73 research outputs found
The Geometry of Black Hole singularities
Recent results show that important singularities in General Relativity can be
naturally described in terms of finite and invariant canonical geometric
objects. Consequently, one can write field equations which are equivalent to
Einstein's at non-singular points, but in addition remain well-defined and
smooth at singularities. The black hole singularities appear to be less
undesirable than it was thought, especially after we remove the part of the
singularity due to the coordinate system. Black hole singularities are then
compatible with global hyperbolicity, and don't make the evolution equations
break down, when these are expressed in terms of the appropriate variables. The
charged black holes turn out to have smooth potential and electromagnetic
fields in the new atlas. Classical charged particles can be modeled, in General
Relativity, as charged black hole solutions. Since black hole singularities are
accompanied by dimensional reduction, this should affect Feynman's path
integrals. Therefore, it is expected that singularities induce dimensional
reduction effects in Quantum Gravity. These dimensional reduction effects are
very similar to those postulated in some approaches to making Quantum Gravity
perturbatively renormalizable. This may provide a way to test indirectly the
effects of singularities, otherwise inaccessible.Comment: To appear in Advances in High Energy Physic
Schwarzschild Singularity is Semi-Regularizable
It is shown that the Schwarzschild spacetime can be extended so that the
metric becomes analytic at the singularity. The singularity continues to exist,
but it is made degenerate and smooth, and the infinities are removed by an
appropriate choice of coordinates. A family of analytic extensions is found,
and one of these extensions is semi-regular. A degenerate singularity doesn't
destroy the topology, and when is semi-regular, it allows the field equations
to be rewritten in a form which avoids the infinities, as it was shown
elsewhere (arXiv:1105.0201, arXiv:1105.3404). In the new coordinates, the
Schwarzschild solution extends beyond the singularity. This suggests a
possibility that the information is not destroyed in the singularity, and can
be restored after the evaporation.Comment: 11 pages, 3 figure
On the wavefunction collapse
Wavefunction collapse is usually seen as a discontinuous violation of the
unitary evolution of a quantum system, caused by the observation. Moreover, the
collapse appears to be nonlocal in a sense which seems at odds with General
Relativity. In this article the possibility that the wavefunction evolves
continuously and hopefully unitarily during the measurement process is
analyzed. It is argued that such a solution has to be formulated using a time
symmetric replacement of the initial value problem in Quantum Mechanics. Major
difficulties in apparent conflict with unitary evolution are identified, but
eventually its possibility is not completely ruled out. This interpretation is
in a weakened sense both local and realistic, without contradicting Bell's
theorem. Moreover, if it is true, it makes Quantum Mechanics consistent with
General Relativity in the semiclassical framework.Comment: Available at: http://quanta.ws/ojs/index.php/quanta/article/view/4
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