in the backgrounds of a spinning braneworld black hole. With the increase of the tidal charge, we find that both the energies of the accelerated plasma and decelerated plasma decrease for the observer located at infinity. To achieve the purpose extracting the net energy from the black hole, the decelerated plasma should take negative energy. The…
The coupling between the angular momentum of a compact object and an external tidal field gives rise to the "rotational" tidal Love numbers, which affect the tidal deformability of a spinning self-gravitating body and enter the gravitational waveform of a binary inspiral at high post-Newtonian order. We provide numerical evidence for a surprising "hidden" symmetry among the rotational tidal Love numbers with opposite parities, which are associated to perturbations belonging to separate sectors. This symmetry, whose existence had been suggested on the basis of a Lagrangian description of the ti…
The open question of whether a black hole can become tidally deformed by an external gravitational field has profound implications for fundamental physics, astrophysics and gravitational-wave astronomy. Love tensors characterize the tidal deformability of compact objects such as astrophysical (Kerr) black holes under an external static tidal field. We prove that all Love tensors vanish identically for a Kerr black hole in the nonspinning limit or for an axisymmetric tidal perturbation. In contrast to this result, we show that Love tensors are generically nonzero for a spinning black hole. Spec…
Teukolsky equations for $|s|=2$ provide efficient ways to solve for curvature perturbations around Kerr black holes. Imposing regularity conditions on these perturbations on the future (past) horizon corresponds to imposing an in-going (out-going) wave boundary condition. For exotic compact objects (ECOs) with external Kerr spacetime, however, it is not yet clear how to physically impose boundary conditions for curvature perturbations on their boundaries. We address this problem using the Membrane Paradigm, by considering a family of fiducial observers (FIDOs) that float right above the horizo…
The open question of whether a Kerr black hole can become tidally deformed or not has profound implications for fundamental physics and gravitational-wave astronomy. We consider a Kerr black hole embedded in a weak and slowly varying, but otherwise arbitrary, multipolar tidal environment. By solving the static Teukolsky equation for the gauge-invariant Weyl scalar $ψ_0$, and by reconstructing the corresponding metric perturbation in an ingoing radiation gauge, for a general harmonic index $\ell$, we compute the linear response of a Kerr black hole to the tidal field. This linear response vanis…
In this paper we investigate the innermost stable circular orbit (ISCO) for a classical spinning test particle in the background of Kerr-Newman black hole. It is shown that the orbit of the spinning particle is related to the spin of the test particle. The motion of the spinning test particle will be superluminal if its spin is too large. We give an additional condition by considering the superluminal constraint for the ISCO in the black hole backgrounds. We obtain numerically the relations between the ISCO and the properties of the black holes and the test particle. It is found that the radiu…
It is well known that some black holes can act as accelerators for particles without spin. Recently, there are some works considering collision of two spinning particles in the background of Schwarzschild and Kerr black holes and it was shown that {the center-of-mass energy of the test particles is related to the spin}. In this paper we extend the results to some more general cases. We consider Kerr-Newman black holes as accelerators for spinning particles. We derive the center-of-mass energy of the spinning particles and use numerical method to investigate how the center-of-mass energy is aff…
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…
The geodesic motion of pseudo-classical spinning particles in Euclidean Taub-NUT space is analysed. The constants of motion are expressed in terms of Killing-Yano tensors. Some previous results from the literature are corrected.
We obtain generalized Raychaudhuri equations for spinning test particles corresponding to congruences of particle's world-lines, momentum, and spin. These are physical examples of the Raychaudhuri equation for a non-normalized vector, unit time-like vector, and unit space-like vector. We compute and compare the evolution of expansion-like parameters associated with these congruences for spinning particles confined in the equatorial plane of the Kerr space-time.
We find that spinning particles with suitable couplings propagating in certain supersymmetric backgrounds of $D=4$, $N=2$ and $D=5$, $N=1$ minimal supergravities are invariant under symmetries generated by the twisted covariant form hierarchies of these theories. We also compare our results with the symmetries of spinning particles generated by Killing-Yano forms which are responsible for the separability properties of some gravitational backgrounds.
