Abstract
We consider a free theory of multiple scalar fields at finite temperature and study the induced geometry defined through a free flow of the scalar fields, following the method proposed by the present authors as a possible candidate of the constructive approach for AdS/CFT correspondence. We find that the holographic metric has the following properties: i) It is an asymptotic Anti-de Sitter (AdS) black brane metric with some unknown matter contribution. ii) It has no coordinate singularity and milder curvature singularity. iii) Its time component decays exponentially at a certain AdS radial slice. We find that the matter spreads all over the space, which we speculate to be due to thermal excitation of infinitely many massless higher spin fields. We conjecture that the above three are generic features of a black hole holographically realized by the flow equation method.
Highlights
A black hole is a key object to build a bridge between general relativity and quantum field theory
The resolution of the black hole singularity as well as some coordinate singularity such as the horizon in a quantum gravity may be natural from the viewpoint of string theory, in which black holes consist of branes and the microscopic degrees of freedom carried by the black hole are accounted for by strings ending on the branes [25,26,27]
The purpose of this paper is to apply the flow equation method to a finite temperature system and study its induced geometry, which is supposed to be described by a black hole or a black brane solution if the flow method correctly describes the holography. (See [40].) As a first step we study a free theory with multiple scalar fields at finite temperature
Summary
A black hole is a key object to build a bridge between general relativity and quantum field theory. The black hole radiates particles carrying only the thermodynamic information, while it gradually evaporates losing more detailed information of its initial state, which is a non-unitary transition from a pure state to a mixed one This information loss puzzle has been investigated actively up to the present developing various new ideas and techniques (See [10,11,12,13,14,15,16,17] for earlier studies.). The resolution of the black hole singularity as well as some coordinate singularity such as the horizon in a quantum gravity may be natural from the viewpoint of string theory, in which black holes consist of branes and the microscopic degrees of freedom carried by the black hole are accounted for by strings ending on the branes [25,26,27] In this realization a black hole may be a fuzzy object with no apparent horizon [28] (See [29, 30].).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
