On Black Hole Mimickers: Embedding in Asymptotic de Sitter Space

Sammanfattning

The black hole information paradox remains an enduring challenge in theoretical physics, with a definitive resolution still lacking after nearly fifty years. While black hole mimickers offer great promise as a testable solution to this paradox, existing research has predominantly focused on asymptotically flat space (Λ). In this thesis, we investigate the possibilities and challenges of embedding black hole mimickers in asymptotically de Sitter space (k2:=Λ/3>0). We begin by replacing a static de Sitter black hole with an AdS black shell, a black hole mimicker. However, we find that current literature lacks the tools necessary to develop an exact solution for rotating black hole mimickers. To address this, we propose combining the Quevedo-Mashhoon and the Kerr-de Sitter metrics to obtain a new Quevedo-Mashhoon-de Sitter (QMdS) metric. We achieve this by taking a perturbative expansion in small k2 and q2,0, where we set all other qn,m=0. Working in a prolate spheroidal type coordinate system, we expand for large x (far from both horizons). Initially, we find that the base metric yields the correct Ricci scalar and Einstein tensor up to order O(x-1). By introducing a mixed metric term (k2 q2,0gmix) containing terms down to order x-4, we successfully solve the Einstein equations up to order O(x-5).