General Relativistic theory of viscous accretion disks around Black Holes
Final Report Abstract
The prediction of black holes is one of the outstanding achievements of General Relativity. Accretion disks (AD) around black holes provide a way for exploring them via the gravitational interaction. In addition, accretion disks ’feed’ the black holes as the disk matter is attracted towards the black holes due to gravity and to the release of enormous amounts of gravitational potential as well as rotational energy in the form of heat and radiation. Importantly, the viscosity, in particular the shear viscosity is widely believed to play a vital role in the the angular momentum transport of the infalling matter. Typically a viscous AD is modelled by a non-ideal relativistic fluid. But conservation laws of the relativistic theory of non-ideal fluids are acausal and unstable under linear perturbations. Therefore we first developed the causal theory of non-ideal fluids by employing the gradient expansion scheme in the Eckart frame, a natural choice of frame for studying ADs. As a result, all dissipative flux quantities involving the shear viscosity are described by second-order gradients of hydrodynamic variables. Additionally, curvature terms are present which provides a novel but expected feature of studying viscous ADs: the equation of motion of rigid extended bodies couples to the curvature, and the viscosity of a fluid describes a body in a state “between” a solid body and dust. In order to understand the consequences of shear viscosity on ADs, we considered the simplest model, namely the relativistic torus modelled by a viscous fluid around the Schwarzschild black hole. We have investigated the impacts of both the shear viscosity tensor and black hole curvature on the shape of a torus from the stationary solutions by numerically solving the causal conservation laws. It is found that the morphology of the torus gets noticeably modified under the influence of shear viscosity and curvature. We have then studied stationary solutions of magnetized, viscous torus around a Schwarzschild black hole where we assumed that the torus is endowed with a toroidal magnetic field and obey a constant angular momentum law. Again, we have determined the stationary solutions in the framework of a causality-preserving, second-order gradient expansion scheme in the Eckart frame description by numerically solving the general relativistic momentum conservation equation. Our results have revealed that the effects of the shear viscosity and curvature are particularly noticeable only close to the cusp of the disks. The surfaces of constant pressure are affected by viscosity and spacetime curvature. In addition, the location of the self-crossing iscocontour, i.e. the cusp, is particularly modified, but differently, by the shear viscosity for mildly and highly magnetised cases.
Publications
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“A toy model of viscous relativistic geometrically thick disk in Schwarzschild geometry”
Sayantani Lahiri & Claus Lämmerzahl
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Second order causal hydrodynamics in Eckart frame: using gradient expansion scheme. Classical and Quantum Gravity, 37(7), 075010.
Lahiri, Sayantani
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Stationary models of magnetized viscous tori around a Schwarzschild black hole. Physical Review D, 103(4).
Lahiri, Sayantani; Gimeno-Soler, Sergio; Font, José A. & Mejías, Alejandro Mus
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Stationary Models of Relativistic Viscous Torus. Lecture Notes in Physics, 31-65. Springer Nature Switzerland.
Lahiri, Sayantani
