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Title: Dilaton field minimally coupled to 2+1 gravity; uniqueness of the static Chan-Mann black hole and new dilaton stationary metrics

Using the Schwarzschild coordinate frame for a static cyclic symmetric metric in 2+1 gravity coupled minimally to a dilaton logarithmically depending on the radial coordinate in the presence of an exponential potential, by solving first order linear Einstein equations, the general solution is derived and it is identified with the Chan–Mann dilaton solution. In these coordinates, a new stationary dilaton solution is obtained; it does not allow for a de Sitter–Anti-de Sitter limit at spatial infinity, where its structural functions increase indefinitely. On the other hand, it is horizonless and allows for a naked singularity at the origin of coordinates; moreover, one can identify at a large radial coordinate a (quasi-local) mass parameter and in the whole space a constant angular momentum. Via a general SL(2,R)–transformation, applied on the static cyclic symmetric metric, a family of stationary dilaton solutions has been generated. A particular SL(2,R)–transformation is identified, which gives rise to the rotating Chan–Mann dilaton solution. All the exhibited solutions have been characterized by their quasi-local energy, mass, and momentum through their series expansions at spatial infinity. The algebraic structure of the Ricci–energy-momentum, and Cotton tensors is given explicitly.
Authors:
 [1]
  1. Departamento de Física, Centro de Investigación y de Estudios Avanzados del IPN, Apdo. Postal 14-740, 07000 México DF, México. and Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, Apdo. (Mexico)
Publication Date:
OSTI Identifier:
22264060
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1577; Journal Issue: 1; Conference: 5. Leopoldo Garcia-Colin Mexican meeting on mathematical and experimental physics, Mexico City (Mexico), 9-13 Sep 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ANGULAR MOMENTUM; BLACK HOLES; EINSTEIN FIELD EQUATIONS; FUNCTIONS; GRAVITATION; MATHEMATICAL SOLUTIONS; SERIES EXPANSION; SINGULARITY; TENSORS