21 research outputs found
Redshifts and Killing Vectors
Courses in introductory special and general relativity have increasingly
become part of the curriculum for upper-level undergraduate physics majors and
master's degree candidates. One of the topics rarely discussed is symmetry,
particularly in the theory of general relativity. The principal tool for its
study is the Killing vector. We provide an elementary introduction to the
concept of a Killing vector field, its properties, and as an example of its
utility apply these ideas to the rigorous determination of gravitational and
cosmological redshifts.Comment: 16 Latex pages, 6 postscript figures, submitted to Am. J. Phy
Active Mass Under Pressure
After a historical introduction to Poisson's equation for Newtonian gravity,
its analog for static gravitational fields in Einstein's theory is reviewed. It
appears that the pressure contribution to the active mass density in Einstein's
theory might also be noticeable at the Newtonian level. A form of its
surprising appearance, first noticed by Richard Chase Tolman, was discussed
half a century ago in the Hamburg Relativity Seminar and is resolved here.Comment: 28 pages, 4 figure
The influence of the cosmological expansion on local systems
Following renewed interest, the problem of whether the cosmological expansion
affects the dynamics of local systems is reconsidered. The cosmological
correction to the equations of motion in the locally inertial Fermi normal
frame (the relevant frame for astronomical observations) is computed. The
evolution equations for the cosmological perturbation of the two--body problem
are solved in this frame. The effect on the orbit is insignificant as are the
effects on the galactic and galactic--cluster scales.Comment: To appear in the Astrophysical Journal, Late
Long wavelength iteration of Einstein's equations near a spacetime singularity
We clarify the links between a recently developped long wavelength iteration
scheme of Einstein's equations, the Belinski Khalatnikov Lifchitz (BKL) general
solution near a singularity and the antinewtonian scheme of Tomita's. We
determine the regimes when the long wavelength or antinewtonian scheme is
directly applicable and show how it can otherwise be implemented to yield the
BKL oscillatory approach to a spacetime singularity. When directly applicable
we obtain the generic solution of the scheme at first iteration (third order in
the gradients) for matter a perfect fluid. Specializing to spherical symmetry
for simplicity and to clarify gauge issues, we then show how the metric behaves
near a singularity when gradient effects are taken into account.Comment: 35 pages, revtex, no figure
Isometric Embedding of BPS Branes in Flat Spaces with Two Times
We show how non-near horizon p-brane theories can be obtained from two
embedding constraints in a flat higher dimensional space with 2 time
directions. In particular this includes the construction of D3 branes from a
flat 12-dimensional action, and M2 and M5 branes from 13 dimensions. The
worldvolume actions are determined by constant forms in the higher dimension,
reduced to the usual expressions by Lagrange multipliers. The formulation
affords insight in the global aspects of the spacetime geometries and makes
contact with recent work on two-time physics.Comment: 29 pages, 10 figures, Latex using epsf.sty and here.sty; v2:
reference added and some small correction
Taub's plane-symmetric vacuum spacetime revisited
The gravitational properties of the {\em only} static plane-symmetric vacuum
solution of Einstein's field equations without cosmological term (Taub's
solution, for brevity) are presented: some already known properties (geodesics,
weak field limit and pertainment to the Schwarzschild family of spacetimes) are
reviewed in a physically much more transparent way, as well as new results
about its asymptotic structure, possible matchings and nature of the source are
furnished. The main results point to the fact that the solution must be
interpreted as representing the exterior gravitational field due to a {\em
negative} mass distribution, confirming previous statements to that effect in
the literature. Some analogies to Kasner's spatially homogeneous cosmological
model are also referred to.Comment: plain LaTex, four Postscript figure
Perfect-fluid cylinders and walls - sources for the Levi-Civita space-time
The diagonal metric tensor whose components are functions of one spatial
coordinate is considered. Einstein's field equations for a perfect-fluid source
are reduced to quadratures once a generating function, equal to the product of
two of the metric components, is chosen. The solutions are either static fluid
cylinders or walls depending on whether or not one of the spatial coordinates
is periodic. Cylinder and wall sources are generated and matched to the vacuum
(Levi--Civita) space--time. A match to a cylinder source is achieved for
-\frac{1}{2}<\si<\frac{1}{2}, where \si is the mass per unit length in the
Newtonian limit \si\to 0, and a match to a wall source is possible for
|\si|>\frac{1}{2}, this case being without a Newtonian limit; the positive
(negative) values of \si correspond to a positive (negative) fluid density.
The range of \si for which a source has previously been matched to the
Levi--Civita metric is 0\leq\si<\frac{1}{2} for a cylinder source.Comment: 22 pages, LaTeX, one included figure. Revised version: three
(non-perfect-fluid) interior solutions are added, one of which falsifies the
original conjecture in Sec. 4, and the circular geodesics of the Levi-Civita
space-time are discussed in a footnot
Stellar structure and compact objects before 1940: Towards relativistic astrophysics
Since the mid-1920s, different strands of research used stars as "physics
laboratories" for investigating the nature of matter under extreme densities
and pressures, impossible to realize on Earth. To trace this process this paper
is following the evolution of the concept of a dense core in stars, which was
important both for an understanding of stellar evolution and as a testing
ground for the fast-evolving field of nuclear physics. In spite of the divide
between physicists and astrophysicists, some key actors working in the
cross-fertilized soil of overlapping but different scientific cultures
formulated models and tentative theories that gradually evolved into more
realistic and structured astrophysical objects. These investigations culminated
in the first contact with general relativity in 1939, when J. Robert
Oppenheimer and his students George Volkoff and Hartland Snyder systematically
applied the theory to the dense core of a collapsing neutron star. This
pioneering application of Einstein's theory to an astrophysical compact object
can be regarded as a milestone in the path eventually leading to the emergence
of relativistic astrophysics in the early 1960s.Comment: 83 pages, 4 figures, submitted to the European Physical Journal