1,590 research outputs found
Spuren der Vergangenheit – Phänomenologie des Gedächtnisses als Grundlage für Geschichtsphilosophie
Boundary Term in Metric f(R) Gravity: Field Equations in the Metric Formalism
The main goal of this paper is to get in a straightforward form the field
equations in metric f(R) gravity, using elementary variational principles and
adding a boundary term in the action, instead of the usual treatment in an
equivalent scalar-tensor approach. We start with a brief review of the
Einstein-Hilbert action, together with the Gibbons-York-Hawking boundary term,
which is mentioned in some literature, but is generally missing. Next we
present in detail the field equations in metric f(R) gravity, including the
discussion about boundaries, and we compare with the Gibbons-York-Hawking term
in General Relativity. We notice that this boundary term is necessary in order
to have a well defined extremal action principle under metric variation.Comment: 12 pages, title changes by referee recommendation. Accepted for
publication in General Relativity and Gravitation. Matches with the accepted
versio
On Conformal Infinity and Compactifications of the Minkowski Space
Using the standard Cayley transform and elementary tools it is reiterated
that the conformal compactification of the Minkowski space involves not only
the "cone at infinity" but also the 2-sphere that is at the base of this cone.
We represent this 2-sphere by two additionally marked points on the Penrose
diagram for the compactified Minkowski space. Lacks and omissions in the
existing literature are described, Penrose diagrams are derived for both,
simple compactification and its double covering space, which is discussed in
some detail using both the U(2) approach and the exterior and Clifford algebra
methods. Using the Hodge * operator twistors (i.e. vectors of the
pseudo-Hermitian space H_{2,2}) are realized as spinors (i.e., vectors of a
faithful irreducible representation of the even Clifford algebra) for the
conformal group SO(4,2)/Z_2. Killing vector fields corresponding to the left
action of U(2) on itself are explicitly calculated. Isotropic cones and
corresponding projective quadrics in H_{p,q} are also discussed. Applications
to flat conformal structures, including the normal Cartan connection and
conformal development has been discussed in some detail.Comment: 38 pages, 8 figures, late
Strong Cosmic Censorship and Causality Violation
We investigate the instability of the Cauchy horizon caused by causality
violation in the compact vacuum universe with the topology , which Moncrief and Isenberg considered. We show that if
the occurrence of curvature singularities are restricted to the boundary of
causality violating region, the whole segments of the boundary become curvature
singularities. This implies that the strong cosmic censorship holds in the
spatially compact vacuum space-time in the case of the causality violation.
This also suggests that causality violation cannot occur for a compact
universe.Comment: corrected version, 8 pages, one eps figure is include
An NMR-based nanostructure switch for quantum logic
We propose a nanostructure switch based on nuclear magnetic resonance (NMR)
which offers reliable quantum gate operation, an essential ingredient for
building a quantum computer. The nuclear resonance is controlled by the magic
number transitions of a few-electron quantum dot in an external magnetic field.Comment: 4 pages, 2 separate PostScript figures. Minor changes included. One
reference adde
Unwrapping Closed Timelike Curves
Closed timelike curves (CTCs) appear in many solutions of the Einstein
equation, even with reasonable matter sources. These solutions appear to
violate causality and so are considered problematic. Since CTCs reflect the
global properties of a spacetime, one can attempt to change its topology,
without changing its geometry, in such a way that the former CTCs are no longer
closed in the new spacetime. This procedure is informally known as unwrapping.
However, changes in global identifications tend to lead to local effects, and
unwrapping is no exception, as it introduces a special kind of singularity,
called quasi-regular. This "unwrapping" singularity is similar to the string
singularities. We give two examples of unwrapping of essentially 2+1
dimensional spacetimes with CTCs, the Gott spacetime and the Godel universe. We
show that the unwrapped Gott spacetime, while singular, is at least devoid of
CTCs. In contrast, the unwrapped Godel spacetime still contains CTCs through
every point. A "multiple unwrapping" procedure is devised to remove the
remaining circular CTCs. We conclude that, based on the two spacetimes we
investigated, CTCs appearing in the solutions of the Einstein equation are not
simply a mathematical artifact of coordinate identifications, but are indeed a
necessary consequence of General Relativity, provided only that we demand these
solutions do not possess naked quasi-regular singularities.Comment: 29 pages, 9 figure
Cosmic distance-duality as probe of exotic physics and acceleration
In cosmology, distances based on standard candles (e.g. supernovae) and
standard rulers (e.g. baryon oscillations) agree as long as three conditions
are met: (1) photon number is conserved, (2) gravity is described by a metric
theory with (3) photons travelling on unique null geodesics. This is the
content of distance-duality (the reciprocity relation) which can be violated by
exotic physics. Here we analyse the implications of the latest cosmological
data sets for distance-duality. While broadly in agreement and confirming
acceleration we find a 2-sigma violation caused by excess brightening of SN-Ia
at z > 0.5, perhaps due to lensing magnification bias. This brightening has
been interpreted as evidence for a late-time transition in the dark energy but
because it is not seen in the d_A data we argue against such an interpretation.
Our results do, however, rule out significant SN-Ia evolution and extinction:
the "replenishing" grey-dust model with no cosmic acceleration is excluded at
more than 4-sigma despite this being the best-fit to SN-Ia data alone, thereby
illustrating the power of distance-duality even with current data sets.Comment: 6 pages, 4 colour figures. Version accepted as a Rapid Communication
in PR
On the `Stationary Implies Axisymmetric' Theorem for Extremal Black Holes in Higher Dimensions
All known stationary black hole solutions in higher dimensions possess
additional rotational symmetries in addition to the stationary Killing field.
Also, for all known stationary solutions, the event horizon is a Killing
horizon, and the surface gravity is constant. In the case of non-degenerate
horizons (non-extremal black holes), a general theorem was previously
established [gr-qc/0605106] proving that these statements are in fact generally
true under the assumption that the spacetime is analytic, and that the metric
satisfies Einstein's equation. Here, we extend the analysis to the case of
degenerate (extremal) black holes. It is shown that the theorem still holds
true if the vector of angular velocities of the horizon satisfies a certain
"diophantine condition," which holds except for a set of measure zero.Comment: 30pp, Latex, no figure
The Dirac system on the Anti-de Sitter Universe
We investigate the global solutions of the Dirac equation on the
Anti-de-Sitter Universe. Since this space is not globally hyperbolic, the
Cauchy problem is not, {\it a priori}, well-posed. Nevertheless we can prove
that there exists unitary dynamics, but its uniqueness crucially depends on the
ratio beween the mass of the field and the cosmological constant
: it appears a critical value, , which plays a role
similar to the Breitenlohner-Freedman bound for the scalar fields. When
there exists a unique unitary dynamics. In opposite, for
the light fermions satisfying , we construct several asymptotic
conditions at infinity, such that the problem becomes well-posed. In all the
cases, the spectrum of the hamiltonian is discrete. We also prove a result of
equipartition of the energy.Comment: 33 page
Quantum corrections to the mass of the supersymmetric vortex
We calculate quantum corrections to the mass of the vortex in N=2
supersymmetric abelian Higgs model in (2+1) dimensions. We put the system in a
box and apply the zeta function regularization. The boundary conditions
inevitably violate a part of the supersymmetries. Remaining supersymmetry is
however enough to ensure isospectrality of relevant operators in bosonic and
fermionic sectors. A non-zero correction to the mass of the vortex comes from
finite renormalization of couplings.Comment: Latex, 18 pp; v2 reference added; v3 minor change
- …