2024/04/12 by Reinoud Jan Slagter, Slagter, Reinoud Jan
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect
paper · pdf · doi:10.48550/arxiv.2404.08346
openalex publication_date 2024/04/12 · openalex created_date 2024/04/18 · openalex updated_date 2026/07/28
We investigated an exact solution in a conformal invariant Randall-Sundrum 5D warped brane world model on a time dependent Kerr-like spacetime. The singular points are determined by a quintic polynomial in the complex plane and fulfills Cauchy's theorem on holomorphic functions. The solution, which is determined by a first-degree differential equation, shows many similarities with an instanton. In order to describe the quantum mechanical aspects of the black hole solution, we apply the antipodal boundary condition. The solution is invariant under time reversal and also valid in Riemannian space. Moreover, CPT invariance in maintained. The vacuum instanton solution follows from the 5D as well as the effective 4D brane equations, only when we allow the contribution of the projected 5D Weyl tensor on the brane (the KK-'particles'). The topology of the effective 4D space of the brane is the projective ℝP3 (elliptic space) by identifying antipodal points on S3. The 5D is completed by using the Klein bottle embedding. This model fits very well with the description of the Hawking radiation, which remains pure. We have also indicated a possible way to include fermions. Our 5D space admits a double cover of S3 and after fibering to the S2, we obtain the effective black hole horizon. The connection with the icosahedron discrete symmetry group is investigated. It seem that Bekenstein's conjecture that the area of a black hole is quantized, can be applied to our model.