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Donald Lynden-Bell

Publications and source records attributed to Donald Lynden-Bell.

30 records · Page 2Linked to original sources
arXiv2003

Do Rotations Beyond the Cosmological Horizon Affect the Local Inertial Frame?

If perturbations beyond the horizon have the velocities prescribed everywhere then the dragging of inertial frames near the origin is suppressed by an exponential factor. However if perturbations are prescribed in terms of their angular momenta there is no such suppression. We resolve this paradox and in doing so give new explicit results on the dragging of inertial frames in closed, flat and open universe with and without a cosmological constant.

gr-qc↗
arXiv2003

Toroidal Perturbations of Friedmann-Robertson-Walker Universes

Explicit expressions are found for the axisymmetric metric perturbations of the closed, flat and open FRW universes caused by toroidal motions of the cosmic fluid. The perturbations are decomposed in vector spherical harmonics on 2-spheres, but the radial dependence is left general. Solutions for general odd-parity $l$-pole perturbations are given for either angular velocities or angular momenta prescribed. In particular, in case of closed universes the solutions require a special treatment of the Legendre equation.

gr-qc↗
arXiv2002

A Magic Electromagnetic Field

An electromagnetic field of simple algebraic structure is simply derived. It turns out to be the G=0 limit of the charged rotating Kerr-Newman metrics. These all have gyromagnetic ratio 2, the same as the Dirac electron. The charge and current distributions giving this high gyromagnetic ratio have charges of both signs rotating at close to the velocity of light. It is conjectured that something similar may occur in the quantum electrodynamic charge distribution surrounding the point electron.

astro-ph↗
arXiv2000

Wandering Among Newton Wonders

In the electromagnetic fields t^2 B = b(r/t), E = r x B/t trajectories of non-relativistic charged particles conserve (r-vt)^2. The transformation r'=r/t t'=1/t maps such trajectories into orbits in the constant magnetic field all of which conserve kinetic energy. The transformation may also be used to transform any fields obeying Curl E = B/dt, div B = 0 into others and relates the particle trajectories in them.

astro-ph↗
arXiv2000

Magnetic Activity in Stars, Discs and Quasars

Although magnetic fields in interstellar matter were postulated almost fifty years ago, magnetohydrodynamic theory was then much hampered by our inability to see what the magnetic field configurations were like and, after a decade of innovative development, cynics, not without some justification, began to claim that anything can happen when magnetism and an imaginative theorist get together. Thus cosmic lightning in particular received a bad press. More recently great advances in observational techniques that we shall hear of from Title, Beck, Moran and Mirabel have enabled us to see not only the sun's magnetic field with unprecedented clarity but the fields in galaxies, quasars and microquasars are now measured and not merely figments of fertile imaginations.

astro-ph↗
arXiv2000

The Newton Wonder in Mechanics

Application of Newton's ideas from "Principia" gives many new results in mechanics. Here we explore the question ``What form of extra force will maintain the magnitude of a vector constant of the motion while changing its direction?''

astro-ph↗
arXiv2000

Rotation, Statistical Dynamics and Kinematics of Globular Clusters

Evolution with mass segregation and the evolution of the rotation of cores are both discussed for self-similar core collapse. Evolution with angular velocity proportional to the square root of the density is predicted. On the Dynamical Main Sequence of globular clusters the energy emission from binaries balances the energy expended in expanding the halo. Newton's exactly solved N-body problem is then given, along with recent generalisations, all of which have no violent relaxation, but a new type of statistical equilibrium is discussed. Finally, we set the creation of streams in the Galaxy's halo in the historical context of their discovery.

astro-ph↗
arXiv1998

Gravomagnetic Lensing by NUT Space

Using the fact that the null geodesics in NUT space lie on spatial cones, we consider the gravomagnetic lens effect on light rays passing a NUT deflector. We show that this effect changes the observed shape, size and orientation of a source. Compared to the Schwarzschild lens, there is an extra shear (a differential twist around the lens axis) due to the gravomagnetic field which shears the shape of the source. Gravomagnetic monopoles can thus be recognized by the spirality that they produce in the lensing pattern. All the results obtained in this case (magnification factor, orientation of images, multiplicity of images, etc.) depend on $Q$, the strength of the gravomagnetic monopole represented by NUT metric. One recovers the results of the usual Schwarzschild lens effect by putting this factor equal to zero.

gr-qc↗
arXiv1996

Classical Monopoles: Newton, NUT-space, gravomagnetic lensing and atomic spectra

Stimulated by a scholium in Newton's Principia we find some beautiful results in classical mechanics which can be interpreted in terms of the orbits in the field of a mass endowed with a gravomagnetic monopole. All the orbits lie on cones! When the cones are slit open and flattened the orbits are exactly the ellipses and hyperbolae that one would have obtained without the gravomagnetic monopole. The beauty and simplicity of these results has led us to explore the similar problems in Atomic Physics when the nuclei have an added Dirac magnetic monopole. These problems have been explored by others and we sketch the derivations and give details of the predicted spectrum of monopolar hydrogen. Finally we return to gravomagnetic monopoles in general relativity. We explain why NUT space has a non-spherical metric although NUT space itself is the spherical space-time of a mass with a gravomagnetic monopole. We demonstrate that all geodesics in NUT space lie on cones and use this result to study the gravitational lensing by bodies with gravomagnetic monopoles. We remark that just as electromagnetism would have to be extended beyond Maxwell's equations to allow for magnetic monopoles and their currents so general relativity would have to be extended to allow torsion for general distributions of gravomagnetic monopoles and their currents. Of course if monopoles were never discovered then it would be a triumph for both Maxwellian Electromagnetism and General Relativity as they stand!

gr-qc↗
arXiv1996

An analytic approximation to the isothermal sphere

We present a useful analytic approximation to the solution of the Lane-Emden equation for infinite polytropic index - the isothermal sphere. The optimized expression obtained for the density profile can be accurate to within 0.04% within 5 core-radii and to 0.1% within 10 core-radii.

astro-ph↗
arXiv1994

Wiener Reconstruction of Density, Velocity, and Potential Fields from All-Sky Galaxy Redshift Surveys

We present a new method for recovering the cosmological density, velocity, and potential fields from all-sky redshift catalogues. The method is based on an expansion of the fields in orthogonal radial (Bessel) and angular (spherical harmonic) functions. In this coordinate system, peculiar velocities introduce a coupling of the radial harmonics describing the density field in redshift space but leave the angular modes unaffected. In the harmonic transform space, this radial coupling is described by a distortion matrix which can be computed analytically within the context of linear theory; the redshift space harmonics can then be converted to their real space values by inversion of this matrix. Statistical noise is mitigated by regularizing the matrix inversion with a Wiener filter. The method yields a minimum variance estimate of the density field in real space. In this coordinate system, the minimum variance harmonics of the peculiar velocity and potential fields are related to those of the density field by simple linear transformations. Tests of the method with simulations of a CDM universe and comparison with previously proposed methods demonstrate it to be a very promising new reconstruction method for the local density and velocity field. A first application to the 1.2 Jy IRAS redshift survey is presented.

astro-ph↗