On some aspects of spinning objects in curved spacetime

Mukherjee, Sajal (2019) On some aspects of spinning objects in curved spacetime. PhD thesis, Indian Institute of Science Education and Research Kolkata.

Text (PhD thesis of Sajal Mukherjee (13IP029)) 13IP029.pdf - Submitted Version Restricted to Repository staff only Download (4MB)

Abstract

With the recent developments in various observational avenues relating black holes and other compact objects, the pursuit of understanding the two-body dynamics in relativistic scenarios is enriched with modern signs of progress. Given that the relativistic two-body problem cannot be solved in a closed form within the framework of Einstein field equations, there exist approximate techniques such as post-Newtonian, effective one body, the addition of self-force, etc., to overcome the hindrances. In the case of a two-body system with comparable masses, the post-Newtonian approximation is useful and engaged in numerous works. However, in the case of binaries composed of incomparable masses, either the effective one body or the self-force method can reliably solve the problem. While the effective one body treats the two body system as a single object moves in an effective potential, the self-force mechanism kind of relaxes the test particle approximation and consider the effects of the lighter companion on the background geometry. In either of these approximate techniques, the internal structure of the lighter object plays a crucial role in determining its governing dynamics. For an extreme mass ratio binary, most of the times the lighter companion is presumed to follow a geodesic motion in the field of the heavier object. However, there exists a regime in which the masses are neither comparable nor the lighter companion should be treated as a point particle. This is when the internal structure of the object contributes to the equations of motion. In the present thesis, we investigate this particular subject while emphasizing some of the intriguing features associated with them. The mass of an object is considered as the monopole term, and any additional moment would essentially introduce a further correction to the test particle model. In the present thesis, we are mostly concerned with the first order contribution or the dipole moment. Conventionally, a particle with both monopole and dipole moment is known as pole-dipole or spinning particle while the quadrupole contribution introduces pole-dipole-quadrupole particle. We start the thesis with a preliminary discussion on the foundation of extended objects in chapter one to chapter three. Moreover, we continue to explore various aspects attributed to their orbital motion. In the fourth chapter, we study the off-equatorial circular orbits for a spinning particle in the Kerr spacetime. We demonstrate that the addition of the dipole moment would introduce the circular orbits on the θ = constant ≠π/2 surfaces, which is unlikely to appear in the case of geodesic trajectories. In addition, we explore the possibilities of stable circular orbits for different spin supplementary conditions and state that for a given spin vector of the form Sμ = (0; S¹; S²; 0), there exists a unique circular orbit at r = rc with inclination θ = θc, defined by the simultaneous minima of energy, angular momentum, and Carter constant. This corresponds to the innermost stable circular orbit (ISCO) which is located on an off-equatorial plane. In the fifth chapter, we provide a special case in which the coupling between the higher order moments of an extended object and the background geometry becomes zero. We then extend our discussions on several aspects of vanishing acceleration while endowing the massive central object with various multipole moments. The interaction between the extended test object, following either Mathisson-Papapetrou or Mathisson-Papapetrou-Dixon equations, and the central object leads to different possibilities of acceleration free trajectories. Chapter six is devoted to studying the collision of spinning particles and energy extraction from a rotating black hole. The modifications as introduced due to the spin of the test particle are emphasized while investigating various mechanisms of collisional-Penrose process. Following this, in the seventh chapter we discuss the periastron precession due to a spinning particle while highlighting their distinctive characteristics from a geodesic trajectory. Various aspects are explored while presuming the background geometry consists of a naked singularity. In addition, the useful imprints of naked singularity which possibly disentangle it from a black hole geometry, are also mentioned in the context of precession frequency. Finally, chapter eight provides a brief concluding remark based on the discussions presented in the thesis.

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