8,147 research outputs found
Uncertainty Principle of Morgan type and Schr\"odinger Evolutions
We prove unique continuation properties for solutions of evolution
Schr\"odinger equation with time dependent potentials. In the case of the free
solution these correspond to uncertainly principles referred to as being of
Morgan type. As an application of our method we also obtain results concerning
the possible concentration profiles of solutions of semi-linear Schr\"odinger
equations
Exterior spacetime for stellar models in 5-dimensional Kaluza-Klein gravity
It is well-known that Birkhoff's theorem is no longer valid in theories with
more than four dimensions. Thus, in these theories the effective 4-dimensional
picture allows the existence of different possible, non-Schwarzschild,
scenarios for the description of the spacetime outside of a spherical star,
contrary to general relativity in 4D. We investigate the exterior spacetime of
a spherically symmetric star in the context of Kaluza-Klein gravity. We take a
well-known family of static spherically symmetric solutions of the Einstein
equations in an empty five-dimensional universe, and analyze possible stellar
exteriors that are conformal to the metric induced on four-dimensional
hypersurfaces orthogonal to the extra dimension. All these exteriors are
continuously matched with the interior of the star. Then, without making any
assumptions about the interior solution, we prove the following statement: the
condition that in the weak-field limit we recover the usual Newtonian physics
singles out an unique exterior. This exterior is "similar" to Scharzschild
vacuum in the sense that it has no effect on gravitational interactions.
However, it is more realistic because instead of being absolutely empty, it is
consistent with the existence of quantum zero-point fields. We also examine the
question of how would the deviation from the Schwarzschild vacuum exterior
affect the parameters of a neutron star. In the context of a model star of
uniform density, we show that the general relativity upper limit M/R < 4/9 is
significantly increased as we go away from the Schwarzschild vacuum exterior.
We find that, in principle, the compactness limit of a star can be larger than
1/2, without being a black hole. The generality of our approach is also
discussed.Comment: Typos corrected. Accepted for publication in Classical and Quantum
Gravit
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