Electromagnetic Self-force Research Articles

Spin and Susceptibility Effects of Electromagnetic Self-Force in Effective Field Theory.

The classic Abraham-Lorentz-Dirac self-force of pointlike particles is generalized within an effective field theory setup to include linear spin and susceptibility effects described perturbatively, in that setup, by effective couplings in the action. Electromagnetic self-interactions of the pointlike particle are integrated out using the in-in supersymmetric worldline quantum field theory formalism. Divergences are regularized with dimensional regularization, and the resulting equations of motion are in terms only of an external electromagnetic field and the particle degrees of freedom.

Calculation of the electromagnetic self-force of a non-lorentz-contractible uniformly charged spherical shell in arbitrary rectilinear motion

Calculation of the electromagnetic self-force of a non-lorentz-contractible uniformly charged spherical shell in arbitrary rectilinear motion

Resonance crossing of a charged body in a magnetized Kerr background: An analog of extreme mass ratio inspiral

We investigate resonance crossings of a charged body moving around a Kerr black hole immersed in an external homogeneous magnetic field. This system can serve as an electromagnetic analogue of a weakly non-integrable extreme mass ratio inspiral (EMRI). In particular, the presence of the magnetic field renders the conservative part of the system non-integrable in the Liouville sense, while the electromagnetic self-force causes the charged body to inspiral. By studying the system without the self-force, we show the existence of an approximate Carter-like constant and discuss how resonances grow as a function of the perturbation parameter. Then, we apply the electromagnetic self-force to investigate crossings of these resonances during an inspiral. Averaging the energy and angular momentum losses during crossings allows us to employ an adiabatic approximation for them. We demonstrate that such adiabatic approximation provides results qualitatively equivalent to the instantaneous self-force evolution, which indicates that the adiabatic approximation may describe the resonance crossing with sufficiently accuracy in EMRIs.

Particle Motion under the Conservative Piece of the Self-Force is Hamiltonian.

We consider the motion of a point particle in a stationary spacetime under the influence of a scalar, electromagnetic, or gravitational self-force. We show that the conservative piece of the first-order self-force gives rise to Hamiltonian dynamics, and we derive an explicit expression for the Hamiltonian on phase space. Specialized to the Kerr spacetime, our result generalizes the Hamiltonian function previously obtained by Fujita etal. [Classical Quantum Gravity 34, 134001 (2017).CQGRDG0264-938110.1088/1361-6382/aa7342], which is valid only for nonresonant orbits.

Electromagnetic self-force on a charged particle on Kerr spacetime: Equatorial circular orbits

We calculate the self-force acting on a charged particle on a circular geodesic orbit in the equatorial plane of a rotating black hole. We show by direct calculation that the dissipative self-force balances with the sum of the flux radiated to infinity and through the black hole horizon. Prograde orbits are found to stimulate black hole superradiance, but we confirm that the condition for floating orbits cannot be met. We calculate the conservative component of the self-force by application of the mode sum regularization method, and we present a selection of numerical results. By numerical fitting, we extract the leading-order coefficients in post-Newtonian expansions. The self-force on the innermost stable circular orbits of the Kerr spacetime is calculated, and comparisons are drawn between the electromagnetic and gravitational self forces.

Self-force effects in post-Minkowskian scattering

Abstract We revisit the old problem of the self-force on a particle moving in a weak-field spacetime in the context of renewed interest in two-body gravitational scattering. We analytically calculate the scalar, electromagnetic, and gravitational self-force on a particle moving on a straight-line trajectory at a large distance from a Newtonian star, and use these results to find the associated correction to its motion. In the gravitational case we must also include the matter-mediated force, which acts at the same perturbative order as the gravitational self-force. We further augment the gravitational results with geodesic calculations at second order in the central body mass to determine the full, explicit solution to the two-body gravitational scattering problem at second post-Minkowskian order (2PM). We calculate the momentum transfer (which reproduces Westpfahl’s old result), the change in mechanical angular momentum (which matches the radiative flux recently computed by Damour), and the change in mechanical mass moment (the time-space components of the angular momentum tensor), which has not previously appeared. Besides the new 2PM results of explicit trajectories and all conserved quantities, this work clarifies the role of gravitational self-force in PM scattering theory and provides a foundation for higher-order calculations.

