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Register a new userClassical black hole scattering from a worldline quantum field theory
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A precise link is derived between scalar-graviton S-matrix elements and expectation values of operators in a worldline quantum field theory (WQFT), both used to describe classical scattering of a pair of black holes. The link is formally provided by a worldline path integral representation of the graviton-dressed scalar propagator, which may be inserted into a traditional definition of the S-matrix in terms of time-ordered correlators. To calculate expectation values in the WQFT a new set of Feynman rules is introduced which treats the gravitational field $h_{mu u}(x)$ and position $x_i^mu(tau_i)$ of each black hole on equal footing. Using these both the next-order classical gravitational radiation $langle h^{mu u}(k)rangle$ (previously unknown) and deflection $Delta p_i^mu$ from a binary black hole scattering event are obtained. The latter can also be obtained from the eikonal phase of a $2to2$ scalar S-matrix, which we show to correspond to the free energy of the WQFT.
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We develop an effective theory which describes black holes with quantum mechanical horizons that is valid at scales long compared to the Schwarzschild radius but short compared to the lifetime of the black hole. Our formalism allows one to calculate the quantum mechanical effects in scattering processes involving black hole asymptotic states. We point out that the EFT Wightman functions which describe Hawking radiation in the Unruh vacuum are not Planck suppressed and are actually {it enhanced} relative to those in the Boulware vacuum, for which such radiation is absent. We elaborate on this point showing how the non-Planck suppressed effects of Hawking radiation cancel in classical observables.
Using the recently established formalism of a worldline quantum field theory (WQFT) description of the classical scattering of two spinless black holes, we compute the far-field time-domain waveform of the gravitational waves produced in the encounter at leading order in the post-Minkowskian (weak field, but generic velocity) expansion. We reproduce previous results of Kovacs and Thorne in a highly economic way. Then using the waveform we extract the leading-order total radiated angular momentum and energy (including differential results). Our work may enable crucial improvements of gravitational-wave predictions in the regime of large relative velocities.
We investigate the propagation of gravitational waves on a black hole background within the low energy effective field theory of gravity, where effects from heavy fields are captured by higher dimensional curvature operators. Depending on the spin of the particles integrated out, the speed of gravitational waves at low energy can be either superluminal or subluminal as compared to the causal structure observed by other species. Interestingly however, gravitational waves are always exactly luminal at the black hole horizon, implying that the horizon is identically defined for all species. We further compute the corrections on quasinormal frequencies caused by the higher dimensional curvature operators and highlight the corrections arising from the low energy effective field.
In this paper we aim to investigate the process of massless scalar wave scattering due to a self-dual black hole through the partial wave method. We calculate the phase shift analytically at the low energy limit and we show that the dominant term of the differential cross section at the small angle limit is modified by the presence of parameters related to the polymeric function and minimum area of a self-dual black hole. We also find that the result for the absorption cross section is given by the event horizon area of the self-dual black hole at the low frequency limit. We also show that, contrarily to the case of a Schwarzschild black hole, the differential scattering/absorption cross section of a self-dual black hole is nonzero at the zero mass limit. In addition, we verify these results by numerically solving the radial equation for arbitrary frequencies.
The quantum field theoretic description of general relativity is a modern approach to gravity where gravitational force is carried by spin-2 gravitons. In the classical limit of this theory, general relativity as described by the Einstein field equations is obtained. This limit, where classical general relativity is derived from quantum field theory is the topic of this thesis. The Schwarzschild-Tangherlini metric, which describes the gravitational field of an inertial point particle in arbitrary space-time dimensions, $D$, is analyzed. The metric is related to the three-point vertex function of a massive scalar interacting with a graviton to all orders in $G_N$, and the one-loop contribution to this amplitude is computed from which the $G_N^2$ contribution to the metric is derived. To understand the gauge-dependence of the metric, covariant gauge is used which introduces the parameter, $xi$, and the gauge-fixing function $G_sigma$. In the classical limit, the gauge-fixing function turns out to be the coordinate condition, $G_sigma=0$. As gauge-fixing function a novel family of gauges, which depends on an arbitrary parameter $alpha$ and includes both harmonic and de Donder gauge, is used. Feynman rules for the graviton field are derived and important results are the graviton propagator in covariant gauge and a general formula for the n-graviton vertex in terms of the Einstein tensor. The Feynman rules are used both in deriving the Schwarzschild-Tangherlini metric from amplitudes and in the computation of the one-loop correction to the metric. The one-loop correction to the metric is independent of the covariant gauge parameter, $xi$, and satisfies the gauge condition $G_sigma=0$ where $G_sigma$ is the family of gauges depending on $alpha$. In space-time $D=5$ a logarithm appears in position space and this phenomena is analyzed in terms of redundant gauge freedom.
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