Collapse in f(R) gravity and the method of R matching View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2020-09-29

AUTHORS

Sandip Chowdhury, Kunal Pal, Kuntal Pal, Tapobrata Sarkar

ABSTRACT

Collapsing solutions in f(R) gravity are restricted due to junction conditions that demand continuity of the Ricci scalar and its normal derivative across the time-like collapsing hypersurface. These are obtained via the method of R-matching, which is ubiquitous in f(R) collapse scenarios. In this paper, we study spherically symmetric collapse with the modification term αR2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha R^2$$\end{document}, and use R-matching to exemplify a class of new solutions. After discussing some mathematical preliminaries by which we obtain an algebraic relation between the shear and the anisotropy in these theories, we consider two metric ansatzes. In the first, the collapsing metric is considered to be a separable function of the co-moving radius and time, and the collapse is shear-free, and in the second, a non-separable interior solution is considered, that represents gravitational collapse with non-zero shear viscosity. We arrive at novel solutions that indicate the formation of black holes or locally naked singularities, while obeying all the necessary energy conditions. The separable case allows for a simple analytic expression of the energy-momentum tensor, that indicates the positivity of the pressures throughout collapse, and is further used to study the heat flux evolution of the collapsing matter, whose analytic solutions are presented under certain approximations. These clearly highlight the role of modified gravity in the examples that we consider. More... »

PAGES

902

References to SciGraph publications

  • 2016-04-08. Spherically symmetric collapse of a perfect fluid in f(R) gravity in GENERAL RELATIVITY AND GRAVITATION
  • 2018-10-26. Conformally flat collapsing stars in f(R) gravity in GENERAL RELATIVITY AND GRAVITATION
  • 1997-05. The Expanding Universe in GENERAL RELATIVITY AND GRAVITATION
  • 1996-02. Kinematics and dynamics off(R) theories of gravity in GENERAL RELATIVITY AND GRAVITATION
  • 2008-02-20. Radiating gravitational collapse with shear viscosity revisited in GENERAL RELATIVITY AND GRAVITATION
  • 2010-06-23. f(R) Theories in LIVING REVIEWS IN RELATIVITY
  • 2010-02-03. On the stability of the shear–free condition in GENERAL RELATIVITY AND GRAVITATION
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1140/epjc/s10052-020-08459-w

