<p>We examine generalized almost <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\eta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>-Ricci solitons on spacetimes, providing two explicit examples to confirm their existence. Under the assumption that the potential vector field satisfies conditions such as parallelism, conformality, Killing, concircularity, or torse-forming behavior, the manifold is shown to be a generalized quasi-Einstein spacetime. Furthermore, when the soliton field coincides with a unit timelike torse-forming vector, the gradient of its governing scalar function aligns with this vector, ensuring a perfect fluid structure. We also demonstrate that <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {W}_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">W</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-flat spacetimes admitting such solitons inherently possess generalized Robertson–Walker geometry alongside perfect fluid properties. Finally, gradient solitons in this context correspond to a generalized quasi-Einstein spacetime.</p>

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Generalized Almost \(\eta \)-Ricci Solitons on Spacetimes

  • Mehdi Jafari,
  • Shahroud Azami,
  • Uday Chand De

摘要

We examine generalized almost \(\eta \) η -Ricci solitons on spacetimes, providing two explicit examples to confirm their existence. Under the assumption that the potential vector field satisfies conditions such as parallelism, conformality, Killing, concircularity, or torse-forming behavior, the manifold is shown to be a generalized quasi-Einstein spacetime. Furthermore, when the soliton field coincides with a unit timelike torse-forming vector, the gradient of its governing scalar function aligns with this vector, ensuring a perfect fluid structure. We also demonstrate that \(\mathcal {W}_2\) W 2 -flat spacetimes admitting such solitons inherently possess generalized Robertson–Walker geometry alongside perfect fluid properties. Finally, gradient solitons in this context correspond to a generalized quasi-Einstein spacetime.