Hidden symmetries and black holes spacetimes
This thesis is about hidden symmetries of spacetimes and gives a few examples of black hole spacetimes, as for instance a view on a particular 11 dimensional black holes spacetime compactified down to 5 dimensions. We start off by investigating the hidden symmetries of Goryachev-Chaplygin and Kovalevskaya gyrostats spacetimes, as well as the Brdicka-Eardley-Nappi-Witten pp-waves and we find out that these spacetimes possess higher rank conformal Stackel-Killing and Killing-Yano tensors an important result for higher hidden symmetries. We then go into the realm of string theory and we seek solutions in the framework of 11-dimensional N=2 theory, which we then compactify down to 5 dimensions and we find microstates of multiple collinear/one non-collinear black holes embedded in a multi-center Taub-NUT spacetime are sought in 4 dimensions then lifted to 5 dimensions. A set of coupled ordinary partial differential equations are obtained and solved for almost-BPS states, where some supersymmetry is preserved in the context of N=2 supergravity in 5 dimensions. The regularity of solutions is being carefully considered and we ensure that no CTC (closed time-like curves) are present. Then we investigate the Chong-Cvetic-Lu-Pope black hole spacetime, which is a solution of the 5-dimensional minimal gauged supergravity, endowed with a Sasaki structure deformed by torsion. We also explicitly construct a Killing spinor for the above mentioned specific 5 dimensional minimal gauged supergravity solution. Finally, we present a result in entanglement wedge reconstruction, retrieving the spin 1/2 in the center of the bulk via solving what is called here the modular Dirac equation. We also present as a background material a brief review of some aspects of the physics of classical and quantum black holes, since this thesis mainly deals with black holes solutions and also a brief review of some of the results in the literature on black holes interiors, a chapter on hidden symmetries and Killing spinors, one 5-dimensional minimal gauged/ungauged supergravity and a brief overview of aspects of the entanglement wedge reconstruction project.