We compare the rigorous equations describing the motion of spinning test particles in gravitational and electromagnetic fields, and show that if the Mathisson-Pirani spin condition holds then exact gravito-electromagnetic analogies emerge. These analogies provide a familiar formalism to treat gravitational problems, as well as a means for comparing the two interactions. Fundamental differences are manifest in the symmetries and time projections of the electromagnetic and gravitational tidal tensors. The physical consequences of the symmetries of the tidal tensors are explored comparing the fol…
We develop a general formalism for computing classical observables for relativistic scattering of spinning particles, directly from on-shell amplitudes. We then apply this formalism to minimally coupled Einstein-gravity amplitudes for the scattering of massive spin 1/2 and spin 1 particles with a massive scalar, constructed using the double copy. In doing so we reproduce recent results at first post-Minkowskian order for the scattering of spinning black holes, through quadrupolar order in the spin-multipole expansion.
We construct the world-line action for a Dirac particle coupled to a classical scalar or pseudo-scalar background field. This action can be used to compute loop diagrams and the effective action in the Yukawa model using the world-line path-integral formalism for spinning particles.
We investigate the stable circular orbits of the spinning test particles around the accelerating Kerr black hole on the equatorial plane. To this end, we first calculate the equations of motion and analyze the parameter space for the particles. We study the effect of the particle's spin and the black hole's acceleration on the conserved angular momentum, conserved energy and radius of the spinning test particle on the innermost stable circular orbit. We find that the effect of the particle's spin on the orbit parameters is almost linear, the effect of the black hole's acceleration on those par…
A model-independent formulation of anyons as spinning particles is presented. The general properties of the classical theory of (2+1)-dimensional relativistic fractional spin particles and some properties of their quantum theory are investigated. The relationship between all the known approaches to anyons as spinning particles is established. Some widespread misleading notions on the general properties of (2+1)-dimensional anyons are removed.
The Mathisson-Papapetrou equations are used for investigations of influence of the spin-gravity coupling on a highly relativistic spinning particle in Schwarzschild's field. It is established that interaction of the particle spin with the gravitomagnetic components of the field, estimated in the proper frame of the particle, causes the large acceleration of the spinning particle relative to geodesic free fall. As a result the accelerated charged spinning particle can generate intensive electromagnetic radiation when its velocity is highly relativistic. The significant contribution of the highl…
Structure of spinning particle based on the rotating black hole solution is considered. It has gyromagnetic ratio $g=2$ and a nontrivial twistorial and stringy systems. The mass and spin appear from excitations of the Kerr circular string, while the Dirac equation describes excitations of an {\it axial} stringy system which is responsible for scattering. Complex Kerr geometry contains an open twistor-string, target space of which is equivalent to the Witten's `diagonal' of the $ CP^3\times CP^{*3}$.
The gravitational and electromagnetic fields of a moving charged spinning point particle are obtained in the Lorentz covariant form by transforming the Kerr--Newman solution in Boyer--Lindquist coordinates to the one in the coordinate system which resembles the isotropic coordinates and then covariantizing it. It is shown that the general relativistic proper time at the location of the particle is the same as the special relativistic one and the gravitational and electromagnetic self forces vanish.
Static horizonless solutions to the Einstein--Maxwell field equations, with only a circular cosmic string singularity, are extended to exact rotating asymptotically flat solutions. The possible interpretation of these field configurations as spinning elementary particles or as macroscopic rotating cosmic rings is discussed.
In this paper, we investigate the motion of a classical spinning test particle orbiting around a static spherically symmetric black hole in a novel four-dimensional Einstein-Gauss-Bonnet gravity [D. Glavan and C. Lin, Phys. Rev. Lett. 124, 081301 (2020)]. We find that the effective potential of a spinning test particle in the background of the black hole has two minima when the Gauss-Bonnet coupling parameter $α$ is nearly in a special range $-6.1<α/M^2<-2$ ($M$ is the mass of the black hole), which means such particle can be in two separate orbits with the same spin angular momentum and orbit…
We generate from the static charged BTZ black hole a family of spinning charged solutions to the Einstein-Maxwell equations in 2+1 dimensions. These solutions go over, in a suitable limit, to self-dual spinning charged solutions, which are horizonless and regular, with logarithmically divergent mass and spin. To cure this divergence, we add a topological Chern-Simons term to the gauge field action. The resulting self-dual solution is horizonless, regular, and asymptotic to the extreme BTZ black hole.
