Exact radial solution in 2+1 gravity with a real scalar field

Abstract

In this paper we give some general considerations about circularly symmetric, static space-times in 2+1 dimensions, focusing first on the surprising (at the time) existence of the BTZ black hole solution. We show that BTZ black holes and Schwarzschild black holes in 3+1 dimensions originate from different definitions of a black hole. There are two by-products of this general discussion: (i) we give a new and simple derivation of 2+1 dimensional Anti-de Sitter (AdS) space-time; (ii) we present an exact solution to 2+1 dimensional gravity coupled to a self-interacting real scalar field. The spatial part of the metric of this solution is flat but the temporal part behaves asymptotically like AdS space-time. The scalar field has logarithmic behavior as one would expect for a massless scalar field in flat space-time. The solution can be compared to gravitating scalar field solutions in 3+1 dimensions but with certain oddities connected with the 2+1 dimensional character of the space-time. The solution is unique to 2+1 dimensions; it does not carry over to 3+1 dimensions.

13 pages, minor revisions, updated references, to be published PLB

References in corpus (30)

• The Black Hole in Three Dimensional Space Time
• Geometry of the 2+1 Black Hole
• Cosmology with a Primordial Scaling Field
• Massive Gravity in Three Dimensions
• Kaluza-Klein Gravity
• TOPICAL REVIEW: General relativistic boson stars
• The (2+1)-Dimensional Black Hole
• Structure formation with a self-tuning scalar field
• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• Static Charged Black Holes in $(2+1)$ Dimensional Dilaton Gravity
• Massive 3D Supergravity
• Cosmology in three dimensions: steps towards the general solution
• Note on Scalar Fields Non-Minimally Coupled to (2+1)-Gravity
• Collapse of a Scalar Field in 2+1 Gravity
• A new class of stable $(2+1)$ dimensional thin shell wormhole
• Massive Gravity with Mass Term in Three Dimensions
• Properties of Solutions in 2+1 Dimensions
• Accelerating black hole in 2+1 dimensions and 3+1 black (st)ring
• Dynamical formation and evolution of (2+1)-dimensional charged black holes
• The tetralogy of Birkhoff theorems
• Nonstatic charged BTZ-like black holes in N+1 dimensions
• A Particle Probing Thermodynamics in Three-Dimensional Black Hole
• Higher dimensional charged BTZ-like wormhole
• Accelerating BTZ spacetime
• Another Mass Gap in the BTZ Geometry?
• Circular Symmetry in Topologically Massive Gravity
• The massive scalar field in a closed Friedmann universe model - new rigorous results
• Singularity free stars in (2+1) dimensions
• Beta Function and Asymptotic Safety in Three-dimensional Higher Derivative Gravity
• On Effective Potential in Tortoise Coordinate

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