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<p>In the present article, we consider nearly vacuum static equations (NVSEs, in short) on homothetic hyperbolic Kenmotsu manifolds (HHKMs, in short). We prove that if an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\eta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>-Einstein HHKM of dimension (2m+1) admits a NVSE, then the solution is a constant. We also deduce that if a HHKM of dimension 3 admits a non-trivial solution of NVSE, then the scalar curvature is a constant. We construct an example to test the existence of this result. Finally, we apply NVSE in imperfect fluid GRW spacetimes.</p>

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Nearly vacuum static equation on homothetic hyperbolic Kenmotsu manifolds and its applications on spacetimes

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • Uday Chand De,
  • Tarak Mandal

摘要

In the present article, we consider nearly vacuum static equations (NVSEs, in short) on homothetic hyperbolic Kenmotsu manifolds (HHKMs, in short). We prove that if an \(\eta \) η -Einstein HHKM of dimension (2m+1) admits a NVSE, then the solution is a constant. We also deduce that if a HHKM of dimension 3 admits a non-trivial solution of NVSE, then the scalar curvature is a constant. We construct an example to test the existence of this result. Finally, we apply NVSE in imperfect fluid GRW spacetimes.