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<p>In this work, we analyze the solutions to the Einstein field equations under the assumption that the gravitational field originates from a perfect fluid. Bach almost solitons on perfect fluid spacetimes are investigated with this novel and inventive method. First, we show that if a perfect fluid spacetime with concircular vector field satisfying some state equation obeys Bach almost solitons whose potential vector field is point-wise collinear with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\zeta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ζ</mi> </math></EquationSource> </InlineEquation>, then the spacetime becomes Bach flat. Moreover, we prove that under certain restriction, if a perfect fluid spacetime with V-Ric vector field obeys steady Bach almost solitons, then the perfect fluid spacetime satisfies the state equation <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(p=-\frac{3-m}{1-m}\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>=</mo> <mo>-</mo> <mfrac> <mrow> <mn>3</mn> <mo>-</mo> <mi>m</mi> </mrow> <mrow> <mn>1</mn> <mo>-</mo> <mi>m</mi> </mrow> </mfrac> <mi>σ</mi> </mrow> </math></EquationSource> </InlineEquation> and in dimension 4, it represents phantom era under certain restriction on the associated scalars.</p>

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Bach almost solitons and perfect fluid spacetimes

  • 期刊论文

  • 发表日期：

    2026年7月20日

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  • Krishnendu De,
  • Arpan Sardar

摘要

In this work, we analyze the solutions to the Einstein field equations under the assumption that the gravitational field originates from a perfect fluid. Bach almost solitons on perfect fluid spacetimes are investigated with this novel and inventive method. First, we show that if a perfect fluid spacetime with concircular vector field satisfying some state equation obeys Bach almost solitons whose potential vector field is point-wise collinear with \(\zeta \) ζ , then the spacetime becomes Bach flat. Moreover, we prove that under certain restriction, if a perfect fluid spacetime with V-Ric vector field obeys steady Bach almost solitons, then the perfect fluid spacetime satisfies the state equation \(p=-\frac{3-m}{1-m}\sigma \) p = - 3 - m 1 - m σ and in dimension 4, it represents phantom era under certain restriction on the associated scalars.