The generalized Killing equations and the symmetries of Taub-NUT spinning space are investigated. For spinless particles the Runge-Lenz vector defines a constant of motion directly, whereas for spinning particles it now requires a non-trivial contribution from spin. The generalized Runge-Lenz vector for spinning Taub-NUT space is completely evaluated.
The motion of a classical spinning test particle in the field of a weak plane gravitational wave is studied. It is found that the characteristic dimensions of the particle's orbit is sensitive to the ratio of the spin to the mass of the particle. The results are compared with the corresponding motion of a particle without spin.
We report on the multipolar equations of motion for spinning test bodies in the de Sitter spacetime of constant positive curvature. The dynamics of spinning particles is discussed for the two supplementary conditions of Frenkel and Tulczyjew. Furthermore, the 4-momentum and the spin are explicitly expressed in terms of the spacetime coordinates with the help of the 10 Killing vectors available in de Sitter spacetime.
The onset of chaos in one-dimensional spinning particle models derived from pseudoclassical mechanical hamiltonians with a bosonic Duffing potential is examined. Using the Melnikov method, we indicate the presence of homoclinic entanglements in models with general potentials for the spins, and thus show that chaotic motions occur in these models.
Integrable spinning extension of a free particle on 2-sphere is constructed in which spin degrees of freedom are represented by a 3-vector obeying the Bianchi type-V algebra. Generalizations involving a scalar potential giving rise to two quadratic constants of the motion, or external field of the Dirac monopole, or the motion on the group manifold of SU(2) are built. A link to the model of a relativistic spinning particle propagating on the near horizon 7d Myers-Perry black hole background is considered. Implications of the construction in this work for the D(2,1;a) superconformal mechanics a…
The most general N=1 Lagrangian for the spinning particle with local supersymmetry is found and the constraints of the system are analysed. The Dirac quantisation of the model is also investigated.
The Kirillov-Souriau-Kostant construction is applied to derive the classical and quantum mechanics for the massive spinning particle in arbitrary dimension.
Inserting the correct Lorentz factor into the definition of the 4-velocity v^mu for spinning particles entails new kinematical properties for v^2. The well-known constraint (identically true for scalar particles, but entering also the Dirac theory, and assumed a priori in all spinning particle models) p_mu v^mu = m is here derived in a self-consistent way.
The Mathisson-Papapetrou equations in the Schwarzschild background both at Mathisson-Pirani and Tulczyjew-Dixon supplementary condition are considered. The region of existence of highly relativistic circular orbits of a spinning particle in this background and dependence of the particle's orbital velocity on its spin and radial coordinate are investigated. It is shown that in contrast to the highly relativistic circular orbits of a spinless particle, which exist only for $r=1.5 r_g(1+δ)$, $0<δ\ll 1$, the corresponding orbits of a spinning particle are allowed in a wider space region, and the d…
The Mathisson-Papapetrou equations in Kerr's background are considered. The region of existence of highly relativistic planar circular orbits of a spinning particle in this background and dependence of the particle's Lorentz $γ$-factor on its spin and radial coordinate are investigated. It is shown that in contrast to the highly relativistic circular orbits of a spinless particle the corresponding orbits of a spinning particle are allowed in much wider space region. Some of these orbits show the significant attractive action of the spin-gravity coupling on a particle and others are caused by t…
The general model of an arbitrary spin massive particle in any dimensional space-time is derived on the basis of Kirillov - Kostant - Souriau approach. Keywords: spinning particles, Poincaré group, orbit method, constrained dynamics, geometric quantization.
We construct the action of a non-relativistic spinning particle moving in a general torsionless Newton-Cartan background. The particle does not follow the geodesic equations, instead the motion is governed by the non-relativistic analog of Papapetrou equation. The spinning particle is described in terms of Grassmann variables. In the flat case the action is invariant under the non-relativistic analog of space-time vector supersymmetry.
