TY  - JOUR
TI  - Perfect fluid spacetimes and k -almost Yamabe solitons
AB  - In this article, we presumed that a perfect fluid is the source of the gravitational field while analyzing the solutions to the Einstein field equations. With this new and creative approach, here we study k -almost Yamabe solitons and gradient k -almost Yamabe solitons. First, two examples are constructed to ensure the existence of gradient k -almost Yamabe solitons. Then we show that if a perfect fluid spacetime admits a k -almost Yamabe soliton, then its potential vector field is Killing if and only if the divergence of the potential vector field vanishes. Besides, we prove that if a perfect fluid spacetime permits a k -almost Yamabe soliton ( g, k, ρ, λ ), then the integral curves of the vector field ρ are geodesics, the spacetime becomes stationary and the isotopic pressure and energy density remain invariant under the velocity vector field ρ . Also, we establish that if the potential vector field is pointwise collinear with the velocity vector field and ρ(a) = 0 where a is a scalar, then either the perfect fluid spacetime represents a phantom era, or the potential function Φ is invariant under the velocity vector field ρ . Finally, we prove that if a perfect fluid spacetime permits a gradient k -almost Yamabe soliton ( g, k, DΦ, λ ) and R, λ, k are invariant under ρ , then the vorticity of the fluid vanishes.
AU  - Gezer, Aydin
AU  - De, Krishnendu
AU  - DE, UDAY CHAND
DO  - 10.55730/1300-0098.3423
PY  - 2023
JO  - Turkish Journal of Mathematics
VL  - 47
IS  - 4
SN  - 1300-0098
SP  - 1236
EP  - 1246
DB  - TRDizin
UR  - http://search/yayin/detay/1180410
ER  -