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 |
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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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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.</description><identifier>ISSN: 0022-2488</identifier><identifier>EISSN: 1089-7658</identifier><identifier>DOI: 10.1063/1.3475798</identifier><identifier>CODEN: JMAPAQ</identifier><language>eng</language><publisher>Melville, NY: American Institute of Physics</publisher><subject>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</subject><ispartof>Journal of mathematical physics, 2010-08, Vol.51 (8), p.082504-082504-21</ispartof><rights>American Institute of Physics</rights><rights>2010 American Institute of Physics</rights><rights>2015 INIST-CNRS</rights><rights>Copyright American Institute of Physics Aug 2010</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c438t-f3f168525c7fd82c6db04092b6775b8e049a1cf1973200c8da20a7cff7b57d103</citedby><cites>FETCH-LOGICAL-c438t-f3f168525c7fd82c6db04092b6775b8e049a1cf1973200c8da20a7cff7b57d103</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jmp/article-lookup/doi/10.1063/1.3475798$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>230,314,776,780,790,881,1553,4498,27901,27902,76127,76133</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23247989$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.osti.gov/biblio/21483626$$D View this record in Osti.gov$$Hfree_for_read</backlink></links><search><creatorcontrib>Angulo Santacruz, C.</creatorcontrib><creatorcontrib>Batic, D.</creatorcontrib><creatorcontrib>Nowakowski, M.</creatorcontrib><title>On the existence of certain axisymmetric interior metrics</title><title>Journal of mathematical physics</title><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.</description><subject>AMPLITUDES</subject><subject>ANISOTROPY</subject><subject>AXIAL SYMMETRY</subject><subject>COMMUTATION RELATIONS</subject><subject>DELTA FUNCTION</subject><subject>Differential equations</subject><subject>DISTRIBUTION</subject><subject>EINSTEIN FIELD EQUATIONS</subject><subject>ENERGY-MOMENTUM TENSOR</subject><subject>EQUATIONS</subject><subject>Exact sciences and technology</subject><subject>FIELD EQUATIONS</subject><subject>FIELD THEORIES</subject><subject>FUNCTIONS</subject><subject>GAUSS FUNCTION</subject><subject>GEOMETRY</subject><subject>KERR METRIC</subject><subject>MASS DISTRIBUTION</subject><subject>Mathematical methods in physics</subject><subject>MATHEMATICAL OPERATORS</subject><subject>MATHEMATICAL SOLUTIONS</subject><subject>MATHEMATICS</subject><subject>MECHANICS</subject><subject>METRICS</subject><subject>Normal distribution</subject><subject>Physics</subject><subject>PHYSICS OF ELEMENTARY PARTICLES AND FIELDS</subject><subject>POSITION OPERATORS</subject><subject>QUANTUM FIELD THEORY</subject><subject>QUANTUM MECHANICS</subject><subject>QUANTUM OPERATORS</subject><subject>SCHWARZSCHILD METRIC</subject><subject>Sciences and techniques of general use</subject><subject>SINGULARITY</subject><subject>SPATIAL DISTRIBUTION</subject><subject>SYMMETRY</subject><subject>TENSORS</subject><subject>Theorems</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9kEtLAzEUhYMoWKsL_8GguFAYzTuZhQsRX1DoRtchk0kwYpOaRLH_3pQpuhBdXe7lO4dzDwCHCJ4jyMkFOidUMNHJLTBBUHat4ExugwmEGLeYSrkL9nJ-gRAhSekEdPPQlGfb2E-fiw3GNtE1xqaifWh0Pa4WC1uSN40PxSYfUzPueR_sOP2a7cFmTsHT7c3j9X07m989XF_NWkOJLK0jDnHJMDPCDRIbPvSQwg73XAjWSwtpp5FxqBMEQ2jkoDHUwjgneiYGBMkUHI--MRevsvHFmmcTQ7CmKIyoJBzzSh2N1DLFt3ebi3qJ7ynUYEowTghlkFXodIRMijkn69Qy-YVOK4WgWtenkNrUV9mTjaHORr-6pIPx-VuACaYV6yp3OXLrZLr4GP42nQdVu1bfXavoqv7sL_1HTD9atRz-hX9_8AWK6J6J</recordid><startdate>20100801</startdate><enddate>20100801</enddate><creator>Angulo Santacruz, C.</creator><creator>Batic, D.</creator><creator>Nowakowski, M.</creator><general>American Institute of Physics</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>OTOTI</scope></search><sort><creationdate>20100801</creationdate><title>On the existence of certain axisymmetric interior metrics</title><author>Angulo Santacruz, C. ; Batic, D. ; Nowakowski, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c438t-f3f168525c7fd82c6db04092b6775b8e049a1cf1973200c8da20a7cff7b57d103</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>AMPLITUDES</topic><topic>ANISOTROPY</topic><topic>AXIAL SYMMETRY</topic><topic>COMMUTATION RELATIONS</topic><topic>DELTA FUNCTION</topic><topic>Differential equations</topic><topic>DISTRIBUTION</topic><topic>EINSTEIN FIELD EQUATIONS</topic><topic>ENERGY-MOMENTUM TENSOR</topic><topic>EQUATIONS</topic><topic>Exact sciences and technology</topic><topic>FIELD EQUATIONS</topic><topic>FIELD THEORIES</topic><topic>FUNCTIONS</topic><topic>GAUSS FUNCTION</topic><topic>GEOMETRY</topic><topic>KERR METRIC</topic><topic>MASS DISTRIBUTION</topic><topic>Mathematical methods in physics</topic><topic>MATHEMATICAL OPERATORS</topic><topic>MATHEMATICAL SOLUTIONS</topic><topic>MATHEMATICS</topic><topic>MECHANICS</topic><topic>METRICS</topic><topic>Normal distribution</topic><topic>Physics</topic><topic>PHYSICS OF ELEMENTARY PARTICLES AND FIELDS</topic><topic>POSITION OPERATORS</topic><topic>QUANTUM FIELD THEORY</topic><topic>QUANTUM MECHANICS</topic><topic>QUANTUM OPERATORS</topic><topic>SCHWARZSCHILD METRIC</topic><topic>Sciences and techniques of general use</topic><topic>SINGULARITY</topic><topic>SPATIAL DISTRIBUTION</topic><topic>SYMMETRY</topic><topic>TENSORS</topic><topic>Theorems</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Angulo Santacruz, C.</creatorcontrib><creatorcontrib>Batic, D.</creatorcontrib><creatorcontrib>Nowakowski, M.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>OSTI.GOV</collection><jtitle>Journal of mathematical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Angulo Santacruz, C.</au><au>Batic, D.</au><au>Nowakowski, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the existence of certain axisymmetric interior metrics</atitle><jtitle>Journal of mathematical physics</jtitle><date>2010-08-01</date><risdate>2010</risdate><volume>51</volume><issue>8</issue><spage>082504</spage><epage>082504-21</epage><pages>082504-082504-21</pages><issn>0022-2488</issn><eissn>1089-7658</eissn><coden>JMAPAQ</coden><abstract>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.</abstract><cop>Melville, NY</cop><pub>American Institute of Physics</pub><doi>10.1063/1.3475798</doi><tpages>21</tpages></addata></record> |
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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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