<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article  PUBLIC "-//NLM//DTD Journal Publishing DTD v3.0 20080202//EN" "http://dtd.nlm.nih.gov/publishing/3.0/journalpublishing3.dtd"><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" dtd-version="3.0" xml:lang="en" article-type="research article"><front><journal-meta><journal-id journal-id-type="publisher-id">JMP</journal-id><journal-title-group><journal-title>Journal of Modern Physics</journal-title></journal-title-group><issn pub-type="epub">2153-1196</issn><publisher><publisher-name>Scientific Research Publishing</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.4236/jmp.2020.1111110</article-id><article-id pub-id-type="publisher-id">JMP-104027</article-id><article-categories><subj-group subj-group-type="heading"><subject>Articles</subject></subj-group><subj-group subj-group-type="Discipline-v2"><subject>Physics&amp;Mathematics</subject></subj-group></article-categories><title-group><article-title>
 
 
  Why the Spacetime Embedding Incompressible Cores of Pulsars Must Be Conformally Flat?
 
</article-title></title-group><contrib-group><contrib contrib-type="author" xlink:type="simple"><name name-style="western"><surname>Ahmad</surname><given-names>A. Hujeirat</given-names></name><xref ref-type="aff" rid="aff1"><sub>1</sub></xref><xref ref-type="corresp" rid="cor1"><sup>*</sup></xref></contrib></contrib-group><aff id="aff1"><label>1</label><addr-line>IWR, Universit&amp;amp;auml;t Heidelberg, Heidelberg, Germany</addr-line></aff><pub-date pub-type="epub"><day>04</day><month>11</month><year>2020</year></pub-date><volume>11</volume><issue>11</issue><fpage>1779</fpage><lpage>1784</lpage><history><date date-type="received"><day>1,</day>	<month>October</month>	<year>2020</year></date><date date-type="rev-recd"><day>8,</day>	<month>November</month>	<year>2020</year>	</date><date date-type="accepted"><day>11,</day>	<month>November</month>	<year>2020</year></date></history><permissions><copyright-statement>&#169; Copyright  2014 by authors and Scientific Research Publishing Inc. </copyright-statement><copyright-year>2014</copyright-year><license><license-p>This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/</license-p></license></permissions><abstract><p><html>
 <head></head>
 
  The multi-messenger observations of the merger event in GW170817 did not rule out the possibility that the remnant might be a dynamically stable neutron star with 
  <img src="Edit_01b04c31-b94c-4b32-bd17-d6383ca16545.bmp" alt="" />. Based on this and other recent events, I argue that the universal maximum density hypothesis should be revived. Accordingly, the central densities in the cores of ultra-compact objects must be upper-limited by the critical density number 
  <em>n</em>
  <sub><em>cr</em></sub>, beyond which supranuclear dense matter becomes purely incompressible. Based on the spacetime-matter coupling in GR, it is shown that the topology of spacetime embedding incompressible quantum fluids with 
  <em>n</em>=
  <em style="white-space:normal;">n</em>
  <sub style="white-space:normal;"><em>cr </em></sub>must be Minkowski flat, which implies that spacetime at the background of ultra-compact objects should be bimetric.
 
