<p>This study explores the role of <i>f</i>(<i>R</i>,&#xa0;<i>T</i>) gravity in modeling massive pulsars, with particular attention to potential contributions from dark matter effects. We consider a static, spherically symmetric spacetime and derive the modified Einstein field equations for the specific functional form <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\( f(R, T) = R + 2\xi T \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>R</mi> <mo>,</mo> <mi>T</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>R</mi> <mo>+</mo> <mn>2</mn> <mi>ξ</mi> <mi>T</mi> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\( \xi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ξ</mi> </math></EquationSource> </InlineEquation> denotes the matter-geometry coupling constant. The matter distribution is modeled using a modified Chaplygin equation of state (EoS) to relate the energy density and radial pressure. To observe the physical relevance and viability of the model, two well-known pulsars: <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(PSR~J0348+0432\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>P</mi> <mi>S</mi> <mi>R</mi> <mspace width="3.33333pt" /> <mi>J</mi> <mn>0348</mn> <mo>+</mo> <mn>0432</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(PSR ~J0030+0451\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>P</mi> <mi>S</mi> <mi>R</mi> <mspace width="3.33333pt" /> <mi>J</mi> <mn>0030</mn> <mo>+</mo> <mn>0451</mn> </mrow> </math></EquationSource> </InlineEquation> are used. Our analysis demonstrates that for coupling values <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\xi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ξ</mi> </math></EquationSource> </InlineEquation>= <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(-\)</EquationSource> <EquationSource Format="MATHML"><math> <mo>-</mo> </math></EquationSource> </InlineEquation>0.1, <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\(-\)</EquationSource> <EquationSource Format="MATHML"><math> <mo>-</mo> </math></EquationSource> </InlineEquation>0.2, <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\(-\)</EquationSource> <EquationSource Format="MATHML"><math> <mo>-</mo> </math></EquationSource> </InlineEquation>0.3, the central densities range from <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\(3.43\times 10^{15}\,\textrm{g}~\textrm{cm}^{-3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3.43</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>15</mn> </msup> <mspace width="0.166667em" /> <mtext>g</mtext> <mspace width="3.33333pt" /> <msup> <mtext>cm</mtext> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\(3.98\times 10^{15}\,\textrm{g}~\textrm{cm}^{-3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>3.98</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>15</mn> </msup> <mspace width="0.166667em" /> <mtext>g</mtext> <mspace width="3.33333pt" /> <msup> <mtext>cm</mtext> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>, while the surface densities remain near <InlineEquation ID="IEq15"> <EquationSource Format="TEX">\(1.98\times 10^{15}\,\textrm{g}~\textrm{cm}^{-3}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1.98</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>15</mn> </msup> <mspace width="0.166667em" /> <mtext>g</mtext> <mspace width="3.33333pt" /> <msup> <mtext>cm</mtext> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation>. The central pressure <InlineEquation ID="IEq16"> <EquationSource Format="TEX">\(p_{r}(0)\sim 3.5\times 10^{34} \,\textrm{dyne}~\textrm{cm}^{-2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>p</mi> <mi>r</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mn>0</mn> <mo stretchy="false">)</mo> </mrow> <mo>∼</mo> <mn>3.5</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>34</mn> </msup> <mspace width="0.166667em" /> <mtext>dyne</mtext> <mspace width="3.33333pt" /> <msup> <mtext>cm</mtext> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> ensures a regular and causal behavior throughout the configuration. We further examine the energy conditions, compactness factor, Harrison–Zeldovich–Novikov stability criterion, adiabatic index, and gravitational redshift. The results suggest that the proposed <i>f</i>(<i>R</i>,&#xa0;<i>T</i>) gravity model provides a viable framework for describing ultra-dense pulsars under the influence of modified gravity effects.</p>

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Viable model of anisotropic ultra-dense pulsars \(PSR~J0348+0432\) and \(PSR~J0030+0451\) in modified gravity

  • S. A. Mardan,
  • A. Khalid,
  • A. Zahra,
  • Muhammad Bilal Riaz

摘要

This study explores the role of f(RT) gravity in modeling massive pulsars, with particular attention to potential contributions from dark matter effects. We consider a static, spherically symmetric spacetime and derive the modified Einstein field equations for the specific functional form \( f(R, T) = R + 2\xi T \) f ( R , T ) = R + 2 ξ T , where \( \xi \) ξ denotes the matter-geometry coupling constant. The matter distribution is modeled using a modified Chaplygin equation of state (EoS) to relate the energy density and radial pressure. To observe the physical relevance and viability of the model, two well-known pulsars: \(PSR~J0348+0432\) P S R J 0348 + 0432 and \(PSR ~J0030+0451\) P S R J 0030 + 0451 are used. Our analysis demonstrates that for coupling values \(\xi \) ξ = \(-\) - 0.1, \(-\) - 0.2, \(-\) - 0.3, the central densities range from \(3.43\times 10^{15}\,\textrm{g}~\textrm{cm}^{-3}\) 3.43 × 10 15 g cm - 3 to \(3.98\times 10^{15}\,\textrm{g}~\textrm{cm}^{-3}\) 3.98 × 10 15 g cm - 3 , while the surface densities remain near \(1.98\times 10^{15}\,\textrm{g}~\textrm{cm}^{-3}\) 1.98 × 10 15 g cm - 3 . The central pressure \(p_{r}(0)\sim 3.5\times 10^{34} \,\textrm{dyne}~\textrm{cm}^{-2}\) p r ( 0 ) 3.5 × 10 34 dyne cm - 2 ensures a regular and causal behavior throughout the configuration. We further examine the energy conditions, compactness factor, Harrison–Zeldovich–Novikov stability criterion, adiabatic index, and gravitational redshift. The results suggest that the proposed f(RT) gravity model provides a viable framework for describing ultra-dense pulsars under the influence of modified gravity effects.