For a particular type of {\bf k-}essence scalar field, the {\bf k-}essence emergent gravity metric is exactly mapped on to the Barriola-Vilenkin (BV) type metric for Schwarzschild background established by Gangopadhyay and Manna. Based on the S. Chandrasekhar, we report the exciting features of the time-like geodesic structure in the presence of dark energy in an emergent gravity scenario for this Barriola-Vilenkin type metric. We trace the different kinds of trajectories for time-like geodesic in the presence of dark energy for the {\bf k-}essence emergent Barriola-Vilenkin spacetime, which is same as the Schwarzchild spacetime in view of the basic orientation, but the allowed ranges of the aphelion and perihelion distances are much more different. The bound and unbound orbits are plotted for a fixed value of the dark energy density.

中文翻译：

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涌现的 Barriola-Vilenkin 型时空的类时间测地线结构

对于特定类型的 {\bf k-}essence 标量场，{\bf k-}essence 涌现重力度量精确映射到由 Gangopadhyay 和 Manna 建立的 Schwarzschild 背景的 Barriola-Vilenkin (BV) 类型度量。基于 S. Chandrasekhar，我们报告了这种 Barriola-Vilenkin 类型度量在紧急重力场景中存在暗能量的情况下类时间测地线结构的令人兴奋的特征。我们为 {\bf k-} 本质涌现 Barriola-Vilenkin 时空追踪类时测地线在暗能量存在下的不同轨迹，该时空在基本方向上与 Schwarzchild 时空相同，但允许远日点和近日点距离的范围有很大不同。为暗能量密度的固定值绘制束缚轨道和未束缚轨道。