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Register a new userPerturbative correction terms to electromagnetic self-force due to metric perturbation : astrophysical and cosmological implications
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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 P. Zimmerman and E. 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.
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Much of the success of gravitational-wave astronomy rests on perturbation theory. Historically, perturbative analysis of gravitational-wave sources has largely focused on post-Newtonian theory. However, strong-field perturbation theory is essential in many cases such as the quasinormal ringdown following the merger of a binary system, tidally perturbed compact objects, and extreme-mass-ratio inspirals. In this review, motivated primarily by small-mass-ratio binaries but not limited to them, we provide an overview of essential methods in (i) black hole perturbation theory, (ii) orbital mechanics in Kerr spacetime, and (iii) gravitational self-force theory. Our treatment of black hole perturbation theory covers most common methods, including the Teukolsky and Regge-Wheeler-Zerilli equations, methods of metric reconstruction, and Lorenz-gauge formulations, presenting them in a new consistent and self-contained form. Our treatment of orbital mechanics covers quasi-Keplerian and action-angle descriptions of bound geodesics and accelerated orbits, osculating geodesics, near-identity averaging transformations, multiscale expansions, and orbital resonances. Our summary of self-force theorys foundations is brief, covering the main ideas and results of matched asymptotic expansions, local expansion methods, puncture schemes, and point particle descriptions. We conclude by combining the above methods in a multiscale expansion of the perturbative Einstein equations, leading to adiabatic and post-adiabatic evolution schemes. Our presentation is intended primarily as a reference for practitioners but includes a variety of new results. In particular, we present the first complete post-adiabatic waveform-generation framework for generic (nonresonant) orbits in Kerr.
The causal set approach to quantum gravity models spacetime as a discrete structure - a causal set. Recent research has led to causal set models for the retarded propagator for the Klein-Gordon equation and the dAlembertian operator. These models can be compared to their continuum counterparts via a sprinkling process. It has been shown that the models agree exactly with the continuum quantities in the limit of an infinite sprinkling density - the continuum limit. This paper obtains the correction terms for these models for sprinkled causal sets with a finite sprinkling density. These correction terms are an important step towards testable differences between the continuum and discrete models that could provide evidence of spacetime discreteness.
This is a comment on the recent paper by G. S. Adkins and J. McDonnell ``Orbital precession due to central-force perturbations published in Phys. Rev. D75 (2007), 082001 [arXiv:gr-qc/0702015]. We show that the main result of this paper, the formula for the precession of Keplerian orbits induced by central-force perturbations, can be obtained very simply by the use of Hamiltons vector.
Inspirals of stellar-mass objects into massive black holes will be important sources for the space-based gravitational-wave detector LISA. Modelling these systems requires calculating the metric perturbation due to a point particle orbiting a Kerr black hole. Currently, the linear perturbation is obtained with a metric reconstruction procedure that puts it in a no-string radiation gauge which is singular on a surface surrounding the central black hole. Calculating dynamical quantities in this gauge involves a subtle procedure of gauge completion as well as cancellations of very large numbers. The singularities in the gauge also lead to pathological field equations at second perturbative order. In this paper we re-analyze the point-particle problem in Kerr using the corrector-field reconstruction formalism of Green, Hollands, and Zimmerman (GHZ). We clarify the relationship between the GHZ formalism and previous reconstruction methods, showing that it provides a simple formula for the gauge completion. We then use it to develop a new method of computing the metric in a more regular gauge: a Teukolsky puncture scheme. This scheme should ameliorate the problem of large cancellations, and by constructing the linear metric perturbation in a sufficiently regular gauge, it should provide a first step toward second-order self-force calculations in Kerr. Our methods are developed in generality in Kerr, but we illustrate some key ideas and demonstrate our puncture scheme in the simple setting of a static particle in Minkowski spacetime.
Up to now there has been no reliable method to calculate the Casimir force when surface roughness becomes comparable with the separation between bodies. Statistical analysis of rough Au films demonstrates rare peaks with heights considerably larger than the root-mean-square (rms) roughness. These peaks define the minimal distance between rough surfaces and can be described with extreme value statistics. We show that the contributions of high peaks to the force can be calculated independently of each other while the contribution of normal roughness can be evaluated perturbatively beyond the proximity force approximation. The developed method allows a reliable force estimation for short separations. Our model explains the strong hitherto unexplained deviation from the normal Casimir scaling observed experimentally at short separations.
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