172 research outputs found
No-go theorem for bimetric gravity with positive and negative mass
We argue that the most conservative geometric extension of Einstein gravity
describing both positive and negative mass sources and observers is bimetric
gravity and contains two copies of standard model matter which interact only
gravitationally. Matter fields related to one of the metrics then appear dark
from the point of view of an observer defined by the other metric, and so may
provide a potential explanation for the dark universe. In this framework we
consider the most general form of linearized field equations compatible with
physically and mathematically well-motivated assumptions. Using gauge-invariant
linear perturbation theory, we prove a no-go theorem ruling out all bimetric
gravity theories that, in the Newtonian limit, lead to precisely opposite
forces on positive and negative test masses.Comment: 19 pages, no figures, journal versio
Gravitating Opposites Attract
Generalizing previous work by two of us, we prove the non-existence of
certain stationary configurations in General Relativity having a spatial
reflection symmetry across a non-compact surface disjoint from the matter
region. Our results cover cases such that of two symmetrically arranged
rotating bodies with anti-aligned spins in () dimensions, or
two symmetrically arranged static bodies with opposite charges in 3+1
dimensions. They also cover certain symmetric configurations in
(3+1)-dimensional gravity coupled to a collection of scalars and abelian vector
fields, such as arise in supergravity and Kaluza-Klein models. We also treat
the bosonic sector of simple supergravity in 4+1 dimensions.Comment: 13 pages; slightly amended version, some references added, matches
version to be published in Classical and Quantum Gravit
Shape selection in non-Euclidean plates
We investigate isometric immersions of disks with constant negative curvature
into , and the minimizers for the bending energy, i.e. the
norm of the principal curvatures over the class of isometric
immersions. We show the existence of smooth immersions of arbitrarily large
geodesic balls in into . In elucidating the
connection between these immersions and the non-existence/singularity results
of Hilbert and Amsler, we obtain a lower bound for the norm of the
principal curvatures for such smooth isometric immersions. We also construct
piecewise smooth isometric immersions that have a periodic profile, are
globally , and have a lower bending energy than their smooth
counterparts. The number of periods in these configurations is set by the
condition that the principal curvatures of the surface remain finite and grows
approximately exponentially with the radius of the disc. We discuss the
implications of our results on recent experiments on the mechanics of
non-Euclidean plates
EinfĂŒhrung in die Maxwellsche Theorie der ElektrizitĂ€t : mit einem einleitenden Abschnitte ĂŒber das Rechnen mit VektorgröĂen in der Physik
von A. Föppl ; M. Abraham(VLID)36021
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