Perfect fluid spacetimes and $k$-almost Yamabe solitons

Abstract

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 permit 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 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.

$K$-Ricci-Bourguignon Almost Solitons

“…Because of their connection to GR, there was a notable increase of quest in researching Ricci solitons and related generalizations in a variety of geometrical contexts. Many researchers have investigated many sorts of solitons in P F spacetimes including Ricci and gradient type Ricci solitons ( [17], [18]), η-Ricci solitons [4], Yamabe and gradient type Yamabe solitons [17], k-almost Yamabe solitons [15], η-Einstein solitons of gradient type [18], gradient ϱ-Einstein solitons [13], m-quasi Einstein solitons of gradient type [17], gradient Schouten solitons [18], Ricci-Yamabe solitons [14], respectively.…”

Analyzing Curvature Properties and Geometric Solitons of the Twisted Sasaki Metric on the Tangent Bundle over a Statistical Manifold

“…They obtained a number of interesting results and inspired the idea of this paper. De and Gezer [32] studied k-almost Yamabe solitons for the perfect fluid spacetime of general relativity. In particular, they constructed two examples to prove the existence of k-almost Yamabe solitons.…”

Eigenvalue of (p,q)-Biharmonic System along the Ricci Flow

“…Bracken and Azami obtained some results on the evolution of the first eigenvalue recently [4][5][6]. Other remarkable work can be found in [7][8][9][10]. We call the smooth function u : M → R a harmonic function if ∆u = 0.…”