Soft mode dynamics in Gravity

Black holes have long since posed a puzzle since their discovery, the information loss paradox requires nothing less than a consistent quantum theory of gravity to know how it is resolved. String theory as the only known theory of quantum gravity has provided many insights in this regard. Chiefly it has lead to the holographic conjecture which implies that gravity is dual to a strongly interacting large-N theory in one less dimension. In the past decade there have been numerous works in this area trying to understand how black holes radiate away their information using such a holographic perspective. This has lead to investigations into what is being called the scrambling time for black holes in AdS or large-N theories dual to it. The scrambling time is considered to be a good estimate as to how fast a black-hole radiates away information which has fallen into it past its half-life. On the other hand past few years have also seen studies investigating how diffeomorphisms or large gauge transformations of the metric(graviton) or the Maxwell gauge field(photon) can store information pertaining to the soft sector of any scattering process in asymptotically flat spaces. These have been shown to further relate to asymptotic symmetries of flat space which give rise to Weinbergs soft theorems as Ward identities. This provides a loop hole in the No Hair theorem which states that black holes of given mass, charge and angular momentum are identical. Although stating that at least the soft charges associated with the particles that went in to form the black hole are stored in a holographic manner at null infinity after being emitted from the horizon, there have been no investigations to understand better the dynamics of this process. This is where the research proposal wants to make important progress. It was shown that the Lyapunov index- which can be seen as a measure of chaos, is maximal for large-N systems which are holographically dual to gravity in AdS. Further, the nature of the modes responsible in gravity for such a behaviour are since being unearthed and forms a current area of research. This proposal first wants to investigate the nature of such modes in AdS black holes and see if similar modes exist for black holes in asymptotically flat spaces. Also the proposal wishes to ascertain the manner in which soft charges associated with gravitons and photons sees the chaotic behaviour of black hole dynamics, thereby getting a better understanding of how holography works in flat space by possibly associating the asymptotic symmetries of latter with black hole dynamics.

Black holes are the most chaotic objects found in nature. Understanding their mechanism for such a chaotic behaviour is important for understanding their dynamics. A measure of chaos is the Lyapunov index which was theoretically believed to be proportional to the black hole's temperature. The project has successfully showed that for rotating black holes the Lyapunov index also additionally gets contribution from its angular momentum. This contribution is such that instead of going to zero as the black approaches zero temperature, the Lyapunov index tends to be finite. A black holes angular momentum lowers it temperature and zero temperature ones are termed as extremal black holes. As most black holes found in nature are close to extremality, the results of this project would prove quite important as advances in observational sciences in gravitational waves would allow finer analysis of black hole dynamics. On the theoretical front the results of this project afford a valuable insight in the near horizon dynamics of near extremal black holes. It was famously realized in the works of Jensen, Maldacena and others that near extremal and near horizon dynamics of black holes could studied using a 2 dimensional model of gravity first analyzed by Jackiw and Teitelboim- since termed as JT gravity. Using this model they were able to explain why near extremal black holes displayed a chaotic behaviour proportional to its temperature. Later works showed how dynamics of higher dimensional black holes reduce to that described by Jensen and Maldacena et al. The project successfully showed that the JT model can also be used to explain how rotating black holes could have a larger Lyapunov index due to its rotation. While doing so the project also generalized the previous techniques found in literature to incorporate possible rotational effects of the black hole.