    DOI

    http://dx.doi.org/10.1140/epjc/s10052-020-08459-w

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1131297926


    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/2008/02", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Physical Sciences", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0202", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Atomic, Molecular, Nuclear, Particle and Plasma Physics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0206", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Quantum Physics", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Department of Physics, Indian Institute of Technology, 208016, Kanpur, India", 
              "id": "http://www.grid.ac/institutes/grid.417965.8", 
              "name": [
                "Department of Physics, Indian Institute of Technology, 208016, Kanpur, India"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Chowdhury", 
            "givenName": "Sandip", 
            "id": "sg:person.07651506543.38", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07651506543.38"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Physics, Indian Institute of Technology, 208016, Kanpur, India", 
              "id": "http://www.grid.ac/institutes/grid.417965.8", 
              "name": [
                "Department of Physics, Indian Institute of Technology, 208016, Kanpur, India"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Pal", 
            "givenName": "Kunal", 
            "id": "sg:person.016541040353.45", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016541040353.45"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Physics, Indian Institute of Technology, 208016, Kanpur, India", 
              "id": "http://www.grid.ac/institutes/grid.417965.8", 
              "name": [
                "Department of Physics, Indian Institute of Technology, 208016, Kanpur, India"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Pal", 
            "givenName": "Kuntal", 
            "id": "sg:person.01044632674.34", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01044632674.34"
            ], 
            "type": "Person"
          }, 
          {
            "affiliation": {
              "alternateName": "Department of Physics, Indian Institute of Technology, 208016, Kanpur, India", 
              "id": "http://www.grid.ac/institutes/grid.417965.8", 
              "name": [
                "Department of Physics, Indian Institute of Technology, 208016, Kanpur, India"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Sarkar", 
            "givenName": "Tapobrata", 
            "id": "sg:person.01217741634.65", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01217741634.65"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/s10714-008-0622-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1012013307", 
              "https://doi.org/10.1007/s10714-008-0622-8"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02105423", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1040792426", 
              "https://doi.org/10.1007/bf02105423"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10714-010-0931-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1034300263", 
              "https://doi.org/10.1007/s10714-010-0931-6"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10714-018-2472-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1107865323", 
              "https://doi.org/10.1007/s10714-018-2472-3"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1023/a:1018855621348", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1001258110", 
              "https://doi.org/10.1023/a:1018855621348"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s10714-016-2045-2", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1052093215", 
              "https://doi.org/10.1007/s10714-016-2045-2"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.12942/lrr-2010-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064758169", 
              "https://doi.org/10.12942/lrr-2010-3"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2020-09-29", 
        "datePublishedReg": "2020-09-29", 
        "description": "Collapsing solutions in f(R) gravity are restricted due to junction conditions that demand continuity of the Ricci scalar and its normal derivative across the time-like collapsing hypersurface. These are obtained via the method of R-matching, which is ubiquitous in f(R) collapse scenarios. In this paper, we study spherically symmetric collapse with the modification term \u03b1R2\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\alpha R^2$$\\end{document}, and use R-matching to exemplify a class of new solutions. After discussing some mathematical preliminaries by which we obtain an algebraic relation between the shear and the anisotropy in these theories, we consider two metric ansatzes. In the first, the collapsing metric is considered to be a separable function of the co-moving radius and time, and the collapse is shear-free, and in the second, a non-separable interior solution is considered, that represents gravitational collapse with non-zero shear viscosity. We arrive at novel solutions that indicate the formation of black holes or locally naked singularities, while obeying all the necessary energy conditions. The separable case allows for a simple analytic expression of the energy-momentum tensor, that indicates the positivity of the pressures throughout collapse, and is further used to study the heat flux evolution of the collapsing matter, whose analytic solutions are presented under certain approximations. These clearly highlight the role of modified gravity in the examples that we consider.", 
        "genre": "article", 
        "id": "sg:pub.10.1140/epjc/s10052-020-08459-w", 
        "inLanguage": "en", 
        "isAccessibleForFree": true, 
        "isPartOf": [
          {
            "id": "sg:journal.1049394", 
            "issn": [
              "1434-6044", 
              "1434-6052"
            ], 
            "name": "European Physical Journal C", 
            "publisher": "Springer Nature", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "9", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "80"
          }
        ], 
        "keywords": [
          "energy-momentum tensor", 
          "simple analytic expression", 
          "mathematical preliminaries", 
          "R matching", 
          "metric ansatz", 
          "Ricci scalar", 
          "algebraic relations", 
          "analytic solution", 
          "certain approximations", 
          "normal derivative", 
          "modification term", 
          "junction conditions", 
          "analytic expressions", 
          "black holes", 
          "interior solution", 
          "naked singularity", 
          "symmetric collapse", 
          "gravitational collapse", 
          "separable case", 
          "energy conditions", 
          "necessary energy condition", 
          "flux evolution", 
          "separable functions", 
          "heat flux evolution", 
          "gravity", 
          "new solutions", 
          "solution", 
          "ansatz", 
          "approximation", 
          "singularity", 
          "scalar", 
          "hypersurfaces", 
          "shear viscosity", 
          "tensor", 
          "anisotropy", 
          "novel solution", 
          "theory", 
          "class", 
          "preliminaries", 
          "holes", 
          "radius", 
          "metrics", 
          "terms", 
          "collapse", 
          "conditions", 
          "function", 
          "shear", 
          "continuity", 
          "matching", 
          "scenarios", 
          "evolution", 
          "derivatives", 
          "viscosity", 
          "cases", 
          "relation", 
          "time", 
          "matter", 
          "positivity", 
          "expression", 
          "pressure", 
          "formation", 
          "role", 
          "method", 
          "example", 
          "paper"
        ], 
        "name": "Collapse in f(R) gravity and the method of R matching", 
        "pagination": "902", 
        "productId": [
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1131297926"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1140/epjc/s10052-020-08459-w"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1140/epjc/s10052-020-08459-w", 
          "https://app.dimensions.ai/details/publication/pub.1131297926"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2022-05-20T07:36", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-springernature-scigraph/baseset/20220519/entities/gbq_results/article/article_835.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://doi.org/10.1140/epjc/s10052-020-08459-w"
      }
    ]
     

    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.10.1140/epjc/s10052-020-08459-w'

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

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1140/epjc/s10052-020-08459-w'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1140/epjc/s10052-020-08459-w'

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

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1140/epjc/s10052-020-08459-w'


     

