arXiv subjects

D. Lynden-Bell

Publications and source records attributed to D. Lynden-Bell.

36 records · Page 2Linked to original sources

arXiv2004

Electromagnetic Magic: The Relativistically Rotating Disk

A closed form analytic solution is found for the electromagnetic field of the charged uniformly rotating conducting disk for all values of the tip speed $v$ up to $c$. For $v=c$ it becomes the Magic field of the Kerr-Newman black hole with $G$ set to zero. The field energy, field angular momentum and gyromagnetic ratio are calculated and compared with those of the electron. A new mathematical expression that sums products of 3 Legendre functions each of a different argument, is demonstrated.

gr-qc↗

arXiv2004

Relaxation to a Perpetually Pulsating Equilibrium

Paper in honour of Freeman Dyson on the occasion of his 80th birthday. Normal N-body systems relax to equilibrium distributions in which classical kinetic energy components are 1/2 kT, but, when inter-particle forces are an inverse cubic repulsion together with a linear (simple harmonic) attraction, the system pulsates for ever. In spite of this pulsation in scale, r(t), other degrees of freedom relax to an ever-changing Maxwellian distribution. With a new time, tau, defined so that r^2d/dt =d/d tau it is shown that the remaining degrees of freedom evolve with an unchanging reduced Hamiltonian. The distribution predicted by equilibrium statistical mechanics applied to the reduced Hamiltonian is an ever-pulsating Maxwellian in which the temperature pulsates like r^-2. Numerical simulation with 1000 particles demonstrate a rapid relaxation to this pulsating equilibrium.

cond-mat.stat-mech↗

arXiv2002

Exact Optics: A unification of optical telescope design

A perfect focus telescope is one in which all rays parallel to the axis meet at a point and give equal magnification there. It is shown that these two conditions define the shapes of both primary and secondary mirrors. Apart from scale, the solution depends upon two parameters, $s$, which gives the mirror separation in terms of the effective focal length, and $K$, which gives the relative position of the final focus in that unit. The two conditions ensure that the optical systems have neither spherical aberration nor coma, no matter how fast the $f$ ratio. All known coma--free systems emerge as approximate special cases. In his classical paper, K. Schwarzschild studied all two mirror systems whose profiles were conic sections. We make no such a priori shape conditions but demand a perfect focus and solve for the mirrors' shapes.

physics.optics↗

arXiv2001

Russell Lecture: Dark Star Formation and Cooling Instability

Optically thin cooling gas at most temperatures above 30K will make condensations by pressure pushing material into cool dense regions. This works without gravity. Cooling condensations will flatten and become planar/similarity solutions. Most star formation may start from cooling condensations - with gravity only important in the later stages. The idea that some of the dark matter could be pristine white dwarfs that condensed slowly on to planetary sized seeds without firing nuclear reactions is found lacking. However, recent observations indicate fifty times more halo white dwarfs than have been previously acknowledged; enough to make the halo fraction observed as MACHOS. A cosmological census shows that only 1% of the mass of the Universe is of known constitution.

astro-ph↗

arXiv2001

One Mass-Radius relation for Planets, White Dwarfs and Neutron Stars

We produce the simple formula for the radius R of a cold body of mass M, (4 pi rho/3)^{1/3} R = I.M^{1/3} / [1+ (M/Mp)^{2/3}], where I is one for white dwarfs with non-relativistic electrons, but depends on the ratio of the total mass to Mch, the Chandrasekhar mass. Mp is the mass of the planet of maximum radius and rho is the density of the material at low pressure. Mp and rho are derived in terms of fundamental constants and Mp/Mch is basically given by the three halves power of the fine structure constant. The aim of the discussion is to emphasise physical principles and to connect the masses derived to the fundamental constants, so mathematical niceties are sacrificed and replaced by interpolations between simple exact limits.

astro-ph↗

arXiv1999

Disc sources for Conformastationary metrics

Conformastationary metrics have been derived by Perjes and by Israel and Wilson as source-free solutions of the Einstein-Maxwell equations. By analogy with the conformastatic metrics which have charged dust sources it was assumed that conformastationary metrics would be the external metrics of charged dust in steady motion. However for axially symmetric conformastationary metrics we show that, as well as moving dust, hoop tensions are always necessary to balance the centrifugal forces induced by the motion. Exact examples of conformastationary metrics with disk sources are worked out in full. Generalisations to non-axially symmetric conformastationary metrics are indicated.

gr-qc↗

arXiv1999

Equiangular Spiral Modes of Power Law Disks

The stability of self-similar power-law disks to non-axially symmetrical disturbances of zero frequency (omega = 0) is discussed. It is established that marginally unstable modes either have (omega = 0) or consist of continua with modes of all frequencies becoming unstable together. A careful study of all modes close to omega = 0 yields a remarkable conclusion.

