1,985 research outputs found
Piecewise Conserved Quantities
We review the treatment of conservation laws in spacetimes that are glued
together in various ways, thus adding a boundary term to the usual conservation
laws. Several examples of such spacetimes will be described, including the
joining of Schwarzschild spacetimes of different masses, and the possibility of
joining regions of different signatures. The opportunity will also be taken to
explore some of the less obvious properties of Lorentzian vector calculus.Comment: To appear in Gravity and the Quantum, Springer 2017
(http://www.springer.com/in/book/9783319516998
Note on Signature Change and Colombeau Theory
Recent work alludes to various `controversies' associated with signature
change in general relativity. As we have argued previously, these are in fact
disagreements about the (often unstated) assumptions underlying various
possible approaches. The choice between approaches remains open.Comment: REVTex, 3 pages; to appear in GR
BOUNDARY CONDITIONS FOR THE SCALAR FIELD IN THE PRESENCE OF SIGNATURE CHANGE
We show that, contrary to recent criticism, our previous work yields a
reasonable class of solutions for the massless scalar field in the presence of
signature change.Comment: 11 pages, Plain Tex, no figure
The Effect of Negative-Energy Shells on the Schwarzschild Black Hole
We construct Penrose diagrams for Schwarzschild spacetimes joined by massless
shells of matter, in the process correcting minor flaws in the similar diagrams
drawn by Dray and 't Hooft, and confirming their result that such shells
generate a horizon shift. We then consider shells with negative energy density,
showing that the horizon shift in this case allows for travel between the
heretofore causally separated exterior regions of the Schwarzschild geometry.
These drawing techniques are then used to investigate the properties of
successive shells, joining multiple Schwarzschild regions. Again, the presence
of negative-energy shells leads to a causal connection between the exterior
regions, even in (some) cases with two successive shells of equal but opposite
total energy.Comment: 12 pages, 10 figure
A New Look at the Ashtekar-Magnon Energy Condition
In 1975, Ashtekar and Magnon showed that an energy condition selects a unique
quantization procedure for certain observers in general, curved spacetimes. We
generalize this result in two important ways, by eliminating the need to assume
a particular form for the (quantum) Hamiltonian, and by considering the
surprisingly nontrivial extension to nonminimal coupling.Comment: REVTeX, 10 page
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