In the realm of theoretical physics and astrophysics, researchers Alex Stornelli and Anish Agashe from the University of Toronto have been delving into the intricate world of charged fluid spheres and their properties. Their recent work, published in the journal Physical Review D, explores the physical acceptability and trapped orbits of static charged polytropic spheres with a cosmological constant.
The researchers considered fluid spheres with a polytropic equation of state, where pressure is proportional to density raised to a power, and a power law charge distribution. They focused on the generalized Tolman-Oppenheimer-Volkoff equation, which describes the equilibrium of a spherically symmetric body in general relativity. By converting this equation into a differential equation for the mass profile, they were able to analyze the physical and geometric properties of these charged fluid spheres for different values of the charge distribution exponent and the polytropic index.
Stornelli and Agashe imposed constraints such as subluminal sound speeds and energy conditions to ensure that their models were physically acceptable. Within these constraints, they studied the internal trapping of circular geodesics, which are the paths that particles follow in a gravitational field. They found trapping regions in the parameter space defined by the charge distribution exponent and the polytropic index.
The researchers went beyond the traditional study of null geodesics, which are the paths followed by particles traveling at the speed of light, to consider orbits of charged and/or massive particles. They discovered that for neutral null particles, the trapping depends solely on the properties of the space-time. However, for the other three cases—charged null particles, massive neutral particles, and charged massive particles—the particle’s own charge and/or energy also play a significant role in their trapping. Overall, they found that trapping of all types of particles is allowed for a broad range of the charge distribution exponent and the polytropic index.
While this research is primarily theoretical, it has potential implications for understanding the behavior of compact objects like neutron stars and black holes, which can be modeled as fluid spheres. The study of trapped orbits is particularly relevant for understanding the accretion disks around these objects, which are crucial for energy generation and radiation. Additionally, the consideration of a cosmological constant in the models can provide insights into the effects of dark energy on these astrophysical phenomena. As such, this research contributes to our fundamental understanding of the universe and may have practical applications in the energy sector, particularly in the study of compact objects and their environments.
Source: Physical Review D, Volume 105, Issue 6, id.064010 (2022)
This article is based on research available at arXiv.