Abstract
We have studied scattering of a probe particle by a four dimensional AdS-Schwarzschild black hole at large impact factor. Our analysis is consistent perturbatively to leading order in the AdS radius and black hole mass parameter. Next we define a proper “soft limit” of the radiation and extract out the “soft factor” from it. We find the correction to the well known flat space Classical Soft graviton theorem due to the presence of an AdS background.
Highlights
With soft photons or/and gravitons to amplitudes without any soft particle, in a quantum theory of photons and gravitons in asymptotically flat space times
Sen et al independently proved these theorems by a classical analysis in [36] and [39]. Both the photon and graviton soft factors for asymptotically flat spacetime can be used to determine the memory effect and a tail term to it arising from scattering processes involving several outgoing light particles and no incoming light particles [40,41,42]. Their works are primarily valid for classical scattering computations in theories in asymptotically flat spacetimes, but the idea can be extended to other curved spaces as well, that does not behave as flat at large distances
This is the key idea of this present work, where we address the issue of soft factor in theories in asymptotically AdS spaces by studying classical radiation [43,44,45,46] in a AdS Schwarzschild background
Summary
We study perturbations of a four dimensional theory of gravity with negative cosmological constant Λ, induced by a point mass moving in an unbound trajectory. The metric function has only one real positive root [52]. It is necessary to impose special boundary conditions at the spatial infinity, r = ∞, to make sure that the fields reach there. Infinity for fields at the AdS boundary. This condition implies a non-vanishing self-force unlike in deSitter space, where the self-force vanishes. This happens because AdS is conformal not to Minkowski space, but to Minkowski space with special boundary conditions. For large l and R l, the time taken to reach the spatial infinity is comparable to R.
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