On a spacetime duality in 2 + 1 gravity
نویسندگان
چکیده
We consider 2 + 1 dimensional gravity with a cosmological constant, and explore a duality that exists between space-times that have the De Sitter group SO(3, 1) as its local isometry group. In particular, the Lorentzian theory with a positive cosmological constant is dual to the Euclidean theory with a negative cosmological constant. We use this duality to construct a mapping between apparently unrelated space-times. More precisely, we exhibit a relation between the Euclidean BTZ family and some T 2-cosmological solutions, and between De-Sitter point particle space-times and the analytic continuations of Anti-De Sitter point particles. We discuss some possible applications for BH and AdS thermodynamics. Pacs No: 04.20.Fy, 04.60.Kz Typeset using REVTEX ∗Electronic Address: [email protected] †Electronic Address: [email protected]
منابع مشابه
Gravity and Duality between Coordinates and Matter Fields
We use the duality between the local Cartezian coordinates and the solutions of the Klein-Gordon equation to parametrize locally the spacetime in terms of wave functions and prepotentials. The components of metric, metric connection, curvature as well as the Einstein equation are given in this parametrization. We also discuss the local duality between coordinates and quantum fields and the metr...
متن کاملAdS/CFT Duality and the Emergence of Spacetime
The AdS/CFT duality has been a source of several strong conceptual claims in the physics literature. In this paper I focus on one of these: the extent to which spacetime geometry and locality can be said to emerge from this duality, so that neither is fundamental. I argue: (1) that the kind of emergence in question is relatively weak, involving one can of spacetime emerging from another kind of...
متن کاملDuality of Coordinates and Matter Fields in Curved Spacetime
We show that there exists a duality between the local coordinates and the solutions of the Klein-Gordon equation in curved spacetime in the same sense as in the Minkowski spacetime. However, the duality in curved spacetime does not have the same generality as in flat spacetime and it holds only if the system satisfies certain constraints. We derive these constraints and the basic equations of d...
متن کاملNoncommutative Spacetime and Emergent Gravity
We argue that a field theory defined on noncommutative (NC) spacetime should be regarded as a theory of gravity, which we refer to as the emergent gravity. A whole point of the emergent gravity is essentially originated from the basic property: A NC spacetime is a (NC) phase space. This fact leads to two important consequences: (I) A NC field theory can basically be identified with a matrix mod...
متن کاملInstantons and Emergent Geometry
Gravity is a mysterious force; we still don’t know what gravity is. But recent developments from string and M theories gradually reveal an intriguing picture on gravity (for recent reviews, see, for example, [1, 2]): Gravity may be a collective phenomenon emergent from gauge fields. That is, the spin-two graviton might arise as a composite of two spin-one gauge bosons. Although the emergent gra...
متن کامل