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Abstract <p> A perfect fluid spacetime is not a generalized Robertson–Walker spacetime, and also the converse does not hold in general. The purpose of this study is to determine the conditions under which a generalized Robertson–Walker spacetime is a perfect fluid spacetime. It is established that if the metric of a generalized Robertson–Walker spacetime is a <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\rho\)</EquationSource> </InlineEquation>-Einstein soliton, then the spacetime turns into a perfect fluid spacetime. Conversely, a perfect fluid spacetime with divergence-free velocity vector obeying <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\rho\)</EquationSource> </InlineEquation>-Einstein solitons represents a generalized Robertson–Walker spacetime. Also, we obtain the same result if the metric is either a gradient <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\rho\)</EquationSource> </InlineEquation>-Einstein soliton or a gradient <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(m\)</EquationSource> </InlineEquation>-quasi Einstein soliton. As a consequence of the above studies, we acquire some fascinating results. </p>

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Solitons and Gradient Solitons on \(GRW\) Spacetimes

  • 期刊论文

  • 发表日期：

    2025年10月1日

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  • U. C. De,
  • A. Sardar

摘要

Abstract

A perfect fluid spacetime is not a generalized Robertson–Walker spacetime, and also the converse does not hold in general. The purpose of this study is to determine the conditions under which a generalized Robertson–Walker spacetime is a perfect fluid spacetime. It is established that if the metric of a generalized Robertson–Walker spacetime is a \(\rho\) -Einstein soliton, then the spacetime turns into a perfect fluid spacetime. Conversely, a perfect fluid spacetime with divergence-free velocity vector obeying \(\rho\) -Einstein solitons represents a generalized Robertson–Walker spacetime. Also, we obtain the same result if the metric is either a gradient \(\rho\) -Einstein soliton or a gradient \(m\) -quasi Einstein soliton. As a consequence of the above studies, we acquire some fascinating results.