Analysis of the Fisher solution
Abstract
We study the ddimensional Fisher solution which represents a static, spherically symmetric, asymptotically flat spacetime with a massless scalar field. The solution has two parameters, the mass M and the 'scalar charge' {Sigma}. The Fisher solution has a naked curvature singularity which divides the spacetime manifold into two disconnected parts. The part which is asymptotically flat we call the Fisher spacetime, and another part we call the Fisher universe. The ddimensional SchwarzschildTangherlini solution and the Fisher solution belong to the same theory and are dual to each other. The duality transformation acting in the parameter space (M,{Sigma}) maps the exterior region of the SchwarzschildTangherlini black hole into the Fisher spacetime which has a naked timelike singularity, and interior region of the black hole into the Fisher universe, which is an anisotropic expandingcontracting universe and which has two spacelike singularities representing its 'big bang' and 'big crunch'. The big bang singularity and the singularity of the Fisher spacetime are radially weak in the sense that a 1dimensional object moving along a timelike radial geodesic can arrive to the singularities intact. At the vicinity of the singularity the Fisher spacetime of nonzero mass has a region where its MisnerSharp energy is negative.more »
 Authors:

 Theoretical Physics Institute, University of Alberta, Edmonton, Alberta, T6G 2G7 (Canada)
 Publication Date:
 OSTI Identifier:
 21409095
 Resource Type:
 Journal Article
 Journal Name:
 Physical Review. D, Particles Fields
 Additional Journal Information:
 Journal Volume: 81; Journal Issue: 2; Other Information: DOI: 10.1103/PhysRevD.81.024035; (c) 2010 The American Physical Society; Journal ID: ISSN 05562821
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ANISOTROPY; BLACK HOLES; DUALITY; EXPANSION; MANYDIMENSIONAL CALCULATIONS; MASS; MASSLESS PARTICLES; MATHEMATICAL SOLUTIONS; ONEDIMENSIONAL CALCULATIONS; SCALAR FIELDS; SIMULATION; SINGULARITY; SPACETIME; SURFACES; SYMMETRY; UNIVERSE; ELEMENTARY PARTICLES
Citation Formats
Abdolrahimi, Shohreh, and Shoom, Andrey A. Analysis of the Fisher solution. United States: N. p., 2010.
Web. doi:10.1103/PHYSREVD.81.024035.
Abdolrahimi, Shohreh, & Shoom, Andrey A. Analysis of the Fisher solution. United States. https://doi.org/10.1103/PHYSREVD.81.024035
Abdolrahimi, Shohreh, and Shoom, Andrey A. Fri .
"Analysis of the Fisher solution". United States. https://doi.org/10.1103/PHYSREVD.81.024035.
@article{osti_21409095,
title = {Analysis of the Fisher solution},
author = {Abdolrahimi, Shohreh and Shoom, Andrey A},
abstractNote = {We study the ddimensional Fisher solution which represents a static, spherically symmetric, asymptotically flat spacetime with a massless scalar field. The solution has two parameters, the mass M and the 'scalar charge' {Sigma}. The Fisher solution has a naked curvature singularity which divides the spacetime manifold into two disconnected parts. The part which is asymptotically flat we call the Fisher spacetime, and another part we call the Fisher universe. The ddimensional SchwarzschildTangherlini solution and the Fisher solution belong to the same theory and are dual to each other. The duality transformation acting in the parameter space (M,{Sigma}) maps the exterior region of the SchwarzschildTangherlini black hole into the Fisher spacetime which has a naked timelike singularity, and interior region of the black hole into the Fisher universe, which is an anisotropic expandingcontracting universe and which has two spacelike singularities representing its 'big bang' and 'big crunch'. The big bang singularity and the singularity of the Fisher spacetime are radially weak in the sense that a 1dimensional object moving along a timelike radial geodesic can arrive to the singularities intact. At the vicinity of the singularity the Fisher spacetime of nonzero mass has a region where its MisnerSharp energy is negative. The Fisher universe has a marginally trapped surface corresponding to the state of its maximal expansion in the angular directions. These results and derived relations between geometric quantities of the Fisher spacetime, the Fisher universe, and the SchwarzschildTangherlini black hole may suggest that the massless scalar field transforms the black hole event horizon into the naked radially weak disjoint singularities of the Fisher spacetime and the Fisher universe which are 'dual to the horizon'.},
doi = {10.1103/PHYSREVD.81.024035},
url = {https://www.osti.gov/biblio/21409095},
journal = {Physical Review. D, Particles Fields},
issn = {05562821},
number = 2,
volume = 81,
place = {United States},
year = {2010},
month = {1}
}