astro-ph↗

arXiv1999

Exact Quantum Solutions of Extraordinary N-body Problems

The wave functions of Boson and Fermion gases are known even when the particles have harmonic interactions. Here we generalise these results by solving exactly the N-body Schrodinger equation for potentials V that can be any function of the sum of the squares of the distances of the particles from one another in 3 dimensions. For the harmonic case that function is linear in r^2. Explicit N-body solutions are given when U(r) = -2M \hbar^{-2} V(r) = ζr^{-1} - ζ_2 r^{-2}. Here M is the sum of the masses and r^2 = 1/2 M^{-2} Sigma Sigma m_I m_J ({\bf x}_I - {\bf x}_J)^2. For general U(r) the solution is given in terms of the one or two body problem with potential U(r) in 3 dimensions. The degeneracies of the levels are derived for distinguishable particles, for Bosons of spin zero and for spin 1/2 Fermions. The latter involve significant combinatorial analysis which may have application to the shell model of atomic nuclei. For large N the Fermionic ground state gives the binding energy of a degenerate white dwarf star treated as a giant atom with an N-body wave function. The N-body forces involved in these extraordinary N-body problems are not the usual sums of two body interactions, but nor are forces between quarks or molecules. Bose-Einstein condensation of particles in 3 dimensions interacting via these strange potentials can be treated by this method.

cond-mat.stat-mech↗

arXiv1998

A spacetime dual to the NUT spacetime

By decomposing the Riemann curvature into electric and magnetic parts, a duality transformation, which involves interchange of active and passive electric parts, has recently been proposed. It was shown that the Schwarzschild solution is dual to the one that describes the Schwarzschild particle with cloud of string dust or a global monopole. Following the same procedure we obtain the solution dual to the NUT spacetime.

gr-qc↗

arXiv1998

On Accelerated Inertial Frames in Gravity and Electromagnetism

When a charged insulating spherical shell is uniformly accelerated, an oppositely directed electric field is produced inside. Outside the field is the Born field of a uniformly accelerated charge, modified by a dipole. Radiation is produced. When the acceleration is annulled by the nearly uniform gravity field of an external shell with a 1 + beta cos theta surface distribution of mass, the differently viewed Born field is static and joins a static field outside the external shell; no radiation is produced. We discuss gravitational analogues of these phenomena. When a massive spherical shell is accelerated, an untouched test mass inside experiences a uniform gravity field and accelerates parallelly to the surrounding shell. In the strong gravity regime we illustrate these effects using exact conformastatic solutions of the Einstein-Maxwell equations with charged dust. We consider a massive charged shell on which the forces due to nearly uniform electrical and gravitational fields balance. Both fields are reduced inside by the ratio of the g_00 inside the shell to that away from it. The acceleration of a free test particle, relative to a static observer, is reduced correspondingly. We give physical explanations of these effects.

gr-qc↗

arXiv1998

Negative Specific Heat in Astronomy, Physics and Chemistry

Starting from Antonov's discovery that there is no maximum to the entropy of a gravitating system of point particles at fixed energy in a spherical box if the density contrast between centre and edge exceeds 709, we review progress in the understanding of gravitational thermodynamics. We pinpoint the error in the proof that all systems have positive specific heat and say when it can occur. We discuss the development of the thermal runaway in both the gravothermal catastrophe and its inverse. The energy range over which microcanonical ensembles have negative heat capacity is replaced by a first order phase transition in the corresponding canonical ensembles. We conjecture that all first order phase transitions may be viewed as caused by negative heat capacities of units within them. We find such units in the theory of ionisation, chemical dissociation and in the Van der Waals gas so these concepts are applicable outside the realm of stars, star clusters and black holes.

cond-mat.stat-mech↗

arXiv1998

From Quasars to Extraordinary N-body Problems

We outline reasoning that led to the current theory of quasars and look at George Contopoulos's place in the long history of the N-body problem. Following Newton we find new exactly soluble N-body problems with multibody forces and give a strange eternally pulsating system that in its other degrees of freedom reaches statistical equilibrium.

astro-ph↗

arXiv1998

Exact General Solutions to Extraordinary N-body Problems

We solve the N-body problems in which the total potential energy is any function of the mass-weighted root-mean-square radius of the system of N point masses. The fundamental breathing mode of such systems vibrates non-linearly for ever. If the potential is supplemented by any function that scales as the inverse square of the radius there is still no damping of the fundamental breathing mode. For such systems a remarkable new statistical equilibrium is found for the other coordinates and momenta, which persists even as the radius changes continually.