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

    176 TRIPLES      22 PREDICATES      98 URIs      82 LITERALS      6 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1140/epjc/s10052-020-08459-w schema:about anzsrc-for:02
    2 anzsrc-for:0202
    3 anzsrc-for:0206
    4 schema:author Nceed501f86294841b30dc9dbb53c035d
    5 schema:citation sg:pub.10.1007/bf02105423
    6 sg:pub.10.1007/s10714-008-0622-8
    7 sg:pub.10.1007/s10714-010-0931-6
    8 sg:pub.10.1007/s10714-016-2045-2
    9 sg:pub.10.1007/s10714-018-2472-3
    10 sg:pub.10.1023/a:1018855621348
    11 sg:pub.10.12942/lrr-2010-3
    12 schema:datePublished 2020-09-29
    13 schema:datePublishedReg 2020-09-29
    14 schema:description Collapsing solutions in f(R) gravity are restricted due to junction conditions that demand continuity of the Ricci scalar and its normal derivative across the time-like collapsing hypersurface. These are obtained via the method of R-matching, which is ubiquitous in f(R) collapse scenarios. In this paper, we study spherically symmetric collapse with the modification term αR2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha R^2$$\end{document}, and use R-matching to exemplify a class of new solutions. After discussing some mathematical preliminaries by which we obtain an algebraic relation between the shear and the anisotropy in these theories, we consider two metric ansatzes. In the first, the collapsing metric is considered to be a separable function of the co-moving radius and time, and the collapse is shear-free, and in the second, a non-separable interior solution is considered, that represents gravitational collapse with non-zero shear viscosity. We arrive at novel solutions that indicate the formation of black holes or locally naked singularities, while obeying all the necessary energy conditions. The separable case allows for a simple analytic expression of the energy-momentum tensor, that indicates the positivity of the pressures throughout collapse, and is further used to study the heat flux evolution of the collapsing matter, whose analytic solutions are presented under certain approximations. These clearly highlight the role of modified gravity in the examples that we consider.
    15 schema:genre article
    16 schema:inLanguage en
    17 schema:isAccessibleForFree true
    18 schema:isPartOf N1a99438d755f40f9819817a5b3099bc1
    19 Nf8da9c5ddb9d4a7fa3235c41d75a99fe
    20 sg:journal.1049394
    21 schema:keywords R matching
    22 Ricci scalar
    23 algebraic relations
    24 analytic expressions
    25 analytic solution
    26 anisotropy
    27 ansatz
    28 approximation
    29 black holes
    30 cases
    31 certain approximations
    32 class
    33 collapse
    34 conditions
    35 continuity
    36 derivatives
    37 energy conditions
    38 energy-momentum tensor
    39 evolution
    40 example
    41 expression
    42 flux evolution
    43 formation
    44 function
    45 gravitational collapse
    46 gravity
    47 heat flux evolution
    48 holes
    49 hypersurfaces
    50 interior solution
    51 junction conditions
    52 matching
    53 mathematical preliminaries
    54 matter
    55 method
    56 metric ansatz
    57 metrics
    58 modification term
    59 naked singularity
    60 necessary energy condition
    61 new solutions
    62 normal derivative
    63 novel solution
    64 paper
    65 positivity
    66 preliminaries
    67 pressure
    68 radius
    69 relation
    70 role
    71 scalar
    72 scenarios
    73 separable case
    74 separable functions
    75 shear
    76 shear viscosity
    77 simple analytic expression
    78 singularity
    79 solution
    80 symmetric collapse
    81 tensor
    82 terms
    83 theory
    84 time
    85 viscosity
    86 schema:name Collapse in f(R) gravity and the method of R matching
    87 schema:pagination 902
    88 schema:productId Ndbe75afd693f435793d9c197572f87cc
    89 Ne39d298f34884393b7b38b056eed3fe5
    90 schema:sameAs https://app.dimensions.ai/details/publication/pub.1131297926
    91 https://doi.org/10.1140/epjc/s10052-020-08459-w
    92 schema:sdDatePublished 2022-05-20T07:36
    93 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    94 schema:sdPublisher N5da1cbe62d804bb5a4b347c0d67086eb
    95 schema:url https://doi.org/10.1140/epjc/s10052-020-08459-w
    96 sgo:license sg:explorer/license/
    97 sgo:sdDataset articles
    98 rdf:type schema:ScholarlyArticle
