We consider the scalar-Einstein-Gauss-Bonnet (sEGB) 4d gravitational model with a scalar field <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\varphi \left( u\right) $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>φ</mi> <mfenced close=")" open="("> <mi>u</mi> </mfenced> </mrow> </math></EquationSource> </InlineEquation>, Einstein and Gauss-Bonnet terms. The model action contains a potential term <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$U\left( \varphi \right) $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>U</mi> <mfenced close=")" open="("> <mi>φ</mi> </mfenced> </mrow> </math></EquationSource> </InlineEquation>, a Gauss-Bonnet coupling function <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$f\left( \varphi \right) $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mfenced close=")" open="("> <mi>φ</mi> </mfenced> </mrow> </math></EquationSource> </InlineEquation> and a parameter <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\varepsilon = \pm 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ε</mi> <mo>=</mo> <mo>±</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\varepsilon = 1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ε</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> corresponds to the canonical scalar field, and <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\varepsilon = -1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ε</mi> <mo>=</mo> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> to the phantom field. In this paper we applied the sEGB reconstruction procedure from our previous work [<CitationRef CitationID="CR11">11</CitationRef>] to the Yılmaz-Rosen metric, a solution potentially describing a quasi-black hole without an event horizon. Within this framework, we also derived analytical solutions based on scalar-tensor theory. Our results indicate that for this configuration, the potential U vanishes and the scalar field is phantom-like. Furthermore, an analysis of the Einstein equations in the Yılmaz-Rosen metric reveals that all energy conditions are violated. The corresponding energy-momentum tensor suggests the presence of exotic matter with negative pressure, as indicated by the negative value of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$T_u^u$</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>T</mi> <mi>u</mi> <mi>u</mi> </msubsup> </math></EquationSource> </InlineEquation>. This could originate from a scalar field (such as the Higgs field or another nonlinear field), or from phenomena like dark energy or quintessence. In addition, we considered the application of our reconstruction method in the sEGB model in the Janis-Newman-Winicour (JNW) metric. As noted in this paper, the Yılmaz-Rosen metric is a limiting case of the JNW metric (as <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$s \rightarrow +\infty $</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>s</mi> <mo stretchy="false">→</mo> <mo>+</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>). Furthermore, we obtained some exact solutions of scalar-tensor theory in the JNW metric.

The Yilmaz-Rosen and Janis-Newman-Winicour metric solutions in the reconstructed scalar-Einstein-Gauss-Bonnet 4d gravitational model

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发表日期：

2026年3月27日

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K. K. Ernazarov

摘要

We consider the scalar-Einstein-Gauss-Bonnet (sEGB) 4d gravitational model with a scalar field $\varphi \left( u\right) $ $φ (u)$ , Einstein and Gauss-Bonnet terms. The model action contains a potential term $U\left( \varphi \right) $ $U (φ)$ , a Gauss-Bonnet coupling function $f\left( \varphi \right) $ $f (φ)$ and a parameter $\varepsilon = \pm 1$ $ε = \pm 1$ , where $\varepsilon = 1$ $ε = 1$ corresponds to the canonical scalar field, and $\varepsilon = -1$ $ε = - 1$ to the phantom field. In this paper we applied the sEGB reconstruction procedure from our previous work [11] to the Yılmaz-Rosen metric, a solution potentially describing a quasi-black hole without an event horizon. Within this framework, we also derived analytical solutions based on scalar-tensor theory. Our results indicate that for this configuration, the potential U vanishes and the scalar field is phantom-like. Furthermore, an analysis of the Einstein equations in the Yılmaz-Rosen metric reveals that all energy conditions are violated. The corresponding energy-momentum tensor suggests the presence of exotic matter with negative pressure, as indicated by the negative value of $T_u^u$ $T_{u}^{u}$ . This could originate from a scalar field (such as the Higgs field or another nonlinear field), or from phenomena like dark energy or quintessence. In addition, we considered the application of our reconstruction method in the sEGB model in the Janis-Newman-Winicour (JNW) metric. As noted in this paper, the Yılmaz-Rosen metric is a limiting case of the JNW metric (as $s \rightarrow +\infty $ $s \to + \infty$ ). Furthermore, we obtained some exact solutions of scalar-tensor theory in the JNW metric.