Abstract
We construct and investigate non conformal anisotropic Bianchi type VII0 solutions in 5 dimensions. The solutions are asymptotically flat with a singularity. We also construct anisotropic solutions of Einstein-Maxwell gravity using a procedure similar to Majumdar-Papapetrou solutions with various profiles of charged dust and explore ways to hide the singularity behind the horizon. We further embed it in one higher dimension to get an asymptotically anti de Sitter space and approximate two point correlator of operators with higher conformal dimensions by calculating geodesic lengths. We find a peculiar power law decay of the correlator as a function of separation.
Highlights
Inception of general relativity has led to great insights into cosmology as well as many open problems
We have constructed an anisotropic 4 dimensional asymptotically flat Riemannian metric which is Ricci flat. We later incorporated it in a 5 dimensional space time along with matter density and electromagnetic flux using a method similar to Majumdar-Papapetrou way of constructing extremal solutions
The singularity problem seems to be addressed for a case of a fictitious choice of matter density for which we arrived at a solution with a horizon hiding the singularity
Summary
Inception of general relativity has led to great insights into cosmology as well as many open problems. Asymptotic AdS (anti-de Sitter), anisotropic solutions were constructed and studied to investigate properties of certain anisotropic. We take up the investigation of such solutions and their properties in this manuscript In this manuscript, we begin with constructing a simple, static but anisotropic solution of pure general relativity which is asymptotically flat. We begin with constructing a simple, static but anisotropic solution of pure general relativity which is asymptotically flat Such simple cases usually lead to singular solutions. We construct a 5 dimensional asymptotically locally anti de Sitter solution by adding a radial direction whose boundary metric is our anisotropic, 4 dimensional solution Various foliations of such space away from the singularity can have well defined field theory on the boundary. The boundary is an anisotropically curved space which can impart peculiar properties to correlators
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