129,349 research outputs found
An observer principle for general relativity
We give a mathematical uniqueness theorem which in particular shows that
symmetric tensors in general relativity are uniquely determined by their
monomial functions on the light cone. Thus, for an observer to observe a tensor
at an event in general relativity is to contract with the velocity vector of
the observer, repeatedly to the rank of the tensor. Thus two symmetric tensors
observed to be equal by all observers at a specific event are necessarily equal
at that event.Comment: arXiv admin note: substantial text overlap with arXiv:0903.522
Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with
We show that the dragging of the axis directions of local inertial frames by
a weighted average of the energy currents in the universe is exact for all
linear perturbations of any Friedmann-Robertson-Walker (FRW) universe with K =
(+1, -1, 0) and of Einstein's static closed universe. This includes FRW
universes which are arbitrarily close to the Milne Universe, which is empty,
and to the de Sitter universe. Hence the postulate formulated by E. Mach about
the physical cause for the time-evolution of the axis directions of inertial
frames is shown to hold in cosmological General Relativity for linear
perturbations. The time-evolution of axis directions of local inertial frames
(relative to given local fiducial axes) is given experimentally by the
precession angular velocity of gyroscopes, which in turn is given by the
operational definition of the gravitomagnetic field. The gravitomagnetic field
is caused by cosmological energy currents via the momentum constraint. This
equation for cosmological gravitomagnetism is analogous to Ampere's law, but it
holds also for time-dependent situtations. In the solution for an open universe
the 1/r^2-force of Ampere is replaced by a Yukawa force which is of identical
form for FRW backgrounds with The scale of the exponential
cutoff is the H-dot radius, where H is the Hubble rate, and dot is the
derivative with respect to cosmic time. Analogous results hold for energy
currents in a closed FRW universe, K = +1, and in Einstein's closed static
universe.Comment: 23 pages, no figures. Final published version. Additional material in
Secs. I.A, I.J, III, V.H. Additional reference
Kaluza-Klein Consistency, Killing Vectors, and Kahler Spaces
We make a detailed investigation of all spaces Q_{n_1... n_N}^{q_1... q_N} of
the form of U(1) bundles over arbitrary products \prod_i CP^{n_i} of complex
projective spaces, with arbitrary winding numbers q_i over each factor in the
base. Special cases, including Q_{11}^{11} (sometimes known as T^{11}),
Q_{111}^{111} and Q_{21}^{32}, are relevant for compactifications of type IIB
and D=11 supergravity. Remarkable ``conspiracies'' allow consistent
Kaluza-Klein S^5, S^4 and S^7 sphere reductions of these theories that retain
all the Yang-Mills fields of the isometry group in a massless truncation. We
prove that such conspiracies do not occur for the reductions on the Q_{n_1...
n_N}^{q_1... q_N} spaces, and that it is inconsistent to make a massless
truncation in which the non-abelian SU(n_i+1) factors in their isometry groups
are retained. In the course of proving this we derive many properties of the
spaces Q_{n_1... n_N}^{q_1... q_N} of more general utility. In particular, we
show that they always admit Einstein metrics, and that the spaces where
q_i=(n_i+1)/\ell all admit two Killing spinors. We also obtain an iterative
construction for real metrics on CP^n, and construct the Killing vectors on
Q_{n_1... n_N}^{q_1... q_N} in terms of scalar eigenfunctions on CP^{n_i}. We
derive bounds that allow us to prove that certain Killing-vector identities on
spheres, necessary for consistent Kaluza-Klein reductions, are never satisfied
on Q_{n_1... n_N}^{q_1... q_N}.Comment: Latex, 43 pages, references added and typos correcte
Boundary Quantum Mechanics
A reformulation of a physical theory in which measurements at the initial and
final moments of time are treated independently is discussed, both on the
classical and quantum levels. Methods of the standard quantum mechanics are
used to quantize boundary phase space to obtain boundary quantum mechanics -- a
theory that does not depend on the distinction between the initial and final
moments of time, a theory that can be formulated without reference to the
causal structure. As a supplementary material, the geometrical description of
quantization of a general (e.g. curved) configuration space is presented.Comment: 35 pages, in Gravitation: Following the Prague Inspiration (To
celebrate the 60th birthday of Jiri Bicak), O.Semerak, J.Podolsky, M.Zofka
(eds.), World Scientific, Singapore, 2002, pp. 289--32
Bundles over Nearly-Kahler Homogeneous Spaces in Heterotic String Theory
We construct heterotic vacua based on six-dimensional nearly-Kahler
homogeneous manifolds and non-trivial vector bundles thereon. Our examples are
based on three specific group coset spaces. It is shown how to construct line
bundles over these spaces, compute their properties and build up vector bundles
consistent with supersymmetry and anomaly cancelation. It turns out that the
most interesting coset is . This space supports a large number of
vector bundles which lead to consistent heterotic vacua, some of them with
three chiral families.Comment: 32 pages, reference adde
Branes: from free fields to general backgrounds
Motivated by recent developments in string theory, we study the structure of
boundary conditions in arbitrary conformal field theories. A boundary condition
is specified by two types of data: first, a consistent collection of reflection
coefficients for bulk fields on the disk; and second, a choice of an
automorphism of the fusion rules that preserves conformal weights.
Non-trivial automorphisms correspond to D-brane configurations for
arbitrary conformal field theories. The choice of the fusion rule automorphism
amounts to fixing the dimension and certain global topological
features of the D-brane world volume and the background gauge field on it. We
present evidence that for fixed choice of the boundary conditions are
classified as the irreducible representations of some commutative associative
algebra, a generalization of the fusion rule algebra. Each of these irreducible
representations corresponds to a choice of the moduli for the world volume of
the D-brane and the moduli of the flat connection on it.Comment: 56 pages, LaTeX2e. Typos corrected; two references adde
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