Black Strings and String Clouds Embedded in Anisotropic Quintessence: Solutions for Scalar Particles and Implications (2502.04894v1)

Abstract: We analyze the spacetime metric associated with a black string surrounded by a cloud of strings and an anisotropic fluid of quintessence in cylindrically symmetric AdS spacetime. We solve Einstein's equation to obtain the explicit form of the metric, investigate typical values for its parameters, and determine their role in the event horizon formation. Within our findings, we show that the intensity of the cloud of strings regulates the size of the event horizon and, when the cloud is absent, the horizon increases drastically for larger values of the quintessence's state parameter $\alpha_{Q}$. Additionally, the metric shows that, unless $\alpha_{Q}$ is close to its lower bound, the contribution from the quintessence fluid is only significant at large distances from the black string. Finally, to explore the quantum implications of this dark energy candidate, we use the confluent Heun function to solve the Klein-Gordon equation for a spin-0 particle near the event horizon. Our results indicate that the presence of quintessence alters the particle's radial wave function. This modification, in principle, could give rise to an observable that we termed as \enquote{dark phase}.