John C. Miller

Astrophysical evidence for the existence of black holes

Following a short account of the history of the idea of black holes, we present a review of the current status of the search for observational evidence of their existence aimed at an audience of relativists rather than astronomers or astrophysicists. We focus on two different regimes: that of stellar-mass black holes and that of black holes with the masses of galactic nuclei.

Kinetic axisymmetric gravitational equilibria in collisionless accretion disk plasmas

A theoretical treatment is presented of kinetic equilibria in accretion disks (AD) around compact objects, for cases where the plasma can be considered as collisionless. The plasma is assumed to be axisymmetric and to be acted on by gravitational and electromagnetic fields; in this paper, the particular case is considered where the magnetic field admits a family of toroidal magnetic surfaces, which are locally mutually nested and closed. It is pointed out that there exist asymptotic kinetic equilibria represented by generalized bi-Maxwellian distribution functions and characterized by primarily toroidal differential rotation and temperature anisotropy. It is conjectured that kinetic equilibria of this type can exist which are able to sustain both toroidal and poloidal electric current densities, the latter being produced via finite Larmor-radius effects associated with the temperature anisotropy. This leads to the possibility of existence of a new kinetic effect—referred to here as a “kinetic dynamo effec...

Kinetic description of quasi-stationary axisymmetric collisionless accretion disk plasmas with arbitrary magnetic field configurations

A kinetic treatment is developed for collisionless magnetized plasmas occurring in high-temperature, low-density astrophysical accretion disks, such as are thought to be present in some radiatively inefficient accretion flows onto black holes. Quasi-stationary configurations are investigated, within the framework of a Vlasov-Maxwell description. The plasma is taken to be axisymmetric and subject to the action of slowly time-varying gravitational and electromagnetic fields. The magnetic field is assumed to be characterized by a family of locally nested but open magnetic surfaces. The slow collisionless dynamics of these plasmas is investigated, yielding a reduced gyrokinetic Vlasov equation for the kinetic distribution function. For doing this, an asymptotic quasi-stationary solution is first determined, represented by a generalized bi-Maxwellian distribution expressed in terms of the relevant adiabatic invariants. The existence of the solution is shown to depend on having suitable kinetic constraints and ...

Curving Newtonian Space

We show that the advance of the perihelion of Mercury (and other planets), as well as the deflection of light by the Sun, can be accurately calculated in Newtonian gravity, if one takes into account the fact of the curvature of space.

Generalized Grad‐Shafranov Equation for Gravitational Hall‐MHD Equilibria

The consistent theoretical description of gravitational Hall‐MHD (G‐Hall‐MHD) equilibria is of fundamental importance for understanding the phenomenology of accretion disks (AD) around compact objects (black holes, neutron stars, etc.). The very existence of these equilibria is actually suggested by observations, which show evidence of quiescent, and essentially non‐relativistic, AD plasmas close to compact stars, thus indicating that accretion disks may be characterized by slowly varying EM and fluid fields. These (EM) fields, in particular the electric field, may locally be extremely intense, so that AD plasmas are likely to be locally non‐neutral and therefore characterized by the presence of Hall currents. This suggests therefore that such equilibria should be described in the framework of the Hall‐MHD theory. In addition, for the description of equilibria occurring close to compact stars, the effect of space‐time curvature is expected to become significant. Extending previous approaches, holding for ...

Axi-symmetric Gravitational MHD Equilibria in the Presence of Plasma Rotation

In this paper, extending the investigation developed in an earlier paper (Cremaschini et al., 2008), we pose the problem of the kinetic description of gravitational Hall‐MHD equilibria which may arise in accretion disks (AD) plasmas close to compact objects. When intense EM and gravitational fields, generated by the central object, are present, a convenient approach can be achieved in the context of the Vlasov‐Maxwell description. In this paper the investigation is focused primarily on the following two aspects:1) the formulation of the kinetic treatment of G‐Hall‐MHD equilibria. Based on the identification of the relevant first integrals of motion, we show that an explicit representation can be given for the equilibrium kinetic distribution function. For each species this is represented as a superposition of suitable generalized Maxwellian distributions;2) the determination of the constraints to be placed on the fluid fields for the existence of the kinetic equilibria. In particular, this permits a uniqu...

Kinetic closure conditions for quasi-stationary collisionless axisymmetric magnetoplasmas

A characteristic feature of fluid theories concerns the difficulty of uniquely defining consistent closure conditions for the fluid equations. In fact it is well known that fluid theories cannot generally provide a closed system of equations for the fluid fields. This feature is typical of collisionless plasmas where, in contrast to collisional plasmas, asymptotic closure conditions do not follow as a consequence of an H-theorem This issue is of particular relevance in astrophysics where fluid approaches are usually adopted. On the other hand, it is well known that the determination of the closure conditions is in principle achievable in the context of kinetic theory. In the case of multi-species thermal magnetoplasmas this requires the determination of the species tensor pressure and of the corresponding heat fluxes. In this paper we investigate this problem in the framework of the Vlasov-Maxwell description for collisionless axisymmetric magnetoplasmas arising in astrophysics, with particular reference to accretion discs around compact objects (like black holes and neutron stars). The dynamics of collisionless plasmas in these environments is determined by the simultaneous presence of gravitational and magnetic fields, where the latter may be both externally produced and self-generated by the plasma currents. Our starting point here is the construction of a solution for the stationary distribution function describing slowly-varying gyrokinetic equilibria. The treatment is applicable to non-relativistic axisymmetric systems characterized by temperature anisotropy and differential rotation flows. It is shown that the kinetic formalism allows one to solve the closure problem and to consistently compute the relevant fluid fields with the inclusion of finite Larmor-radius effects. The main features of the theory and relevant applications are discussed.

