Radiative processes in external gravitational fields

Abstract

Kinematically forbidden processes may be allowed in the presence of external gravitational fields. These can be taken into account by introducing generalized particle momenta. The corresponding transition probabilities can then be calculated to all orders in the metric deviation from the fieldfree expressions by simply replacing the particle momenta with their generalized counterparts. The procedure applies to particles of any spin and to any gravitational fields. Transition probabilities, emission power and spectra are, to leading order, linear in the metric deviation. It is also shown how a small dissipation term in the particle wave equations can trigger a strong back-reaction that introduces resonances in the radiative process and deeply affects the resulting gravitational background.Processes in which massive, on-shell particles emit a photon according to Fig.1 are examples of kinematically forbidden transitions that remain so unless the dispersion relations of at least one of the particles involved are altered. This possibility presents itself when particles travel in a medium or in an external gravitational field.The action of gravitational fields on a particle's dispersion relations can be studied by solving the respective covariant wave equation. This can be done exactly to first order in the metric deviation γ µν = g µν − η µν , where η µν is the Minkowski metric [1-8]. The solutions contain the gravitational field in a phase operator that alters in effect a particle four-momentum by acting on the wave function of the field-free equations. This result applies equally well to fermions and bosons and can be extended to all orders in γ µν . The calculation of even the most elementary Feynman diagrams does therefore require an appropriate treatment when gravitational fields are present. While the inclusion of external electromagnetic fields has met with success in the case of static (Coulomb) fields [9], and can be easily carried out for static (Newtonian) fields, no systematic attempts have been made for relativistic gravity. The procedure developed below is intended to fill in part this gap and applies to weak, static and non-static gravitational fields.Let us assume, for simplicity, that P in Fig.1 is an incoming fermion and that the photon ℓ and outgoing fermion p ′ are produced on-shell. The solution of the covariant Dirac equation, exact to O(γ µν ), is [5] Ψ(x) = − 1 2m (−iγ µ (x)D µ − m) e −iΦT Ψ 0 (x) ≡T Ψ 0 ,

Maximal acceleration and radiative processes

“…There are processes, however, in which massive particles emitting a photon are not kinematically forbidden. This is certainly the case when gravitation alters the dispersion relations of at least one of the particles involved [75,76]. This is also the case with MA [77].…”

“…It now is possible to calculate the power radiated as photons in the process of Fig.1 following the procedure outlined in [75,76]. We find…”

Perspectives on Gravity-Induced Radiative Processes in Astrophysics

“…There are processes, however, in which massive particles emitting a photon are not kinematically forbidden. This is certainly the case when gravitation alters the dispersion relations of at least one of the particles involved [2]. We stress here that even the reduction of a Feynman diagram by a single vertex would result in a cross-section gain of a factor (GM/R) 2 , where M and R are the mass and radius of the gravitational source (unitsh = c = 1).…”

“…It may be argued that a transition amplitude M f →f γ must be added to Equation (8) at O(γ µν ), because the contraction in Equation (8) is, in general, accomplished by means of g µν , and g(x) contains a part that is independent of γ µν . The transition amplitude M , estimated in [2], is given: by [6] …”

“…The calculation of even the most elementary Feynman diagrams does require an appropriate treatment when gravitational fields are present. The procedures developed in [2] fill in part of this gap and apply to linearised gravitational, or inertial fields of any type up to intermediate intensities. The present paper focuses on the applications of the procedures outlined in [2] rather than on the individual reactions, though the aim still is to find physical processes capable of leading to potentially observable results.…”