The present paper focuses on space-times admitting a type of semi-symmetric metric connection whose associated vector is recurrent. At first, we characterize the general properties of such space-times. Then, in space-times admitting such a connection whose Ricci tensor vanishes, we achieve a state equation and state its physical consequences. We demonstrate that such a space-time becomes a generalized Robertson-Walker space-time as well as a perfect fluid space-time and a purely electric space-time. Moreover, we prove that a Ricci-semi symmetric space-time admitting such a connection becomes a quasi-Einstein space-times in the sense of Deszcz. The influence of the semi-symmetric metric <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3595_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="30" /> </InlineMediaObject> <EquationSource Format="TEX">$w-$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>w</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>recurrent spacetime under the f(r)- gravity setting is finally studied. By taking into consideration a novel model <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3595_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="101" /> </InlineMediaObject> <EquationSource Format="TEX">$f(r)=ln(\beta r)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>f</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>l</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mi>β</mi> <mi>r</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12648_2025_3595_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\beta$</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation> is a positive constant, we are able to derive different energy conditions.

Impact of a type of semi-symmetric metric connection on a space-time and f(r)- gravity

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发表日期：

2025年4月3日

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Uday Chand De,
Hülya Bağdatlı Yılmaz,
Krishnendu De

摘要

The present paper focuses on space-times admitting a type of semi-symmetric metric connection whose associated vector is recurrent. At first, we characterize the general properties of such space-times. Then, in space-times admitting such a connection whose Ricci tensor vanishes, we achieve a state equation and state its physical consequences. We demonstrate that such a space-time becomes a generalized Robertson-Walker space-time as well as a perfect fluid space-time and a purely electric space-time. Moreover, we prove that a Ricci-semi symmetric space-time admitting such a connection becomes a quasi-Einstein space-times in the sense of Deszcz. The influence of the semi-symmetric metric $w-$ $w -$ recurrent spacetime under the f(r)- gravity setting is finally studied. By taking into consideration a novel model $f(r)=ln(\beta r)$ $f (r) = l n (β r)$ , where $\beta$ $β$ is a positive constant, we are able to derive different energy conditions.