cond-mat.stat-mech↗

arXiv1998

Instantaneous Inertial Frame but Retarded Electromagnetism in Rotating Relativistic Collapse

Slowly rotating collapsing spherical shells have flat spaces inside and the inertial frames there rotate at omega_s(t) relative to infinity. As first shown by Lindblom & Brill the inertial axes within the shell rotate rigidly without time delays from one point to another. Although the rotation rate of the inertial axes is changing the axes are inertial so, relative to them, there is neither an omega dot_s times r (Euler) fictitious force nor any other. However, Euler and other fictitious forces arise in the frame which is at rest with respect to infinity. An observer at the center who looks in one direction (phi = 0, theta = pi/2 say) fixed to infinity will see that the sky appears to rotate and can compare its apparent rotation with those of the local inertial frame and of the shell itself. By contrast in the electromagnetic analogue there is a time delay in the propagation of the magnetic field inside a rotating collapsing charged shell in flat space. We demonstrate this time delay by devising a null experiment in which the Larmor precession of a charged oscillator would be exactly cancelled by the rotation of the inertial frame but for the delay. In the ``combined'' problem of a collapsing charged shell we show that, due to the coupling of electromagnetic and gravitational perturbations, the instantaneous rotation of inertial frames inside the shell can be caused by pure electric currents in a non-rotating shell.

astro-ph↗

arXiv1996

Equilibria of flat and round galactic disks

A general method is presented for constructing distribution functions for flat systems whose surface density and Toomre's Q number profile is given. The purpose of these functions is to provide plausible galactic models and assess their critical stability with respect to global non axi-symmetric modes. The derivation may be carried out for an azimuthal velocity distribution (or a given specific energy distribution) which may either be observed or chosen to match a specified temperature profile. Distribution functions describing stable models with realistic velocity distributions for power law disks, the Isochrone and the Kuzmin disks are provided. Specially simple inversion formulae are also given for finding distribution functions for flat systems whose surface densities are known.

astro-ph↗

arXiv1996

New sources for Kerr and other metrics: rotating relativistic disks with pressure support

Complete sequences of new analytic solutions of Einstein's equations which describe thin super massive disks are constructed. These solutions are derived geometrically. The identification of points across two symmetrical cuts through a vacuum solution of Einstein's equations defines the gradient discontinuity from which the properties of the disk can be deduced. The subset of possible cuts which lead to physical solutions is presented. At large distances, all these disks become Newtonian, but in their central regions they exhibit relativistic features such as velocities close that of light, and large redshifts. Sections with zero extrinsic curvature yield cold disks. Curved sections may induce disks which are stable against radial instability. The general counter rotating flat disk with planar pressure tensor is found. Owing to gravomagnetic forces, there is no systematic method of constructing vacuum stationary fields for which the non-diagonal component of the metric is a free parameter. However, all static vacuum solutions may be extended to fully stationary fields via simple algebraic transformations. Such disks can generate a great variety of different metrics including Kerr's metric with any ratio of a to m. A simple inversion formula is given which yields all distribution functions compatible with the characteristics of the flow, providing formally a complete description of the stellar dynamics of flattened relativistic disks. It is illustrated for the Kerr disk.

astro-ph↗

arXiv1995

Classical Mechanics without Absolute Space

A relative mechanics with no absolute space is shown to be equivalent to Newtonian mechanics applied in a universe of zero net angular momentum. Closed spaces in General Relativity have no angular momentum and shrivel to one point as the mass-energy contained tends to zero, so obeying Mach's principle on the origin of inertia.

astro-ph↗

arXiv1995

Visual Search for Galaxies near the Northern Crossing of the Supergalactic plane by the Milky Way

We have visually examined twelve Palomar red Plates for galaxies at low Galactic latitude b, where the Supergalactic Plane (SGP) is crossed by the Galactic Plane (GP), at Galactic longitude l ~135 degrees. The catalogue consists of 2575 galaxy candidates, of which 462 have major axis diameters d >= 0.8 arc min (uncorrected for extinction). Galaxy candidates can be identified down to |b| ~ 0 degrees. One of our galaxy candidates (J24 = Dwingeloo 1) has recently been discovered independently in 21cm by Kraan-Korteweg et al. (1994) as a nearby galaxy. Comparisons with the structures seen in the IRAS and UGC catalogues are made. We compare the success rate of identifying galaxies using the IRAS Point Source Catalogue under different colour selection criteria. The criteria that require both the 60 micron and 100 micron fluxes to be of high quality, have the highest probability of selecting a galaxy (with d >= 0.6 arc min), but at the expense of selecting a smaller number of galaxies in total.

astro-ph↗