Perturbative correction terms to electromagnetic self-force due to metric perturbation: astrophysical and cosmological implications

We consider the equation of motion of a charged particle or a charged compact object in curved space-time, under the reaction of electromagnetic radiation and also consider a physical situation such that the charged particle or compact object emits gravitational radiation, thereby gravitational radiation reaction also acts on it. We investigate the effect of this metric perturbation i.e. the gravitational radiation on the electromagnetic self-force. We show that, besides the interaction terms derived by Zimmerman and Poisson (Phys Rev D 90:084030, 2014), additional perturbative terms are generated, which are linear in metric perturbation and are generated due to perturbation of the electromagnetic self-force by the metric perturbation. We discuss the conditions of significance of these perturbative terms and also the interaction terms with respect to the gravitational self-force in various astrophysical and cosmological cases; such as the motion of charged particles around black holes, some extreme mass-ratio inspirals (EMRIs) involving sufficiently accelerated motion of charged stars (specially neutron stars) or charged stellar mass black holes around supermassive black holes, and motion of charged particles around charged primordial black holes formed in the early Universe etc. We find that in some astrophysical and cosmological cases these perturbative terms can have significant effect in comparison with the gravitational radiation-reaction term.

Finite and divergent parts of the self-force of a point charge from its spherically averaged self-field

The electromagnetic self-force of a point charge moving arbitrarily on a rectilinear trajectory is calculated by averaging its retarded electric self-field over a sphere of infinitesimal radius centred on the charge's present position. The finite part of the self-force obtained is the well-established relativistic radiation reaction, while its divergent part implies the pre-relativistic longitudinal electromagnetic mass of Abraham.

Self-force on moving electric and magnetic dipoles: Dipole radiation, Vavilov-Čerenkov radiation, friction with a conducting surface, and the Einstein-Hopf effect

This paper studies the classical electromagnetic self-force on a moving dipole, in vacuum and in a medium, the resulting dipole and Vavilov-\ifmmode \check{C}\else \v{C}\fi{}erenkov radiation, as well as the the quantum black-body friction on a polarizable particle moving in vacuum.

Self-force on a static particle near a black hole

We study the self-force acting on a static charged point-like particle near a Schwarzschild black hole. We obtain the point-like particle as a limit of a spacetime describing a big neutral black hole with a small charged massive object nearby. The massive object is modeled by a black hole or a naked singularity. In this fully interacting system the massive object is supported above the black hole by a strut. Such a strut has a non-zero tension which corresponds to the external force compensating the gravitational force and the electromagnetic self-force acting on the massive object. We discuss details of the limiting procedure leading to the point-like particle situation. As a result, we obtain the standard gravitational force in the static frame of the Schwarzschild spacetime and the electromagnetic self-force. The electromagnetic-self force differs slightly from the classical results in a domain near the horizon. The difference is due to taking into account an influence of the strut on the electromagnetic field. We also demonstrate that higher order corrections to the gravitational force, a sort of the gravitational self-force, are not uniquely defined and they depend on details of the limiting procedure.

Finite-size effects on the self-force

Electromagnetic and linear gravitational radiation do not solely propagate on the null cone in 3+1 dimensions in curved spacetimes, contrary to their well-known behavior in flat spacetime. Their additional propagation inside the null cone is known as the tail effect. A compact body will produce a signal whose tail will interact with its future worldline, thus producing a tail-induced self-force. We present new results for the tail-induced scalar, electromagnetic and gravitational self-force for a test mass in orbit around a central mass, including effects from the internal structure of that body.

Electromagnetic Self-Force of a Point Charge from the Rate of Change of the Momentum of Its Retarded Self-Field

The self-force of a point charge moving on a rectilinear trajectory is obtained, with no need of any explicit removal of infinities, as the negative of the time rate of change of the momentum of its retarded self-field.

Electromagnetic self-force in the five dimensional Myers–Perry space–time

We calculate the effects of the electromagnetic self-force on a charged particle outside a five dimensional Myers–Perry space–time. Based on our earlier work (Mirzaiyan et al., 2018), we obtain the self-force using quaternions in Janis–Newman and Giampieri algorithms. In four dimensional rotating space–time the electromagnetic self-force is repulsive at any point, however, in five dimensional rotational space–time, we find a point r0 where the electromagnetic self-force vanishes. For r<r0 (r>r0) the electromagnetic self-force is attractive (repulsive).

