Abstract
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.
Highlights
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 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 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
In this work we have shown that coexistence of metric perturbations and electromagnetic self-force can lead to an effect, in the motion of charged particles in curved space-time, which does not exist when any one among these two is absent
Summary
There are problems with point-particle notion when terms with second order metric perturbations are considered in calculation, we will not be facing it as we are considering linear metric perturbations only In this context the work by Zimmerman and Poisson [7] is very important, as it is probably the first work treating the case where electromagnetic and gravitational self-forces act together, while deriving their interaction terms. We interpret that these additional terms are just the perturbations to the electromagnetic self-force, due to the gravitational radiation or metric perturbations emitted by the system. We shall only work with the regular metric perturbation hμRν, thereby eliminating the singular behaviour of the retarded metric perturbation, emitted from the particle, on its world-line and all the consequent general relativistic perturbation quantities will be in terms of. The metric perturbations outside the larger massive body would satisfy the first order perturbation-equation of the background equation (7)
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