Hamilton-Jacobi and Schrodinger Separable Solutions of Einstein’s Equations View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1968-12

AUTHORS

Brandon Carter

ABSTRACT

This paper contains an investigation of spaces with a two parameter Abelian isometry group in which the Hamilton-Jacobi equation for the geodesies is soluble by separation of variables in such a way that a certain natural canonical orthonormal tetrad is determined. The spaces satisfying the stronger condition that the corresponding Schrodinger equation is separable are isolated in a canonical form for which Einstein’s vacuum equations and the source-free Einstein-Maxwell equations (with or without a Λ term) can be solved explicitly. A fairly extensive family of new solutions is obtained including the previously known solutions of de Sitter, Kasner, Taub-NUT, and Kerr as special cases. More... »

PAGES

280-310

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf03399503

DOI

http://dx.doi.org/10.1007/bf03399503

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1101127207


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Pure Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Cambridge", 
          "id": "https://www.grid.ac/institutes/grid.5335.0", 
          "name": [
            "Department of Applied Mathematics and Theoretical Physics, Cambridge, UK"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Carter", 
        "givenName": "Brandon", 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/0375-9601(68)90240-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000629467"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/0375-9601(68)90240-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000629467"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9947-1925-1501301-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012672201"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01451624", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019629509", 
          "https://doi.org/10.1007/bf01451624"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.1704018", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1057773960"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1063/1.1704351", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1057774292"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.116.1331", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060422097"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.116.1331", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060422097"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.133.b845", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060428390"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.133.b845", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060428390"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.174.1559", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060439466"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.174.1559", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060439466"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.80.440", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060456990"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrev.80.440", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060456990"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.11.237", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060760845"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.11.237", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060760845"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/revmodphys.38.483", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060838485"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/revmodphys.38.483", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1060838485"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1143/ptp/5.1.82", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1063146023"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/1968433", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069673863"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2307/1969567", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1069674942"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1968-12", 
    "datePublishedReg": "1968-12-01", 
    "description": "This paper contains an investigation of spaces with a two parameter Abelian isometry group in which the Hamilton-Jacobi equation for the geodesies is soluble by separation of variables in such a way that a certain natural canonical orthonormal tetrad is determined. The spaces satisfying the stronger condition that the corresponding Schrodinger equation is separable are isolated in a canonical form for which Einstein\u2019s vacuum equations and the source-free Einstein-Maxwell equations (with or without a \u039b term) can be solved explicitly. A fairly extensive family of new solutions is obtained including the previously known solutions of de Sitter, Kasner, Taub-NUT, and Kerr as special cases.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/bf03399503", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136216", 
        "issn": [
          "0010-3616", 
          "1432-0916"
        ], 
        "name": "Communications in Mathematical Physics", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "4", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "10"
      }
    ], 
    "name": "Hamilton-Jacobi and Schrodinger Separable Solutions of Einstein\u2019s Equations", 
    "pagination": "280-310", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "a7c2dc454a3b226a1a8ee458879998a009e8584bd059e0f3224a667158bafe9c"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf03399503"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1101127207"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf03399503", 
      "https://app.dimensions.ai/details/publication/pub.1101127207"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T13:07", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000367_0000000367/records_88222_00000001.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1007%2FBF03399503"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf03399503'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf03399503'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf03399503'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf03399503'


 

This table displays all metadata directly associated to this object as RDF triples.

