Dvali, G.; Gomez, C.; Isermann, R. S.; Lüst, D.; Stieberger, S.
(2015):
Black hole formation and classicalization in ultraPlanckian 2 > N scattering.
In: Nuclear Physics B, Vol. 893: pp. 187235


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Abstract
We establish a connection between the ultraPlanckian scattering amplitudes in field and string theory and unitarization by black hole formation in these scattering processes. Using as a guideline an explicit microscopic theory in which the black hole represents a boundstate of many soft gravitons at the quantum critical point, we were able to identify and compute a set of perturbative amplitudes relevant for black hole formation. These are the treelevel Ngraviton scattering Smatrix elements in a kinematical regime (called classicalization limit) where the two incoming ultraPlanckian gravitons produce a large number N of soft gravitons. We compute these amplitudes by using the KawaiLewellenTye relations, as well as scattering equations and string theory techniques. We discover that this limit reveals the key features of the microscopic corpuscular black hole Nportrait. In particular, the perturbative suppression factor of a Ngraviton final state, derived from the amplitude, matches the nonperturbative black hole entropy when N reaches the quantum criticality value, whereas final states with different value of N are either suppressed or excluded by nonperturbative corpuscular physics. Thus we identify the microscopic reason behind the black hole dominance over other final states including nonblack hole classical object. In the parameterization of the classicalization limit the scattering equations can be solved exactly allowing us to obtain closed expressions for the highenergy limit of the open and closed superstring treelevel scattering amplitudes for a generic number N of external legs. We demonstrate matching and complementarity between the string theory and field theory in different larges and largeN regimes. (C) 2015 The Authors. Published by Elsevier B.V.