Chennai Mathematical Institute


Date and Time : Monday, 27 June 2022, 11.00 am
Venue : Seminar Hall (Hybrid mode)
Subject : Physics
Asymptotic Symmetries, Horizon Hair, and Memory Effect

Debodirna Ghosh
Chennai Mathematical Institute.


The quest for the correct theory of quantum gravity has occupied many minds for the last few decades. Recently, it was realized by Strominger and his collaborators that diverse aspects of infrared physics are related to one another. These relations, well-known as the infrared (IR) triangle have successfully predicted new symmetries of asymptotically flat spacetimes. These predictions may prove to be the pillars of establishing the holographic dual to flat spacetime. In that context, this thesis explores the theory of asymptotic symmetries of asymptotically flat spacetimes and the spin memory effect in $D=4$ dimensions.

The thesis starts by exploring the supertranslations at timelike infinity where we propose a definition of asymptotic flatness at timelike infinity in four spacetime dimensions. We present a detailed study of the asymptotic equations of motion and the action of supertranslations on asymptotic fields. We show that the Lee-Wald symplectic form $\Omega (g, \delta_1 g, \delta_2 g)$ does not get contributions from future timelike infinity with our boundary conditions. As a result, the ``future charges'' can be computed on any two-dimensional surface surrounding the sources at timelike infinity. We present expressions for supertranslation and Lorentz charges.

In a separate attempt to explore the asymptotic symmetries of asymptotically flat spacetimes, we study the dynamics of a probe Maxwell field on the extreme Reissner-Nordstr\"om solution. The extreme Reissner-Nordstrom solution has a discrete conformal isometry that maps the future event horizon to future null infinity and vice versa, the Couch-Torrence inversion isometry. We present a gauge fixing that is compatible with the inversion symmetry. The gauge fixing allows us to relate the gauge parameter at the future horizon to future null infinity, which further allows us to study global charges for large gauge symmetries in the exterior of the extreme Reissner-Nordstrom black hole. Along the way, we construct Newman-Penrose and Aretakis like conserved quantities along with future null infinity and the future event horizon, respectively, and relate them via the Couch-Torrence inversion symmetry.

Finally, we explore the other corner of Strominger's IR triangle, the memory effect. We derive the leading spin-dependent gravitational tail memory, which appears at the second post-Minkowskian (2 PM) order and behaves as $u^{-2}$ for large retarded time $u$. This result follows from the classical soft graviton theorem at order $\omega\ln\omega$ as a low-frequency expansion of gravitational waveform with frequency $\omega$. First, we conjecture the gravitational waveform from the classical limit of quantum soft graviton theorem up to sub-subleading order in soft expansion and then we derive it for a classical scattering process without any reference to the soft graviton theorem. We show that the final result of the gravitational waveform in the direct derivation completely agrees with the conjectured waveform.