103 TRIPLES      21 PREDICATES      41 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf03399503 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author Nfe97cb02f1a24330924c0f87d94f618b
4 schema:citation sg:pub.10.1007/bf01451624
5 https://doi.org/10.1016/0375-9601(68)90240-5
6 https://doi.org/10.1063/1.1704018
7 https://doi.org/10.1063/1.1704351
8 https://doi.org/10.1090/s0002-9947-1925-1501301-4
9 https://doi.org/10.1103/physrev.116.1331
10 https://doi.org/10.1103/physrev.133.b845
11 https://doi.org/10.1103/physrev.174.1559
12 https://doi.org/10.1103/physrev.80.440
13 https://doi.org/10.1103/physrevlett.11.237
14 https://doi.org/10.1103/revmodphys.38.483
15 https://doi.org/10.1143/ptp/5.1.82
16 https://doi.org/10.2307/1968433
17 https://doi.org/10.2307/1969567
18 schema:datePublished 1968-12
19 schema:datePublishedReg 1968-12-01
20 schema:description This paper contains an investigation of spaces with a two parameter Abelian isometry group in which the Hamilton-Jacobi equation for the geodesies is soluble by separation of variables in such a way that a certain natural canonical orthonormal tetrad is determined. The spaces satisfying the stronger condition that the corresponding Schrodinger equation is separable are isolated in a canonical form for which Einstein’s vacuum equations and the source-free Einstein-Maxwell equations (with or without a Λ term) can be solved explicitly. A fairly extensive family of new solutions is obtained including the previously known solutions of de Sitter, Kasner, Taub-NUT, and Kerr as special cases.
21 schema:genre research_article
22 schema:inLanguage en
23 schema:isAccessibleForFree false
24 schema:isPartOf N64ea9c4031864a84babbdcb5ad539b9d
25 Na439f3150e304006a3321ca270e209b2
26 sg:journal.1136216
27 schema:name Hamilton-Jacobi and Schrodinger Separable Solutions of Einstein’s Equations
28 schema:pagination 280-310
29 schema:productId N37a8fa3ba7bd45e98b0319254b52ea98
30 N3ef206e41887470a89bdbf1d50eb6d4f
31 N4cd350e0bad44180bc1bf6540821e51e
32 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101127207
33 https://doi.org/10.1007/bf03399503
34 schema:sdDatePublished 2019-04-11T13:07
35 schema:sdLicense https://scigraph.springernature.com/explorer/license/
36 schema:sdPublisher N59483b1d9da14dda9aef430d1e306ef8
37 schema:url https://link.springer.com/10.1007%2FBF03399503
38 sgo:license sg:explorer/license/
39 sgo:sdDataset articles
40 rdf:type schema:ScholarlyArticle
41 N37a8fa3ba7bd45e98b0319254b52ea98 schema:name readcube_id
42 schema:value a7c2dc454a3b226a1a8ee458879998a009e8584bd059e0f3224a667158bafe9c
43 rdf:type schema:PropertyValue
44 N3ef206e41887470a89bdbf1d50eb6d4f schema:name doi
45 schema:value 10.1007/bf03399503
46 rdf:type schema:PropertyValue
47 N4cd350e0bad44180bc1bf6540821e51e schema:name dimensions_id
48 schema:value pub.1101127207
49 rdf:type schema:PropertyValue
50 N59483b1d9da14dda9aef430d1e306ef8 schema:name Springer Nature - SN SciGraph project
51 rdf:type schema:Organization
52 N64ea9c4031864a84babbdcb5ad539b9d schema:issueNumber 4
53 rdf:type schema:PublicationIssue
54 Na439f3150e304006a3321ca270e209b2 schema:volumeNumber 10
55 rdf:type schema:PublicationVolume
56 Nddbb6bee66b2419a9dc4c32e3907e096 schema:affiliation https://www.grid.ac/institutes/grid.5335.0
57 schema:familyName Carter
58 schema:givenName Brandon
59 rdf:type schema:Person
60 Nfe97cb02f1a24330924c0f87d94f618b rdf:first Nddbb6bee66b2419a9dc4c32e3907e096
61 rdf:rest rdf:nil
62 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
63 schema:name Mathematical Sciences
64 rdf:type schema:DefinedTerm
65 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
66 schema:name Pure Mathematics
67 rdf:type schema:DefinedTerm
68 sg:journal.1136216 schema:issn 0010-3616
69 1432-0916
70 schema:name Communications in Mathematical Physics
71 rdf:type schema:Periodical
72 sg:pub.10.1007/bf01451624 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019629509
73 https://doi.org/10.1007/bf01451624
74 rdf:type schema:CreativeWork
75 https://doi.org/10.1016/0375-9601(68)90240-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000629467
76 rdf:type schema:CreativeWork
77 https://doi.org/10.1063/1.1704018 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057773960
78 rdf:type schema:CreativeWork
79 https://doi.org/10.1063/1.1704351 schema:sameAs https://app.dimensions.ai/details/publication/pub.1057774292
80 rdf:type schema:CreativeWork
81 https://doi.org/10.1090/s0002-9947-1925-1501301-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012672201
82 rdf:type schema:CreativeWork
83 https://doi.org/10.1103/physrev.116.1331 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060422097
84 rdf:type schema:CreativeWork
85 https://doi.org/10.1103/physrev.133.b845 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060428390
86 rdf:type schema:CreativeWork
87 https://doi.org/10.1103/physrev.174.1559 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060439466
88 rdf:type schema:CreativeWork
89 https://doi.org/10.1103/physrev.80.440 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060456990
90 rdf:type schema:CreativeWork
91 https://doi.org/10.1103/physrevlett.11.237 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060760845
92 rdf:type schema:CreativeWork
93 https://doi.org/10.1103/revmodphys.38.483 schema:sameAs https://app.dimensions.ai/details/publication/pub.1060838485
94 rdf:type schema:CreativeWork
95 https://doi.org/10.1143/ptp/5.1.82 schema:sameAs https://app.dimensions.ai/details/publication/pub.1063146023
96 rdf:type schema:CreativeWork
97 https://doi.org/10.2307/1968433 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069673863
98 rdf:type schema:CreativeWork
99 https://doi.org/10.2307/1969567 schema:sameAs https://app.dimensions.ai/details/publication/pub.1069674942
100 rdf:type schema:CreativeWork
101 https://www.grid.ac/institutes/grid.5335.0 schema:alternateName University of Cambridge
102 schema:name Department of Applied Mathematics and Theoretical Physics, Cambridge, UK
103 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...