17 research outputs found
New Path Equations in Absolute Parallelism Geometry
The Bazanski approach, for deriving the geodesic equations in Riemannian
geometry, is generalized in the absolute parallelism geometry. As a consequence
of this generalization three path equations are obtained. A striking feature in
the derived equations is the appearance of a torsion term with a numerical
coefficients that jumps by a step of one half from equation to another. This is
tempting to speculate that the paths in absolute parallelism geometry might
admit a quantum feature.Comment: 4 pages Latex file Journal Reference: Astrophysics and space science
228, 273, (1995
On quasi-local charges and Newman--Penrose type quantities in Yang--Mills theories
We generalize the notion of quasi-local charges, introduced by P. Tod for
Yang--Mills fields with unitary groups, to non-Abelian gauge theories with
arbitrary gauge group, and calculate its small sphere and large sphere limits
both at spatial and null infinity. We show that for semisimple gauge groups no
reasonable definition yield conserved total charges and Newman--Penrose (NP)
type quantities at null infinity in generic, radiative configurations. The
conditions of their conservation, both in terms of the field configurations and
the structure of the gauge group, are clarified. We also calculate the NP
quantities for stationary, asymptotic solutions of the field equations with
vanishing magnetic charges, and illustrate these by explicit solutions with
various gauge groups.Comment: 22 pages, typos corrected, appearing in Classical and Quantum Gravit
Components of the gravitational force in the field of a gravitational wave
Gravitational waves bring about the relative motion of free test masses. The
detailed knowledge of this motion is important conceptually and practically,
because the mirrors of laser interferometric detectors of gravitational waves
are essentially free test masses. There exists an analogy between the motion of
free masses in the field of a gravitational wave and the motion of free charges
in the field of an electromagnetic wave. In particular, a gravitational wave
drives the masses in the plane of the wave-front and also, to a smaller extent,
back and forth in the direction of the wave's propagation. To describe this
motion, we introduce the notion of `electric' and `magnetic' components of the
gravitational force. This analogy is not perfect, but it reflects some
important features of the phenomenon. Using different methods, we demonstrate
the presence and importance of what we call the `magnetic' component of motion
of free masses. It contributes to the variation of distance between a pair of
particles. We explicitely derive the full response function of a 2-arm laser
interferometer to a gravitational wave of arbitrary polarization. We give a
convenient description of the response function in terms of the spin-weighted
spherical harmonics. We show that the previously ignored `magnetic' component
may provide a correction of up to 10 %, or so, to the usual `electric'
component of the response function. The `magnetic' contribution must be taken
into account in the data analysis, if the parameters of the radiating system
are not to be mis-estimated.Comment: prints to 29 pages including 9 figures, new title, additional
explanations and references in response to referee's comments, to be
published in Class. Quant. Gra
The Generalized Jacobi Equation
The Jacobi equation in pseudo-Riemannian geometry determines the linearized
geodesic flow. The linearization ignores the relative velocity of the
geodesics. The generalized Jacobi equation takes the relative velocity into
account; that is, when the geodesics are neighboring but their relative
velocity is arbitrary the corresponding geodesic deviation equation is the
generalized Jacobi equation. The Hamiltonian structure of this nonlinear
equation is analyzed in this paper. The tidal accelerations for test particles
in the field of a plane gravitational wave and the exterior field of a rotating
mass are investigated. In the latter case, the existence of an attractor of
uniform relative radial motion with speed is pointed
out. The astrophysical implications of this result for the terminal speed of a
relativistic jet is briefly explored.Comment: LaTeX file, 4 PS figures, 28 pages, revised version, accepted for
publication in Classical and Quantum Gravit
Gravitomagnetism and Relative Observer Clock Effects
The gravitomagnetic clock effect and the Sagnac effect for circularly
rotating orbits in stationary axisymmetric spacetimes are studied from a
relative observer point of view, clarifying their relationships and the roles
played by special observer families. In particular Semer\'ak's recent
characterization of extremely accelerated observers in terms of the two-clock
clock effect is shown to be complemented by a similarly special property of the
single-clock clock effect.Comment: 19 pages, LaTeX, IOP macros with package epsf and 1 eps figure, to
appear in Classical and Quantum Gravity, slight revisio
Enthalpy and the Mechanics of AdS Black Holes
We present geometric derivations of the Smarr formula for static AdS black
holes and an expanded first law that includes variations in the cosmological
constant. These two results are further related by a scaling argument based on
Euler's theorem. The key new ingredient in the constructions is a two-form
potential for the static Killing field. Surface integrals of the Killing
potential determine the coefficient of the variation of the cosmological
constant in the first law. This coefficient is proportional to a finite,
effective volume for the region outside the AdS black hole horizon, which can
also be interpreted as minus the volume excluded from a spatial slice by the
black hole horizon. This effective volume also contributes to the Smarr
formula. Since the cosmological constant is naturally thought of as a pressure,
the new term in the first law has the form of effective volume times change in
pressure that arises in the variation of the enthalpy in classical
thermodynamics. This and related arguments suggest that the mass of an AdS
black hole should be interpreted as the enthalpy of the spacetime.Comment: 21 pages; v2 references adde
Some general properties of the renormalized stress-energy tensor for static quantum states on (n+1)-dimensional spherically symmetric black holes
We study the renormalized stress-energy tensor (RSET) for static quantum
states on (n+1)-dimensional, static, spherically symmetric black holes. By
solving the conservation equations, we are able to write the stress-energy
tensor in terms of a single unknown function of the radial co-ordinate, plus
two arbitrary constants. Conditions for the stress-energy tensor to be regular
at event horizons (including the extremal and ``ultra-extremal'' cases) are
then derived using generalized Kruskal-like co-ordinates. These results should
be useful for future calculations of the RSET for static quantum states on
spherically symmetric black hole geometries in any number of space-time
dimensions.Comment: 9 pages, no figures, RevTeX4, references added, accepted for
publication in General Relativity and Gravitatio
Roulettes: a weak lensing formalism for strong lensing - I. Overview
This work is funded by the National Research Foundation (South Africa)