</html></p></abstract><kwd-group><kwd>Relativity: Numerical</kwd><kwd> General</kwd><kwd> Black Hole Physics</kwd><kwd> Pulsars</kwd><kwd> Neutron Stars</kwd><kwd> Pulsars</kwd><kwd> Superfluidity</kwd><kwd> Superconductivity</kwd><kwd> Incompressibility</kwd><kwd> Gluons</kwd><kwd> Quarks</kwd><kwd> Plasmas</kwd><kwd> QCD</kwd></kwd-group></article-meta></front><body><sec id="s1"><title>Acknowledgements</title><p>Dr. Emre Dil is gratefully acknowledged for valuable discussions.</p></sec><sec id="s2"><title>Conflicts of Interest</title><p>The author declares no conflicts of interest regarding the publication of this paper.</p></sec><sec id="s3"><title>Cite this paper</title><p>Hujeirat, A.A. (2020) Why the Spacetime Embedding Incompressible Cores of Pulsars Must Be Conformally Flat? Journal of Modern Physics, 11, 1779-1784. https://doi.org/10.4236/jmp.2020.1111110</p></sec></body><back><ref-list><title>References</title><ref id="scirp.104027-ref1"><label>1</label><mixed-citation publication-type="other" xlink:type="simple">Ozel, F. and Freire, P. (2016) Annual Review of Astronomy and Astrophysics, 54, 401-440. https://doi.org/10.1146/annurev-astro-081915-023322</mixed-citation></ref><ref id="scirp.104027-ref2"><label>2</label><mixed-citation publication-type="other" xlink:type="simple">Camenzind, M. (2007) Compact Objects in Astrophysics. Springer, Heidelberg. https://doi.org/10.4236/jmp.2018.91004</mixed-citation></ref><ref id="scirp.104027-ref3"><label>3</label><mixed-citation publication-type="journal" xlink:type="simple"><name name-style="western"><surname>Hujeirat</surname><given-names> A.A. </given-names></name>,<etal>et al</etal>. (<year>2018</year>)<article-title></article-title><source> Journal of Modern Physics</source><volume> 9</volume>,<fpage> 51</fpage>-<lpage>69</lpage>.<pub-id pub-id-type="doi"></pub-id></mixed-citation></ref><ref id="scirp.104027-ref4"><label>4</label><mixed-citation publication-type="other" xlink:type="simple">Hujeirat, A.A. (2018) Journal of Modern Physics, 9, 532-553. https://doi.org/10.4236/jmp.2018.94037</mixed-citation></ref><ref id="scirp.104027-ref5"><label>5</label><mixed-citation publication-type="other" xlink:type="simple">Raithel, C.A. (2019) The European Physical Journal A, 55, Article No. 80. https://doi.org/10.1140/epja/i2019-12759-5</mixed-citation></ref><ref id="scirp.104027-ref6"><label>6</label><mixed-citation publication-type="other" xlink:type="simple">Piro, L., Troja, E., Zhang, B., et al. (2019) Monthly Notices of the Royal Astronomical Society, 483, 1912-1921. https://doi.org/10.1093/mnras/sty3047</mixed-citation></ref><ref id="scirp.104027-ref7"><label>7</label><mixed-citation publication-type="other" xlink:type="simple">Abbott, B.P., et al. (2019) Physical Review X, 9, Article ID: 011001.</mixed-citation></ref><ref id="scirp.104027-ref8"><label>8</label><mixed-citation publication-type="other" xlink:type="simple">Hujeirat, A.A. and Samtaney, R. (2020) Journal of Modern Physics, 11.</mixed-citation></ref><ref id="scirp.104027-ref9"><label>9</label><mixed-citation publication-type="other" xlink:type="simple">Dil, E. and Zafer, T. (2016) Journal of Gravity, 2016, Article ID: 7636493. https://doi.org/10.1155/2016/7636493</mixed-citation></ref><ref id="scirp.104027-ref10"><label>10</label><mixed-citation publication-type="other" xlink:type="simple">Brito, I. and Ramos, M.P.M. (2019) General Relativity and Gravitation, 51, Article No. 28. https://doi.org/10.1007/s10714-019-2514-5</mixed-citation></ref><ref id="scirp.104027-ref11"><label>11</label><mixed-citation publication-type="other" xlink:type="simple">Zeldowich, Ya.B. (1962) Soviet Physics—JETP, 14, 5.</mixed-citation></ref><ref id="scirp.104027-ref12"><label>12</label><mixed-citation publication-type="other" xlink:type="simple">Bludman, S.A. and Ruderman, M.A. (1968) Physical Review, 170, 1176. https://doi.org/10.1103/PhysRev.170.1176</mixed-citation></ref><ref id="scirp.104027-ref13"><label>13</label><mixed-citation publication-type="other" xlink:type="simple">LHCb Collaboration (2015) Physical Review Letters, 115, Article ID: 072001.</mixed-citation></ref><ref id="scirp.104027-ref14"><label>14</label><mixed-citation publication-type="other" xlink:type="simple">Hujeirat, A.A. and Samtaney, R. (2020) Journal of Modern Physics, 11, 395-406.</mixed-citation></ref></ref-list></back></article>