Sultana--Dyer Black Hole Spacetime and h-Almost Yamabe Solitons
Abstract
This paper investigates Yamabe-type soliton structures on the Sultana-Dyer (SD) black-hole spacetime. By employing the explicit metric and curvature quantities associated with the SD spacetime, we demonstrate that the non-Killing vector field ∂t induces an h-almost Yamabe soliton for explicitly determined functions h and λ. We also establish the condition under which this structure reduces to an almost Yamabe soliton and examine why the coordinate vector fields ∂r and ∂θ do not satisfy the corresponding Yamabe flow conditions. Furthermore, we show that the energy-momentum tensor, consisting of a timelike dust component and a null radiation fluid, is compatible with the Riemann, conformal (Weyl), concircular, conharmonic, and projective curvature structures. This compatibility reveals a strong geometric correspondence between the matter distribution and the causal structure of the spacetime. However, when the time-dependent scalar-curvature profile is subject to the constraints associated with late-stage cosmic expansion, the null, weak, and dominant energy conditions are violated. These findings provide a geometric characterization of the time-dependent Sultana-Dyer spacetime within the framework of generalized Yamabe solitons.
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BibTeX
@misc{shaikh2026sultanadyer,
title = {{Sultana--Dyer Black Hole Spacetime and $h$-Almost Yamabe Solitons}},
author = {Absos Ali Shaikh and Kamiruzzaman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.12019},
eprint = {2609.12019},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12019},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Sultana--Dyer Black Hole Spacetime and h-Almost Yamabe Solitons
AU - Absos Ali Shaikh
AU - Kamiruzzaman
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.12019
UR - https://arxiv.org/abs/2609.12019
AB - This paper investigates Yamabe-type soliton structures on the Sultana-Dyer (SD) black-hole spacetime. By employing the explicit metric and curvature quantities associated with the SD spacetime, we demonstrate that the non-Killing vector field ∂_t induces an h-almost Yamabe soliton for explicitly determined functions h and λ. We also establish the condition under which this structure reduces to an almost Yamabe soliton and examine why the coordinate vector fields ∂_r and ∂_θ do not satisfy the corresponding Yamabe flow conditions. Furthermore, we show that the energy-momentum tensor, consisting of a timelike dust component and a null radiation fluid, is compatible with the Riemann, conformal (Weyl), concircular, conharmonic, and projective curvature structures. This compatibility reveals a strong geometric correspondence between the matter distribution and the causal structure of the spacetime. However, when the time-dependent scalar-curvature profile is subject to the constraints associated with late-stage cosmic expansion, the null, weak, and dominant energy conditions are violated. These findings provide a geometric characterization of the time-dependent Sultana-Dyer spacetime within the framework of generalized Yamabe solitons.
ER -