Classical Soft Theorem in the AdS-Schwarzschild spacetime in small cosmological constant limit

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.

Soft photon theorem in the small negative cosmological constant limit

“…The current paper generalizes our previous work [33] on the effect of the small AdS potential on the classical soft graviton theorem by including an electromagnetic interaction. We also find the effect of the small AdS potential on the classical soft photon theorem.…”

“…Since we are interested in studying the radiation emitted by the scattering of a probe particle moving in an unbounded trajectory on the spacetime (from the point of view of an asymptotic observer) we introduce isotropic coordinates. We refer the reader to [33] for further justification on choosing this particular coordinate system. In these coordinates, the resulting radiation will be isotropic in all spatial directions.…”

“…In the next section we will solve (2.31) and (2.32) for e ij and a i in frequency space using the worldline formalism. The result will involve a Green's function for the 1/l 2 correction which was previously derived in [33].…”

“…Finally to study the "soft limit" of the classical radiation in asymptotically AdS spacetime, we consider a double scaling limit [33]: where the frequency of radiation and cosmological constant simultaneously tend to zero, keeping their ratio finite. This is due to the fact that a radiation mode in a theory that asymptotes to AdS spacetime has a minimum frequency inversely proportional to the size of the AdS and hence the frequency of the radiation cannot limit to a zero value.…”

Charge algebra in Al(A)dSn spacetimes

“…This Λ-BMS n algebra has the interesting property to reduce to the (generalized) BMS n algebra in the flat limit [25,26,30,[48][49][50][51][52][53][54][55][56][57][58]. Furthermore, the Λ-BMS n algebra may be deeply involved in the investigation of the infrared structure of gravity in presence of non-vanishing cosmological constant [59][60][61][62][63][64] and the possible interplay between symmetries [40,42,43,59,61,65], memory effects [64,[66][67][68][69][70][71][72] and consistency conditions for correlation functions [59,61,[73][74][75][76][77], playing a similar role than the BMS n group in asymptotically flat spacetimes (see e.g. [29,[78][79][80][81] for partial reviews).…”