Time-like geodesic structure for the emergent Barriola–Vilenkin type spacetime

Abstract

For a particular type of k-essence scalar field, the 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 k-essence emergent Barriola-Vilenkin spacetime, which are same with 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. II. REVIEW OF K-ESSENCE THEORY AND EMERGENT GRAVITYIn this section, we present a short review of the kessence theory and construction of the effective emergent metric. The k-essence scalar field φ minimally coupled to the background spacetime metric g µν has action [9]- [13] S k [φ, g µν ] = d 4 x √ −gL(X, φ)

Geodesic structure of generalized Vaidya spacetime through the K-essence

“…Since c 6 ≤ r a − At a < t0 2 + c 6 and c 6 ≤ r a − Bt a < t0 2 + c 6 , then for any finite values of c 6 , t 0 , A and B, the values of r a and t a are also finite. By substituting the values D = 2.1, L = 1, and t 0 = 0.1 into equations ( 83), ( 84), (85), and (86), we have obtained two non-radial nulls for c 6 = 0.1 in Figure- (7) and also for c 6 = 10 in Figure- (8).…”

“…The authors of [5] derived the Jacobi metric for different stationary metrics and developed the Jacobi-Maupertuis metric for time-dependent metrics by using the Eisenhart-Duval lift [6,7]. The authors in [8] have documented the remarkable characteristics of the time-like geodesic structure when dark energy is present in an emergent gravity framework, specifically for the Barriola-Vilenkin metric [9]. The K-essence emergent gravity metric is precisely correlated with the Barriola-Vilenkin (BV) metric for the Schwarzschild background, specifically for a certain form of K-essence scalar field [10].…”

“…The K-essence emergent gravity metric is precisely correlated with the Barriola-Vilenkin (BV) metric for the Schwarzschild background, specifically for a certain form of K-essence scalar field [10]. The researchers have analyzed the various paths that time-like geodesics can take in the presence of dark energy in the Barriola-Vilenkin spacetime [8], which is equivalent to the Schwarzschild spacetime in terms of its fundamental structure. However, the permissible ranges for the maximum and minimum distances from the central object are significantly distinct.…”

“…This feature may mitigate the cosmic microwave background (CMB) disruptions on large angular scales [56][57][58]. In this specific situation, Manna et al [8,10,[36][37][38][62][63][64][65][66][67] have developed a fascinating emergent gravity metric referred to as Ḡµν . This metric possesses distinct attributes in contrast to the standard gravitational metric g µν and is derived from the notions of the Dirac-Born-Infeld (DBI) type action, as outlined in the works [70][71][72][73].…”

“…[59][60][61], have examined the empirical evidence supporting the concept of K-essence with a DBI-type non-canonical Lagrangian, along with other modified theories. Furthermore, it has been noted that the K-essence theory may be applied in a model that combines dark energy and dark matter [8,10,47,[62][63][64][65], as well as from a purely gravitational perspective [36-38, 66, 67]. This article is organized as follows: In section 2, we provided a concise explanation of the K-essence geometry and its connection to the conventional generalized Vaidya spacetime, which leads to the construction of a new generalized K-essence Vaidya spacetime.…”