Speaker
Description
This project investigates analytical and numerical black hole solutions in Anti-de-Sitter spacetimes. These geometries are of particular interest due to their holographic interpretation in gauge/gravity duality, representing states of a strongly coupled N=4 super Yang-Mills theory with a large number of colors, residing on a three-sphere. First, we derive the equations of motion from a supergravity action that descends from a consistent truncation of IIB supergravity on a five-dimensional sphere. Furthermore, exact solutions for a constant scalar field are obtained, yielding geometries such as the pure AdS and the Bertotti-Robinson spacetime. For non-trivial scalar field configurations, a computational code is constructed in Mathematica, which numerically integrates the differential equations, relying on a strictly analytical Taylor series expansion to determine the boundary conditions just outside the black hole event horizon. The numerical results demonstrate that the solutions are asymptotically AdS far from the horizon. To study this asymptotic behavior further, we apply the Fefferman-Graham expansion near the AdS boundary. Finally, a thermodynamic analysis is performed by calculating the physical Bekenstein-Hawking entropy density and the Hawking temperature.