Theory of quasi-stationary kinetic dynamos in magnetized accretion discs

Magnetic fields are a distinctive feature of accretion disc plasmas around compact objects (i.e., black holes and neutron stars) and they play a decisive role in their dynamical evolution. A fundamental theoretical question related with this concerns investigation of the so- called gravitational MHD dynamo effect, responsible for the self-generation of magnetic fields in these systems. Experimental observations and theoretical models, based on fluid MHD descrip- tions of various types support the conjecture that accretion discs should be characterized by coherent and slowly time-varying magnetic fields with both poloidal and toroidal components. However, the precise origin of these magnetic structures and their interaction with the disc plasmas is currently unclear. The aim of this paper is to address this problem in the context of kinetic theory. The starting point is the investigation of a general class of Vlasov-Maxwell kinetic equilibria for axi-symmetric collisionless magnetized plasmas characterized by tempera- ture anisotropy and mainly toroidal flow velocity. Retaining finite Larmor-radius effects in the calculation of the fluid fields, we show how these configurations are capable of sustaining both toroidal and poloidal current densities. As a result, we suggest the possible existence of a ki- netic dynamo effect, which can generate a stationary toroidal magnetic field in the disc even without any net radial accretion flow. The results presented may have important implications for equilibrium solutions and stability analysis of accretion disc dynamics. In this paper basic issues concerned with the origin and the structure of magnetic fields in accretion disc (AD) plasmas are discussed, with particular reference to the dynamo phenomenon which leads to the self-generation of the magnetic field appearing in these systems. More precisely, we address the problem of the generation of both the poloidal and toroidal components of the AD magnetic field as a consequence of plasma currents produced purely by collisionless and quasi-stationary kinetic mechanisms. Experimental observations and theoretical models based on fluid MHD descriptions suggest that accretion discs should be characterized by coherent and slowly time-varying magnetic fields with both poloidal and toroidal components (see for example Frank et al., 2002 and Szuszkiewicz & Miller, 2001). An interesting development within this context has been the work by Coppi (2005) and Coppi & Rousseau (2006), who showed that stationary magnetic configurations in AD plasmas, for both low and high magnetic en- ergy densities, can exhibit complex magnetic structures characterized locally by plasma rings with closed nested magnetic surfaces. However, even the most sophisticated fluid models are still not able to give a satisfactory explanation for all of the complexity of the phenomena arising in these systems. In particular, the precise origin of these mag- netic structures and their interaction with the disc plasmas remains unclear. This is especially true for what concerns the toroidal magnetic field. Usually it is thought that such fields are the result of non-stationary processes associated with some ongoing in- stabilities in the plasma (possibly the same ones responsible for the accretion), but the

The Renaissance of General Relativity and Cosmology: Author Addresses

Introduction 1. Exact and inexact solutions of the Einstein field equations G. F. R. Ellis 2. Inertial forces in general relativity M. A. Abramovicz 3. Relativistic radiation hydrodynamics A. M. Anile and V. Romano 4. Relativistic gravitational collapse J. Miller 5. The cosmic censorship hypothesis C. J. S. Clarke 6. The Kerr metric: a gateway to the roots of gravity? F. de Felice 7. Galactic astronomy since 1950 J. J. Binney 8. Galaxy distribution functions W. C. Saslow 9. Nonlinear galaxy clustering B. J. T. Jones 10. Quasars: progress and prospects M. J. Rees 11. Decaying neutrinos in astronomy and cosmology D. W. Sciama 12. Cosmological principles J. D. Barrow 13. Anisotropic and inhomogeneous cosmologies M. A. H. MacCallum 14. Machs principle and isotropic singularities P. K. Tod 15. Implications of superconductivity in cosmic string theory B. Carter 16. The formation and evaporation of primordial black holes B. J. Carr 17. Evaporation of two dimensional black holes S. W. Hawking 18. Topology and topology change in general relativity G. W. Gibbons 19. Decoherence of the cluttered quantum vacuum D. J. Raine 20. Quantum nonlocality and complex reality R. Penrose 21. The different levels of connections between science and objective reality N. Dallaporta.

The Renaissance of General Relativity and Cosmology: Frontmatter

Introduction 1. Exact and inexact solutions of the Einstein field equations G. F. R. Ellis 2. Inertial forces in general relativity M. A. Abramovicz 3. Relativistic radiation hydrodynamics A. M. Anile and V. Romano 4. Relativistic gravitational collapse J. Miller 5. The cosmic censorship hypothesis C. J. S. Clarke 6. The Kerr metric: a gateway to the roots of gravity? F. de Felice 7. Galactic astronomy since 1950 J. J. Binney 8. Galaxy distribution functions W. C. Saslow 9. Nonlinear galaxy clustering B. J. T. Jones 10. Quasars: progress and prospects M. J. Rees 11. Decaying neutrinos in astronomy and cosmology D. W. Sciama 12. Cosmological principles J. D. Barrow 13. Anisotropic and inhomogeneous cosmologies M. A. H. MacCallum 14. Machs principle and isotropic singularities P. K. Tod 15. Implications of superconductivity in cosmic string theory B. Carter 16. The formation and evaporation of primordial black holes B. J. Carr 17. Evaporation of two dimensional black holes S. W. Hawking 18. Topology and topology change in general relativity G. W. Gibbons 19. Decoherence of the cluttered quantum vacuum D. J. Raine 20. Quantum nonlocality and complex reality R. Penrose 21. The different levels of connections between science and objective reality N. Dallaporta.