The Eikonal Approximation and the Gravitational Dynamics of Binary Systems

PhD ThesisIn this thesis we study the conservative gravitational dynamics of binary systems using the eikonal approximation; allowing us to use scattering amplitude techniques to calculate dynamical quantities in classical gravity. This has implications for the study of binary black hole systems and their resulting gravitational waves. In the rst three chapters we introduce some of the basic concepts and results that we will use in the rest of the thesis. In the rst chapter an overview of the topic is discussed and the academic context is introduced. The second chapter includes a basic discussion of gravity as a quantum eld theory, the post-Newtonian (PN) and post- Minkowskian (PM) expansions and the eikonal approximation. In the third chapter we consider various Feynman integrals that are used extensively in subsequent chapters. Speci cally, we give a recipe for expanding the relevant integrands in a so-called high energy expansion and then calculating the resulting integrals. The fourth chapter involves the study of massless states scattering o of a stack of Dp-branes in N = 8 supergravity. The setup we consider provides an ideal scenario to study inelastic contributions to the scattering process and their impact on the formulation of the eikonal approximation. These results will give us a better understanding of the eikonal approximation presented in the second chapter. The fth chapter involves studying the eikonal and corresponding dynamical quantities in a Kaluza-Klein theory of gravity providing further interesting insight into the eikonal approximation and allowing us to compare with various known results. The sixth and seventh chapter apply the concepts developed in this thesis to the problem of binary Schwarzschild black holes in D spacetime dimensions. This allows us to apply the framework exposed in previous chapters to a physically realistic scenario giving us a better understanding of how to extract the relevant dynamical information from scattering amplitudes. The results derived in chapter six also have an impact on our understanding at higher orders in the PM expansion beyond the ones considered in this text. In the seventh chapter we present the Hamiltonian for a system of binary Schwarzschild black holes and show how to extract the Hamiltonian from other dynamical quantities calculated using the eikonal. In the last chapter we provide some concluding remarks and a brief outlook

The subleading eikonal in supergravity theories

In this paper we study the subleading contributions to eikonal scattering in (super)gravity theories with particular emphasis on the role of both elastic and inelastic scattering processes. For concreteness we focus on the scattering of various massless particles off a stack of D$p$-branes in type II supergravity in the limit of large impact parameter $b$. We analyse the relevant field theory Feynman diagrams which naturally give rise to both elastic and inelastic processes. We show that in the case analysed the leading and subleading eikonal only depend on elastic processes, while inelastic processes are captured by a pre-factor multiplying the exponentiated leading and subleading eikonal phase. In addition to the traditional Feynman diagram computations mentioned above, we also present a novel method for computing the amplitudes contributing to the leading and subleading eikonal phases, which, in the large $b$ limit, only involves knowledge of the onshell three and four-point vertices. The two methods are shown to give the same results. Furthermore we derive these results in yet another way, by computing various one-point amplitudes which allow us to extract the classical solution of the gravitational back reaction of the target D$p$-branes. Finally we show how our expressions for the leading and subleading eikonal agree with the calculation of the metric and corresponding deflection angle for massless states moving along geodesics in the relevant curved geometry.Comment: 40 pages, 5 figure