Eikonal particle scattering and dilaton gravity
American Physical Society
Approximating light charged pointlike particles in terms of ~nonextremal! dilatonic black holes is shown to lead to certain pathologies in Planckian scattering in the eikonal approximation, which are traced to the presence of a ~naked! curvature singularity in the metric of these black holes. The existence of such pathologies is confirmed by analyzing the problem in an ‘‘external metric’’ formulation where an ultrarelativistic point particle scatters off a dilatonic black hole geometry at large impact parameters. The maladies disappear almost trivially upon imposing the extremal limit. Attempts to derive an effective three-dimensional ‘‘boundary’’ field theory in the eikonal limit are stymied by four-dimensional ~bulk! terms proportional to the light-cone derivatives of the dilaton field, leading to nontrivial mixing of electromagnetic and gravitational effects, in contrast with the case of general relativity. An eikonal scattering amplitude, showing decoupling of these effects, is shown to be derivable by resummation of graviton, dilaton, and photon exchange ladder diagrams in a linearized version of the theory for an asymptotic value of the dilaton field which makes the string coupling constant nonperturbative.
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Eikonal scattering , Dilaton , Black holes
Das. S., & Majumdar, P. (1997). Eikonal particle scattering and dilaton gravity. Physical review D, 55(4), 2090-2098. http://dx.doi.org/10.1103/PhysRevD.55.2090