53 research outputs found
On the total mass of closed universes
The total mass, the Witten type gauge conditions and the spectral properties
of the Sen-Witten and the 3-surface twistor operators in closed universes are
investigated. It has been proven that a recently suggested expression
for the total mass density of closed universes is vanishing if and only if the
spacetime is flat with toroidal spatial topology; it coincides with the first
eigenvalue of the Sen-Witten operator; and it is vanishing if and only if
Witten's gauge condition admits a non-trivial solution.
Here we generalize slightly the result above on the zero-mass configurations:
if and only if the spacetime is holonomically trivial with toroidal
spatial topology. Also, we show that the multiplicity of the eigenvalues of the
(square of the) Sen-Witten operator is at least two, and a potentially viable
gauge condition is suggested. The monotonicity properties of through
the examples of closed Bianchi I and IX cosmological spacetimes are also
discussed. A potential spectral characterization of these cosmological
spacetimes, in terms of the spectrum of the Riemannian Dirac operator and the
Sen-Witten and the 3-surface twistor operators, is also indicated.Comment: 14 pages, plenary talk at the `Spanish Relativity Meeting in Portugal
2012', Guimar\~aes 3-7 September; Final version, appearing in General
Relativity and Gravitatio
A positive Bondi--type mass in asymptotically de Sitter spacetimes
The general structure of the conformal boundary of
asymptotically de Sitter spacetimes is investigated. First we show that
Penrose's quasi-local mass, associated with a cut of the conformal
boundary, can be zero even in the presence of outgoing gravitational radiation.
On the other hand, following a Witten--type spinorial proof, we show that an
analogous expression based on the Nester--Witten form is finite only if the
Witten spinor field solves the 2-surface twistor equation on , and it
yields a positive functional on the 2-surface twistor space on ,
provided the matter fields satisfy the dominant energy condition. Moreover,
this functional is vanishing if and only if the domain of dependence of the
spacelike hypersurface which intersects in the cut
is locally isometric to the de Sitter spacetime. For non-contorted cuts this
functional yields an invariant analogous to the Bondi mass.Comment: 51 pages; typos corrected, one reference added; final version,
appearing in Class. Quantum Gra
The 'most classical' states of Euclidean invariant elementary quantum mechanical systems
Complex techniques of general relativity are used to determine \emph{all} the
states in the two and three dimensional momentum spaces in which the equality
holds in the uncertainty relations for the non-commuting basic observables of
Euclidean invariant elementary quantum mechanical systems, even with non-zero
intrinsic spin. It is shown that while there is a 1-parameter family of such
states for any two components of the angular momentum vector operator with any
angle between them, such states exist for the component of the linear and the
angular momenta \emph{only if} these components are orthogonal to each other
and hence the problem is reduced to the two-dimensional Euclidean invariant
case. We also show that the analogous states exist for a component of the
linear momentum and of the centre-of-mass vector \emph{only if} the angle
between them is zero or an acute angle. \emph{No} such state (represented by a
square integrable and differentiable wave function) can exist for \emph{any}
pair of components of the centre-of-mass vector operator. Therefore, the
existence of such states depends not only on the Lie algebra, but on the choice
for its generators as well.Comment: 28 pages; v2: typos corrected, discussion improve
On gravity's role in the genesis of rest masses of classical fields
It is shown that in the Einstein-conformally coupled Higgs--Maxwell system
with Friedman-Robertson-Walker symmetries the energy density of the Higgs field
has stable local minimum only if the mean curvature of the
hypersurfaces is less than a finite critical value , while for greater
mean curvature the energy density is not bounded from below. Therefore, there
are extreme gravitational situations in which even quasi-locally defined
instantaneous vacuum states of the Higgs sector cannot exist, and hence one
cannot at all define the rest mass of all the classical fields. On
hypersurfaces with mean curvature less than the energy density has the
`wine bottle' (rather than the familiar `Mexican hat') shape, and the gauge
field can get rest mass via the Brout--Englert--Higgs mechanism. The spacelike
hypersurface with the critical mean curvature represents the moment of
`genesis' of rest masses.Comment: 21 pages, 3 figures; short, journal version of arXiv:1603.0699
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