Test particles and fields in axially symmetric relevant settings

• Ano de defesa: 2024
• Autor(a) principal: Capobianco, Rogério Augusto
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Accretion disks; Black holes; Buracos negros; Discos de acreção; Geodésicas; Geodesics; Gravidade; Gravity; Scalarização espontânea; Spontaneous scalarization
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/76/76134/tde-09122024-092924/

The effects of a gravitational field can be studied using test particles and fields. An exemplary analysis includes a complete description of the equations of motion. This thesis assembles the research results summarized in four papers and focuses on describing the dynamics of test particles and test fields in stationary and axially symmetric space-time. The solutions considered here are either found analytically or numerically for the vacuum and electro-vacuum Einsteins field equations. Firstly, we study a scalar-tensor model in which the scalar field is non-minimally coupled with (a) the electromagnetic field and (b) the curvature of the space-time. We study the spontaneous scalarization of an extended, self-gravitating system that is static, cylindrically symmetric and possesses electromagnetic fields. We demonstrate that a massive, real-valued scalar field condensates on this Melvin magnetic universe for both considered scenarios. We found that, for small values of the scalar field, a node solution exists; it can be expanded in terms of the Laguerre polynomials around the axes and Bessel functions asymptotically. We performed a full numerical integration of equations of motion and verified that solutions do possess nodes. In addition, solutions exist for a finite range of coupling constants. interestingly, we verified that for case (a), the interval of existence of solutions is mutually exclusive, and hence, different node-solutions cannot be interpreted as excited states of a fundamental solution; this does not happen for the (b) case; suggesting that these two couplings are different in nature. Secondly, we consider the geodesic motion in the swirling universe. We demonstrate that the geodesic equations can be decoupled using the Hamilton-Jacobi formalism, where a fourth constant of motion can be found. The set of uncoupled differential equations can be analytically integrated in terms of elementary and elliptic functions. Additionally, a full characterization of the possible physical orbits is provided. A typical orbit is then bounded in the radial direction and escapes to infinity in the z– direction; the only exception is the case of a particle with no angular momentum. Furthermore, we also consider a spacetime describing a Schwarzschild black hole immersed in a swirling universe; in this case, the geodesic equation cannot be decoupled, and hence, the system must be numerically integrated; preliminary results suggest the emergence of chaotic motion for either massive or massless particles. We proceed by considering the motion of charged particles in the electromagnetic swirling universe (EMS). The EMS space-time is a novel solution recently obtained; as in the above case, it is stationary and axially symmetric. It can be understood as the immersion of a Melvin space-time into a swirling universe, or vice-versa. Since this space-time possesses electromagnetic fields, we consider the motion of charged particles, both electric and magnetic charges, for a complete description. Remarkably, the equations of motion can also be decoupled within the Hamilton-Jacobi formalism; the mathematical structure of the decoupled equations of motion resembles much the geodesic motion in the swirling universe. Therefore, the equations can be analytically integrated in terms of elementary and elliptic functions. A typical orbit is qualitatively similar to an orbit in the swirling universe, being bounded in the radial direction and escaping to infinity in the z– direction. However, there is a special case in which the electromagnetic interaction can counterbalance the dragging effect, and therefore, orbits for particles with non-vanishing angular momentum can be planar. Finally, we consider the case of the geometrically thick disks around a Kerr black hole immersed in a swirling universe. Due to the spin-spin interaction between the black hole and the swirling universe background, a conical singularity appears on the symmetry axis, highly affecting the geometrical properties as well as the disk solutions, which are driven away from the equatorial plane even for small variations of the swirling parameter. In order to provide an exemplary description, we consider the Kerr parameter to be within a range that includes a slow, medium, and rapidly rotating black hole; the same is done for the swirling parameter. Additionally, we consider both the prograde and the retrograde motion, which are taken are respect to the black hole rotation. We find that disk solutions exist for either case. Moreover, this spin-spin interaction acts as a stabilizing effect for prograde motion and a destabilizing effect for retrograde motion; this increases with the black hole rotation. In addition, the presence of the background rotation makes the emergence of static orbits appear; however, these are all unstable, and therefore, disk solutions with static surfaces do not exist. The breaking of symmetry regarding the equatorial plane causes vertical distribution of the circular orbits and thick torus solutions. The possible disk solutions are classified in terms of the cusps and the value of the effective potential on the cusps. All possible disk solutions can be classified into two different groups.