Soft factors from classical scattering on the Reissner-Nordström spacetime

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

“…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]. Although 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.…”

Classical sub-subleading soft photon and soft graviton theorems in four spacetime dimensions

“…On the other hand, classical limit of multiple soft graviton theorem determines the low frequency radiative mode of the gravitational waveform in terms of the momenta and spin of the macroscopic objects (scattering data) participating in the scattering process, without the detail knowledge of the interactions responsible for the classical scattering process [20][21][22]. This is also related to the classical gravitational memory [23][24][25][26][27][28][29][30][31][32][33][34] after performing Fourier transformation in the frequency of the gravitational waveform. An analogous inter-connection has been established between soft photon theorem [2][3][4][5][35][36][37][38][39][40][41] and electromagnetic memory [42][43][44][45].…”

Soft photon theorem in the small negative cosmological constant limit

“…Physically, we think of studying a scattering process in an asymptotically flat theory modified by a small potential (inversely proportional to the square of the AdS radius). Thus our results provide us perturbative corrections to order 1/l 2 of known results for classical photon and graviton radiation profiles in the asymptotically flat Reissner-Nordström case [32]. The details of the scattering process we consider will be discussed in later sections.…”

“…The solution ofψ that are leading order in φ and 1/l 2 provide tail contributions to the flat spacetime Green's function, which arises due to the black hole potential and AdS potential. Denoting these tail terms as G M and G l , they have the solutions [32,33]…”

“…In the next section we explicitly carry out the soft expansion ofã i following the prescription described in [32]. We will see that the contribution to the soft photon factor due to the AdS radius will only come from the first line of (3.22).…”