On-shell physics of black holes
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Date
31/07/2021Author
Maybee, Ben
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Abstract
On-shell methods are a key component of the modern amplitudes programme. By
utilising the power of generalised unitarity cuts, and focusing on gauge invariant
quantities, enormous progress has been made in the calculation of amplitudes
required for theoretical input into experiments such as the LHC. Recently, a
new experimental context has emerged in which scattering amplitudes can be of
great utility: gravitational wave astronomy. Indeed, developing new theoretical
techniques for tackling the two-body problem in general relativity is essential for
future precision measurements. Scattering amplitudes have already contributed
new state of the art calculations of post{Minkowskian (PM) corrections to the
classical gravitational potential.
The gravitational potential is an unphysical, gauge dependent quantity. This
thesis seeks to apply the advances of modern amplitudes to classical gravitational
physics by constructing physical, on-shell observables applicable to black hole
scattering, but valid in any quantum eld theory. We will derive formulae for the
impulse (change in momentum), total radiated momentum, and angular impulse
(change in spin vector) from basic principles, directly in terms of scattering
amplitudes.
By undertaking a careful analysis of the classical region of these observables, we
derive from explicit wavepackets how to take the classical limit of the associated
amplitudes. These methods are then applied to examples in both QED and QCD,
through which we obtain new theoretical results; however, the main focus is on
black hole physics. We exploit the double copy relationship between gravity and
gauge theory to calculate amplitudes in perturbative quantum gravity, from whose
classical limits we derive results in the PM approximation of general relativity.
Applying amplitudes to black hole physics o ers more than computational power:
in this thesis we will show that the observables we have constructed provide
particularly clear evidence that massive, spinning particles are the on-shell avatar
of the no-hair theorem. Building on these results, we will furthermore show that
the classically obscure Newman{Janis shift property of the exact Kerr solution can
be interpreted in terms of a worldsheet e ective action. At the level of equations
of motion, we show that the Newman{Janis shift holds also for the leading
interactions of the Kerr black hole. These leading interactions will be conveniently
described using chiral classical equations of motion with the help of the spinor
helicity method familiar from scattering amplitudes, providing a powerful and
purely classical method for computing on-shell black hole observables.