On the existence of certain axisymmetric interior metrics

One of the effects of noncommutative coordinate operators is that the delta function connected to the quantum mechanical amplitude between states sharp to the position operator gets smeared by a Gaussian distribution. Although this is not the full account of the effects of noncommutativity, this eff...

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Veröffentlicht in:Journal of mathematical physics 2010-08, Vol.51 (8), p.082504-082504-21
Hauptverfasser: Angulo Santacruz, C., Batic, D., Nowakowski, M.
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container_title Journal of mathematical physics
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creator Angulo Santacruz, C.
Batic, D.
Nowakowski, M.
description One of the effects of noncommutative coordinate operators is that the delta function connected to the quantum mechanical amplitude between states sharp to the position operator gets smeared by a Gaussian distribution. Although this is not the full account of the effects of noncommutativity, this effect is, in particular, important as it removes the point singularities of Schwarzschild and Reissner–Nordström solutions. In this context, it seems to be of some importance to probe also into ringlike singularities which appear in the Kerr case. In particular, starting with an anisotropic energy-momentum tensor and a general axisymmetric ansatz of the metric together with an arbitrary mass distribution (e.g., Gaussian), we derive the full set of Einstein equations that the noncommutative geometry inspired Kerr solution should satisfy. Using these equations we prove two theorems regarding the existence of certain Kerr metrics inspired by noncommutative geometry.
doi_str_mv 10.1063/1.3475798
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source AIP Journals Complete; AIP Digital Archive; Alma/SFX Local Collection
subjects AMPLITUDES
ANISOTROPY
AXIAL SYMMETRY
COMMUTATION RELATIONS
DELTA FUNCTION
Differential equations
DISTRIBUTION
EINSTEIN FIELD EQUATIONS
ENERGY-MOMENTUM TENSOR
EQUATIONS
Exact sciences and technology
FIELD EQUATIONS
FIELD THEORIES
FUNCTIONS
GAUSS FUNCTION
GEOMETRY
KERR METRIC
MASS DISTRIBUTION
Mathematical methods in physics
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
MATHEMATICS
MECHANICS
METRICS
Normal distribution
Physics
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
POSITION OPERATORS
QUANTUM FIELD THEORY
QUANTUM MECHANICS
QUANTUM OPERATORS
SCHWARZSCHILD METRIC
Sciences and techniques of general use
SINGULARITY
SPATIAL DISTRIBUTION
SYMMETRY
TENSORS
Theorems
title On the existence of certain axisymmetric interior metrics
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