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Fluid discs and tori around black holes are discussed within different approaches and with the emphasis on the role of disc gravity. First reviewed are the prospects of investigating the gravitational field of a black hole--disc system by…
A new theory of eccentric accretion discs is presented. Starting from the basic fluid-dynamical equations in three dimensions, I derive the fundamental set of one-dimensional equations that describe how the mass, angular momentum and…
Accretion disks are observed in young stars, cataclysmic variables, binary X-ray sources et al. Accretion disk theory was first developed as a theory with the local heat balance, where the whole energy produced by a viscous heating was…
These lecture notes and example problems are based on a course given at the University of Cambridge in Part III of the Mathematical Tripos. Fluid dynamics is involved in a very wide range of astrophysical phenomena, such as the formation…
Linear theory is used to determine the stability of the self-gravitating, rapidly (and nonuniformly) rotating, two-dimensional, and collisional particulate disk against small-amplitude gravity perturbations. A gas-kinetic theory approach is…
We review our current knowledge of thermal and viscous instabilities in accretion discs around compact objects. We begin with classical disc models based on analytic viscosity prescriptions, discussing physical uncertainties and exploring…
Fluid flows such as gases or liquids exhibit space-time fluctuations on all scales extending down to molecular scales. Such broadband continuum fluctuations characterise all dynamical systems in nature and are identified as selfsimilar…
In his 1856 Adams Prize essay, James Clark Maxwell demonstrated that Saturn's rings cannot be comprised of a uniform rigid body. This is a consequence of the two-body gravitational interaction between a ring and planet resulting in…
Much of astrophysics consists of the study of ionised gas under the influence of gravitational and magnetic fields. Thus, it is not possible to understand the astrophysical universe without a detailed knowledge of the dynamics of magnetised…
Proto-planetary discs, the birth environment of planets, are an example of a structure commonly found in astrophysics, accretion discs. Identifying the mechanism responsible for accretion is a long-standing problem, dating back several…
The magnetic field due to an axially symmetric, hot and highly conducting plasma, taken as an ideal magnetohydrodynamic fluid, surrounding a slow rotating compact gravitational object is studied within the context of Einstein-Maxwell field…
In this paper we present a new approach to tidal theory. Assuming a Maxwell viscoelastic rheology, we compute the instantaneous deformation of celestial bodies using a differential equation for the gravity field coefficients. This method…
We perform numerical simulations of magneto-rotational instability in a local patch of accretion disk in which radiation pressure exceeds gas pressure. Such conditions may occur in the central regions of disks surrounding compact objects in…
This chapter reviews theoretical work on the stellar dynamics of galaxy disks. All the known collective global instabilities are identified, and their mechanisms described in terms of local wave mechanics. A detailed discussion of warps and…
We investigate charge accretion in vicinity of a slowly rotating compact star with a non-stationary electromagnetic field. Exact solutions to the general relativistic Maxwell equations are obtained for a star formed of a highly degenerate…
The problem of Maxwell's demon in granular gas is revisited in the case of a mixture of two particle species. The phase space is found to be 2d. Existence of cyclic orbits, with periodic segregation, is demonstrated by investigating the…
We discuss the solution of accretion disk when the black hole is chosen to be rotating. We study, how the fluid properties get affected for different rotation parameters of the black hole. We know that no cosmic object is static in…
The past 5 years have dramatically changed our view of the disks of gas and dust around young stars. Observations with the Atacama Large Millimeter/submillimeter Array (ALMA) and extreme adaptive optics systems have revealed that disks are…
[Abridged] The turbulent stresses that lead to angular momentum transport in accretion discs have often been treated as resulting from an isotropic effective viscosity, related to the pressure through the alpha parametrization of Shakura &…
Accretion discs that are tilted with respect to their compact hosts can warp out-of-plane through general relativistic frame-dragging. Warp influences disc dynamics in ways that have been studied extensively, especially as regards…