On the quantum interpretation of the classical Schott term in the theory of radiation damping

The quantum interpretation of classical radiation reaction coming from the near electromagnetic self-force (the so-called “Schott term”) is given for the first time. The analysis is based on the Landau–Lifshitz equation for classical ultrarelativistic motion including radiation reaction effects for the case of channeling radiation in oriented crystals in the wide region of electron energies from few MeV and up to hundreds GeV. This type of radiation is unique in that sense that it has a pronounced quantum character in two extreme cases of low and high energies. We show that quantum transitions between the transverse energy states of channeling particles represent the quantum analog of the classical Schott term. The impetus for this work was the recent reports on the feasibility of detecting experimentally the effects of the action of classical radiative self-force on the motion of electrons (positrons) channeled in oriented crystals at the CERN Secondary Beam Areas (SBA) beamlines, although the basic results of this work are valid for arbitrary ultrarelativistic motion.

Electromagnetic self-force in curved spacetime: New insights from the Janis-Newman algorithm

We present an original approach to compute the electromagnetic self-force acting on a static charge in Kerr spacetime. Our approach is based on an improved version of the Janis-Newman algorithm and extends its range of applicability. It leads to a closed expression which generalizes the existing one and, since it does not involve the electromagnetic potential, it simplifies the calculation of the self-force.

Self-forces on static bodies in arbitrary dimensions

We derive exact expressions for the scalar and electromagnetic self-forces and self-torques acting on arbitrary static extended bodies in arbitrary static spacetimes with any number of dimensions. Non-perturbatively, our results are identical in all dimensions. Meaningful point particle limits are quite different in different dimensions, however. These limits are defined and evaluated, resulting in simple "regularization algorithms" which can be used in concrete calculations. In these limits, self-interaction is shown to be progressively less important in higher numbers of dimensions; it generically competes in magnitude with increasingly high-order extended-body effects. Conversely, we show that self-interaction effects can be relatively large in $1+1$ and $2+1$ dimensions. Our motivations for this work are twofold: First, no previous derivation of the self-force has been provided in arbitrary dimensions, and heuristic arguments presented by different authors have resulted in conflicting conclusions. Second, the static self-force problem in arbitrary dimensions provides a valuable testbed with which to continue the development of general, non-perturbative methods in the theory of motion. Several new insights are obtained in this direction, including a significantly improved understanding of the renormalization process. We also show that there is considerable freedom to use different "effective fields" in the laws of motion---a freedom which can be exploited to optimally simplify specific problems. Different choices give rise to different inertias, gravitational forces, and electromagnetic or scalar self-forces, but there is a sense in which none of these quantities are individually accessible to experiment. Certain combinations are observable, however, and these remain invariant under all possible field redefinitions.

Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit.

Charged particles in curved space-time

Considering the dynamics of geometry and the matter fields, dynamical equations of geometry and the matter fields are re-derived. The solutions of these equations are studied. We focus on a charged particle and explain the axiomatic approach to drive the electromagnetic self-force on its motion, then the energy conservation is considered. A new mathematical concept, which is introduced in axiomatic approach in general, is discussed.

-symmetric interpretation of the electromagnetic self-force

In 1980 Englert examined the classic problem of the electromagnetic self-force on an oscillating charged particle. His approach, which was based on an earlier idea of Bateman, was to introduce a time-reversed (charge-conjugate) particle and to show that the two-particle system is Hamiltonian. Unfortunately, Englert’s model did not solve the problem of runaway modes, and the corresponding quantum theory had ghost states. It is shown here that Englert’s Hamiltonian is symmetric, and that the problems with his model arise because the symmetry is broken at both the classical and the quantum level. However, by allowing the charged particles to interact and by adjusting the coupling parameters to put the model into an unbroken -symmetric region, one eliminates the classical nonrelativistic runaway modes and obtains a corresponding nonrelativistic quantum system that is in equilibrium and ghost free.

Self-force of a rigid ideal fluid, and a charged sphere in hyperbolic motion

We present two results in the treatment of self-force of accelerating bodies. If the total force on an extended rigid object is calculated from the change of momentum summed over planes of simultaneity of successive rest frames, then we show that an ideal fluid, moving rigidly, exerts a net force on its boundary that is independent of both pressure and orientation. Under this same definition of total force, we find the electromagnetic self-force for a spherical charged shell of proper radius $R$ accelerating with constant proper acceleration $g$ is $(2{e}^{2}g/R)[1/12\ensuremath{-}{\ensuremath{\sum}}_{n=0}^{\ensuremath{\infty}}(gR{)}^{2n}((2n\ensuremath{-}3)(2n\ensuremath{-}1)(2n+1{)}^{2}{)}^{\ensuremath{-}1}]$.