On the basis of the Kerr spinning particle, we show that the mass renormalization is perfectly performed by gravity for an arbitrary distribution of source matter. A smooth regularization of the Kerr-Newman solution is considered, leading to a source in the form of a rotating bag filled by a false vacuum. It is shown that gravity controls the phase transition to an AdS or dS false vacuum state inside the bag, providing the mass balance.
It is shown that in the Schwarzschild background there exists direct counterpart of the Bañados-Silk-West effect for spinning particles. This means that if two particles collide near the black hole horizon, their energy in the centre of mass frame can grow unbounded. In doing so, the crucial role is played by so-called near-critical trajectories when particle's parameters are almost fine-tuned. Direct scenario of the collision under discussion is possible with restriction on the energy-to-mass ratio \thinspace $E/m<\frac{1}{2\sqrt{3}}$ only. However, if one takes into account multiple scatteri…
Following the Poincare algebra for a free spinning particle and using the Casimirs of the algebra in the Hamiltonian approach, we construct systematically a set of Lagrangians for the relativistic spinning particle which includes the Lagrangian given in the literature. Then we analyze the dynamics of this generalized system in the Lagrangian formulation and show that the equations of motion support an oscillatory solution corresponding to the spinning nature of the system. Next we analyze the canonical structure of the system and present the correct gauge suitable for the spinning motion of th…
In this letter, we discuss the extension of Feynman's derivation of the equation of motion to the case of spinning particles. We show that a spinning particle interacts only with the electromagnetic and gravitational fields. In the absence of the electromagnetic interactions, we rederive Papapetrou's equations for spinning particles in the background of the conformal gravity. We also find that the effect of spin coupled to non-constant electromagnetic fields leads to further corrections to the Lorentz force equations. Some discussions of these results are given at the end.
A new spinning particle with a definite sign of the energy is defined on spacelike hypersurfaces after a critical discussion of the standard spinning particles. They are the pseudoclassical basis of the positive energy $({1\over 2},0)$ [or negative energy $(0,{1\over 2})$] parts of the $({1\over 2},{1\over 2})$ solutions of the Dirac equation. The study of the isolated system of N such spinning charged particles plus the electromagnetic field leads to their description in the rest-frame Wigner-covariant instant form of dynamics on the Wigner hyperplanes orthogonal to the total 4-momentum of th…
We construct the U(N) spinning particle theories, which describe particles moving on Kahler spaces. These particles have the same relation to the N=2 string as usual spinning particles have to the NSR string. We find the restrictions on the target space of the theories coming from supersymmetry and from global anomalies. Finally, we show that the partition functions of the theories agree with what is expected from their spectra, unlike that of the N=2 string in which there is an anomalous dependence on the proper time.
In this manuscript we study the confinement of bosonic and spinning test particles in smooth Randall-Sundrum models. For this, we show that it is possible to find an effective potential which describe the motion of the particle over the extra dimension. For the bosonic case it is a known fact that free test particles cannot be localized neither in thin nor thick branes. Recently, a coupling to a scalar field has been used to localize a limited range of masses. Up to now, no mechanism has been found that can trap test particles of any mass over the brane. To solve this, we show that a coupling …
We study the interaction of a scalar and a spinning particle with a coherent linearized gravitational wave field treated as a classical spin two external field. The spin degrees of freedom of the spinning particle are described by skew-commuting variables. We derive the explicit expressions for the eigenfunctions and the Green's functions of the theory. The discussion is exact within the approximation of neglecting radiative corrections and we prove that the result is completely determined by the semiclassical contribution.
An explicit construction of theories of spinning particles, both massive and massless, is given with arbitrary extended supersymmetry on the world-line. As an application of our results, we give a universal description of 3D (and via truncation all lower dimensional) supersymmetric scalar multiplets with arbitrary N-extended supersymmetry.
It is shown that dynamics of D+2 elements of the (super)diffeomorphism group in one (1+1 for the super) dimension describes the D - dimensional (spinning) massless relativistic particles. The coordinates of this elements (D+2 einbeins, D+2 connections and 1 additional common coordinate of higher dimensionality) play the role of coordinates, momenta and Lagrange multiplier, needed for the manifestly conformal and reparametrization invariant description of the D - dimensional (spinning) particle in terms of the D+2 - dimensional spacetime.