    99 N1a99438d755f40f9819817a5b3099bc1 schema:volumeNumber 80
    100 rdf:type schema:PublicationVolume
    101 N53a4a77d993f46e7990974304162f1ad rdf:first sg:person.01044632674.34
    102 rdf:rest Nffa1f5033d5a4a20a06104473c0d8a45
    103 N5da1cbe62d804bb5a4b347c0d67086eb schema:name Springer Nature - SN SciGraph project
    104 rdf:type schema:Organization
    105 N75b1cca74ff74f07835315e613bcbe66 rdf:first sg:person.016541040353.45
    106 rdf:rest N53a4a77d993f46e7990974304162f1ad
    107 Nceed501f86294841b30dc9dbb53c035d rdf:first sg:person.07651506543.38
    108 rdf:rest N75b1cca74ff74f07835315e613bcbe66
    109 Ndbe75afd693f435793d9c197572f87cc schema:name doi
    110 schema:value 10.1140/epjc/s10052-020-08459-w
    111 rdf:type schema:PropertyValue
    112 Ne39d298f34884393b7b38b056eed3fe5 schema:name dimensions_id
    113 schema:value pub.1131297926
    114 rdf:type schema:PropertyValue
    115 Nf8da9c5ddb9d4a7fa3235c41d75a99fe schema:issueNumber 9
    116 rdf:type schema:PublicationIssue
    117 Nffa1f5033d5a4a20a06104473c0d8a45 rdf:first sg:person.01217741634.65
    118 rdf:rest rdf:nil
    119 anzsrc-for:02 schema:inDefinedTermSet anzsrc-for:
    120 schema:name Physical Sciences
    121 rdf:type schema:DefinedTerm
    122 anzsrc-for:0202 schema:inDefinedTermSet anzsrc-for:
    123 schema:name Atomic, Molecular, Nuclear, Particle and Plasma Physics
    124 rdf:type schema:DefinedTerm
    125 anzsrc-for:0206 schema:inDefinedTermSet anzsrc-for:
    126 schema:name Quantum Physics
    127 rdf:type schema:DefinedTerm
    128 sg:journal.1049394 schema:issn 1434-6044
    129 1434-6052
    130 schema:name European Physical Journal C
    131 schema:publisher Springer Nature
    132 rdf:type schema:Periodical
    133 sg:person.01044632674.34 schema:affiliation grid-institutes:grid.417965.8
    134 schema:familyName Pal
    135 schema:givenName Kuntal
    136 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01044632674.34
    137 rdf:type schema:Person
    138 sg:person.01217741634.65 schema:affiliation grid-institutes:grid.417965.8
    139 schema:familyName Sarkar
    140 schema:givenName Tapobrata
    141 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01217741634.65
    142 rdf:type schema:Person
    143 sg:person.016541040353.45 schema:affiliation grid-institutes:grid.417965.8
    144 schema:familyName Pal
    145 schema:givenName Kunal
    146 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016541040353.45
    147 rdf:type schema:Person
    148 sg:person.07651506543.38 schema:affiliation grid-institutes:grid.417965.8
    149 schema:familyName Chowdhury
    150 schema:givenName Sandip
    151 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.07651506543.38
    152 rdf:type schema:Person
    153 sg:pub.10.1007/bf02105423 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040792426
    154 https://doi.org/10.1007/bf02105423
    155 rdf:type schema:CreativeWork
    156 sg:pub.10.1007/s10714-008-0622-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012013307
    157 https://doi.org/10.1007/s10714-008-0622-8
    158 rdf:type schema:CreativeWork
    159 sg:pub.10.1007/s10714-010-0931-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1034300263
    160 https://doi.org/10.1007/s10714-010-0931-6
    161 rdf:type schema:CreativeWork
    162 sg:pub.10.1007/s10714-016-2045-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1052093215
    163 https://doi.org/10.1007/s10714-016-2045-2
    164 rdf:type schema:CreativeWork
    165 sg:pub.10.1007/s10714-018-2472-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1107865323
    166 https://doi.org/10.1007/s10714-018-2472-3
    167 rdf:type schema:CreativeWork
    168 sg:pub.10.1023/a:1018855621348 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001258110
    169 https://doi.org/10.1023/a:1018855621348
    170 rdf:type schema:CreativeWork
    171 sg:pub.10.12942/lrr-2010-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064758169
    172 https://doi.org/10.12942/lrr-2010-3
    173 rdf:type schema:CreativeWork
    174 grid-institutes:grid.417965.8 schema:alternateName Department of Physics, Indian Institute of Technology, 208016, Kanpur, India
    175 schema:name Department of Physics, Indian Institute of Technology, 208016, Kanpur, India
    176 rdf:type schema:Organization
     




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


    ...