Planckian Energy Scattering and Surface Terms in the Gravitational Action

The scattering process of two particles at Planck energies or beyond is calculated using the gravitational shock wave metric for a massive black hole. Then, the scattering between a heavy mass particle and a small mass one is deal with. The cross section contains an extra new term of $\sigma \propto G^3$ as the correction term of the leading term derived by 't Hooft. The ultrarelativistic limit of the Lorentz boosted Reissner--Norstrom black hole is also calculated.

In a series of papers Amati, Ciafaloni and Veneziano and 't Hooft conjectured that black holes occur in the collision of two light particles at planckian energies. In this paper we discuss a possible scenario for such a process by using the Chandrasekhar-Ferrari-Xanthopoulos duality between the Kerr black hole solution and colliding plane gravitational waves. We clarify issues arising in the definition of transition amplitude from a quantum state containing only usual matter ...

A method to unitarize the scattering amplitude produced by infinite-range forces is developed and applied to Born terms. In order to apply $S$-matrix techniques, based on unitarity and analyticity, we first derive an $S$-matrix free of infrared divergences. This is achieved by removing a divergent phase factor due to the interactions mediated by the massless particles in the crossed channels, a procedure that is related to previous formalisms to treat infrared divergences. We...

Recently, 't Hooft's S-matrix for black hole evaporation, obtained from the gravitational interactions between the in-falling particles and Hawking radiation, has been generalised to include transverse effects. The action describing the collision turned out to be a string theory action with an antisymmetric tensor background. In this article we show that the model reproduces both the correct longitudinal and transverse dynamics, even when one goes beyond the eikonal approxima...

We argue that, as a consequence of the graviton's spin-2, its bremsstrahlung in trans-planckian-energy ($E\gg M_P$) gravitational scattering at small deflection angle can be nicely expressed in terms of helicity-transformation phases and their transfer within the scattering process. The resulting spectrum exhibits deeply sub-planckian characteristic energies of order $M_P^2/E \ll M_P$ (reminiscent of Hawking radiation), a suppressed fragmentation region, and a reduced rapidit...

We outline the program to apply modern quantum field theory methods to calculate observables in classical general relativity through a truncation to classical terms of the multi-graviton two-body on-shell scattering amplitudes between massive fields. Since only long-distance interactions corresponding to non-analytic pieces need to be included, unitarity cuts provide substantial simplifications for both post-Newtonian and post-Minkowskian expansions. We illustrate this quantu...

In order to facilitate the study of weak ultra-relativistic (and Planckian) scattering we present an appropriate decomposition of the gravitational field together with its whole non-linear action. More generally the results apply to any reduction over a non-degenerate spacetime fiber.

Point particle scattering at Planckian centre-of-mass (cm) energies and low fixed momentum transfers, occurring due both to electromagnetic and gravitational interactions, is surveyed, with particular emphasis on the novel features occurring in electromagnetic charge-monopole scattering. The issue of possible mixing of the shock waves occurring due to both kinds of interactions is then addressed within the framework of Einsteinian general relativity and the dilatonic extensio...

We consider the gravitational scattering of point particles in four dimensions, at Planckian centre of mass energy and low momentum transfer, or the eikonal approximation. The scattering amplitude can be exactly computed by modelling point particles by very generic metrics. A class of such metrics are black hole solutions obtained from dimensional reduction of p-brane solutions with one or more Ramond-Ramond charges in string theory. At weak string coupling, such black holes ...

We study the high-energy limit of projectable Ho\v rava gravity using on-shell graviton scattering amplitudes. We compute the tree-level amplitudes using symbolic computer algebra and analyze their properties in the case of collisions with zero total momentum. The amplitudes grow with collision energy in the way consistent with tree-level unitarity. We discuss their angular dependence and derive the expression for the differential cross section that happens to depend only on ...