We propose the action of d=4 Anti-de Sitter (AdS) spinning particle with arbitrary fixed quantum numbers. Regardless of the spin value, the configuration space of the model is a direct product of d=4 AdS space and two-dimensional sphere corresponds to spinning degrees of freedom. The model is an AdS counterpart of the massive spinning particle in the Minkowski space proposed earlier. Being AdS-invariant, the model possesses two gauge symmetries implying identical conservation law for AdS-counterparts of mass and spin. Two equivalent forms of the action functional, minimal and manifestly covari…
In this work we explore the geodesic deviations of spinning test particles in a string inspired Einstein-Kalb Ramond background. Such a background is known to be equivalent to a spacetime geometry with torsion. We have shown here that the antisymmetric Kalb-Ramond field has significant effect on the geodesic deviation of a spinning test particle. A search for an observational evidence of such an effect in astrophysical experiments may lead to a better undestanding of the geometry of the background spacetime.
A twistorial formulation of a particle of arbitrary spin has been constructed. Equations of the twistor formulation are obtained for massive and massless spinning particles. The twistor space of the massive particle is formed by two twistors and two complex scalars. In the massive case, integral transformations relating twistor fields with usual space-time fields have been constructed.
The classical spinning particles are considered such that quantization of classical model leads to an irreducible massive representation of the Poincaré group. The class of gauge equivalent classical particle world lines is shown to form a $[(d+1)/2]$-dimensional world sheet in $d$-dimensional Minkowski space, irrespectively to any specifics of classical model. For massive spinning particles in $d=3,4$, the world sheets are shown to be cylinders. The radius of cylinder is fixed by representation. In higher dimensions, particle's world sheet turn out to be a toroidal cylinder $\mathbb{R}\times …
The technique of functional integration over velocities is applied to the calculation of the propagator of a spinning particle with and without anomalous magnetic moment. A representation for the spin factor is obtained in this context for the particle in a constant electromagnetic field. As a by-product, we also obtain a Schwinger representation for the first case.
We derive, in 2+1 dimensions, classical solutions for metric and motion of two or more spinning particles, in the conformal Coulomb gauge introduced previously. The solutions are exact in the $N$-body static case, and are perturbative in the particles' velocities in the dynamic two-body case. A natural boundary for the existence of our gauge choice is provided by some ``CTC horizons'' encircling the particles, within which closed timelike curves occur.
This paper introduces the way of the embedding of spinning particle quantum mechanically. Schrödinger equation on its submanifold obtains the gauge field as spin connection, and it reduces to the ones obtained by Ohnuki and Kitakado when we consider $S^2$ in $R^3$. PACS numbers: 03.65
The article is a natural continuation of the papers by Gavrilov and Gitman (Class.Quant.Grav. {\bf 17} (2000) L133; Int. J. Mod. Phys. A15 (2000) 4499) devoted to relativistic particle quantization. Here we generalize the problem, considering the quantization of a spinning particle in arbitrary gravitational background. The nontriviality of such a generalization is related to the neccessity of solving complicated ordering problems. Similar to the flat space-time case, we show in the course of the canonical quantization how a consistent relativistic quantum mechanics of spinning particle in gra…
Twistor formulation of massive arbitrary spin particle has been constructed. Twistor space of such particle is formed two twistors and two complex scalars which form together 'bosonic supertwistor'. The formulation is deduced from space-time one for spinning particle by means of introducing auxiliary harmonic variables and consequent partial fixing of gauges. It is carried out the canonical quantization of twistor massive particle with nonzero spin. It is found the eigenvalues of Casimir operators on particle states and harmonic expansion of wave function in spectrum.
We show that a self-consistent classical theory of the spin, based on a very general Lagrangian extending the Newtonian dynamics, does predict the special case of helicity-0 particles, which at the same time are endowed with nonzero spin and zero intrinsic angular momentum.
Extending our prior investigation, we give a new off-shell construction of theories of spinning particles propagating in Minkowski spaces with arbitrary $N$-extended supersymmetry on the world-line. The basis of the new off-shell formulation is provided by realizations of new algebraic structures ${\cal G}{\cal R}$(${\rm d}, N$) that are certain generalizations of Pauli algebras.
