<p>In this study, we have explored the structure and stability properties of anisotropic dark matter stars in four-dimensional Einstein-Gauss-Bonnet (4DEGB) theory. The model explores the joint role of the Gauss–Bonnet coupling (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>) and an anisotropy strength parameter (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\beta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>) on global observables, integrating sequences to obtain mass-radius, mass-compactness, and mass-central density relations. Our numerical study uncovers two definitive trends: (i) for positive <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\alpha $</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>, the stars can be more massive with a larger radius, while <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\alpha <0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo><</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> favors more compact stars; across <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\alpha \in [-2,2]~\mathrm {km^2}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>∈</mo> <mrow> <mo stretchy="false">[</mo> <mo>-</mo> <mn>2</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">]</mo> </mrow> <mspace width="3.33333pt" /> <msup> <mi mathvariant="normal">km</mi> <mn>2</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$M_{\max }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>M</mi> <mo movablelimits="true">max</mo> </msub> </math></EquationSource> </InlineEquation> shifts from <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\sim 2.47$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>∼</mo> <mn>2.47</mn> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\sim 2.67\,M_\odot $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>∼</mo> <mn>2.67</mn> <mspace width="0.166667em" /> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </math></EquationSource> </InlineEquation> with radii near 13 km; and (ii) increasing <InlineEquation ID="IEq9"> <EquationSource Format="TEX">$\beta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation> toward weaker anisotropy, i.e., from strongly negative values to <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$\beta =0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>β</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, leads to an increase in both mass and radius while lowering the central density at the turning point. We further checked the physical acceptability of all our solutions via the standard stability checks (segments with <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$dM/d\rho _c>0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>d</mi> <mi>M</mi> <mo stretchy="false">/</mo> <mi>d</mi> <msub> <mi>ρ</mi> <mi>c</mi> </msub> <mo>></mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$\gamma (r)>4/3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>γ</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>></mo> <mn>4</mn> <mo stretchy="false">/</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>, and <InlineEquation ID="IEq13"> <EquationSource Format="TEX">$0\le v_{r,\perp }^2\le 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>0</mn> <mo>≤</mo> <msubsup> <mi>v</mi> <mrow> <mi>r</mi> <mo>,</mo> <mo>⊥</mo> </mrow> <mn>2</mn> </msubsup> <mo>≤</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>). These sequences adhere to the Buchdahl bound (<InlineEquation ID="IEq14"> <EquationSource Format="TEX">$M/R<4/9$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mo stretchy="false">/</mo> <mi>R</mi> <mo><</mo> <mn>4</mn> <mo stretchy="false">/</mo> <mn>9</mn> </mrow> </math></EquationSource> </InlineEquation>) and are compatible with observational bands associated with high-mass compact objects (GW190814, PSR J0952–0607, PSR J0348+0432). Overall, the findings indicate that dark-sector microphysics combined with higher-curvature corrections in 4DEGB gravity can support high-mass compact-star configurations in the <InlineEquation ID="IEq15"> <EquationSource Format="TEX">$\sim 2.5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>∼</mo> <mn>2.5</mn> </mrow> </math></EquationSource> </InlineEquation>–<InlineEquation ID="IEq16"> <EquationSource Format="TEX">$2.7\,M_\odot $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2.7</mn> <mspace width="0.166667em" /> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </math></EquationSource> </InlineEquation> range while satisfying the standard necessary conditions of physical acceptability.</p>

Compact Dark Matter Stars with Gravitational Anisotropy in 4D Einstein–Gauss–Bonnet Gravity

期刊论文
发表日期：

2026年6月1日

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Anirudh Pradhan,
Safiqul Islam,
Ayan Banerjee,
Muhammad Aamir

摘要

In this study, we have explored the structure and stability properties of anisotropic dark matter stars in four-dimensional Einstein-Gauss-Bonnet (4DEGB) theory. The model explores the joint role of the Gauss–Bonnet coupling ( $\alpha $ $α$ ) and an anisotropy strength parameter ( $\beta $ $β$ ) on global observables, integrating sequences to obtain mass-radius, mass-compactness, and mass-central density relations. Our numerical study uncovers two definitive trends: (i) for positive $\alpha $ $α$ , the stars can be more massive with a larger radius, while $\alpha <0$ $α < 0$ favors more compact stars; across $\alpha \in [-2,2]~\mathrm {km^2}$ $α \in [- 2, 2] {km}^{2}$ , $M_{\max }$ $M_{max}$ shifts from $\sim 2.47$ $\sim 2.47$ to $\sim 2.67\,M_\odot $ $\sim 2.67 M_{⊙}$ with radii near 13 km; and (ii) increasing $\beta $ $β$ toward weaker anisotropy, i.e., from strongly negative values to $\beta =0$ $β = 0$ , leads to an increase in both mass and radius while lowering the central density at the turning point. We further checked the physical acceptability of all our solutions via the standard stability checks (segments with $dM/d\rho _c>0$ $d M / d ρ_{c} > 0$ , $\gamma (r)>4/3$ $γ (r) > 4 / 3$ , and $0\le v_{r,\perp }^2\le 1$ $0 \leq v_{r, ⊥}^{2} \leq 1$ ). These sequences adhere to the Buchdahl bound ( $M/R<4/9$ $M / R < 4 / 9$ ) and are compatible with observational bands associated with high-mass compact objects (GW190814, PSR J0952–0607, PSR J0348+0432). Overall, the findings indicate that dark-sector microphysics combined with higher-curvature corrections in 4DEGB gravity can support high-mass compact-star configurations in the $\sim 2.5$ $\sim 2.5$ – $2.7\,M_\odot $ $2.7 M_{⊙}$ range while satisfying the standard necessary conditions of physical acceptability.