1,528 research outputs found
The Decomposition of the Optically Active Diazo Ester from Aminolauronic Acid
In 1921 Levene and Mikeska, and in 1922 Noyes and Chiles prepared optically active esters in which the only asymetric carbon was that doubly bound to diazo nitrogen. The theoretical explanation being: that of the five valences of the nitrogen, four are covalences while the fifth is a Polar or ionizing valence. This may be illustrated by ammonium chloride
Uniqueness and non-uniqueness of static vacuum black holes in higher dimensions
We prove the uniqueness theorem for asymptotically flat static vacuum black
hole solutions in higher dimensional space-times. We also construct infinitely
many non-asymptotically flat regular static black holes on the same spacetime
manifold with the same spherical topology.Comment: to appear in Progress of Theoretical Physics Supplement No. 14
Uniqueness properties of the Kerr metric
We obtain a geometrical condition on vacuum, stationary, asymptotically flat
spacetimes which is necessary and sufficient for the spacetime to be locally
isometric to Kerr. Namely, we prove a theorem stating that an asymptotically
flat, stationary, vacuum spacetime such that the so-called Killing form is an
eigenvector of the self-dual Weyl tensor must be locally isometric to Kerr.
Asymptotic flatness is a fundamental hypothesis of the theorem, as we
demonstrate by writing down the family of metrics obtained when this
requirement is dropped. This result indicates why the Kerr metric plays such an
important role in general relativity. It may also be of interest in order to
extend the uniqueness theorems of black holes to the non-connected and to the
non-analytic case.Comment: 30 pages, LaTeX, submitted to Classical and Quantum Gravit
A Mass Bound for Spherically Symmetric Black Hole Spacetimes
Requiring that the matter fields are subject to the dominant energy
condition, we establish the lower bound for the
total mass of a static, spherically symmetric black hole spacetime. ( and denote the area and the surface gravity of the horizon,
respectively.) Together with the fact that the Komar integral provides a simple
relation between and the strong energy condition,
this enables us to prove that the Schwarzschild metric represents the only
static, spherically symmetric black hole solution of a selfgravitating matter
model satisfying the dominant, but violating the strong energy condition for
the timelike Killing field at every point, that is, .
Applying this result to scalar fields, we recover the fact that the only black
hole configuration of the spherically symmetric Einstein-Higgs model with
arbitrary non-negative potential is the Schwarzschild spacetime with constant
Higgs field. In the presence of electromagnetic fields, we also derive a
stronger bound for the total mass, involving the electromagnetic potentials and
charges. Again, this estimate provides a simple tool to prove a ``no-hair''
theorem for matter fields violating the strong energy condition.Comment: 16 pages, LATEX, no figure
Uniqueness Theorem for Static Black Hole Solutions of sigma-models in Higher Dimensions
We prove the uniqueness theorem for self-gravitating non-linear sigma-models
in higher dimensional spacetime. Applying the positive mass theorem we show
that Schwarzschild-Tagherlini spacetime is the only maximally extended, static
asymptotically flat solution with non-rotating regular event horizon with a
constant mapping.Comment: 5 peges, Revtex, to be published in Class.Quantum Gra
THE UNIQUENESS THEOREM FOR ROTATING BLACK HOLE SOLUTIONS OF SELF-GRAVITATING HARMONIC MAPPINGS
We consider rotating black hole configurations of self-gravitating maps from
spacetime into arbitrary Riemannian manifolds. We first establish the
integrability conditions for the Killing fields generating the stationary and
the axisymmetric isometry (circularity theorem). Restricting ourselves to
mappings with harmonic action, we subsequently prove that the only stationary
and axisymmetric, asymptotically flat black hole solution with regular event
horizon is the Kerr metric. Together with the uniqueness result for
non-rotating configurations and the strong rigidity theorem, this establishes
the uniqueness of the Kerr family amongst all stationary black hole solutions
of self-gravitating harmonic mappings.Comment: 18 pages, latex, no figure
Towards the classification of static vacuum spacetimes with negative cosmological constant
We present a systematic study of static solutions of the vacuum Einstein
equations with negative cosmological constant which asymptotically approach the
generalized Kottler (``Schwarzschild--anti-de Sitter'') solution, within
(mainly) a conformal framework. We show connectedness of conformal infinity for
appropriately regular such space-times. We give an explicit expression for the
Hamiltonian mass of the (not necessarily static) metrics within the class
considered; in the static case we show that they have a finite and well defined
Hawking mass. We prove inequalities relating the mass and the horizon area of
the (static) metrics considered to those of appropriate reference generalized
Kottler metrics. Those inequalities yield an inequality which is opposite to
the conjectured generalized Penrose inequality. They can thus be used to prove
a uniqueness theorem for the generalized Kottler black holes if the generalized
Penrose inequality can be established.Comment: the discussion of our results includes now some solutions of Horowitz
and Myers; typos corrected here and there; a shortened version of this
version will appear in Journal of Mathematical Physic
The classification of static vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior
We prove non-existence of static, vacuum, appropriately regular,
asymptotically flat black hole space-times with degenerate (not necessarily
connected) components of the event horizon. This finishes the classification of
static, vacuum, asymptotically flat domains of outer communication in an
appropriate class of space-times, showing that the domains of outer
communication of the Schwarzschild black holes exhaust the space of
appropriately regular black hole exteriors.Comment: This version includes an addendum with a corrected proof of
non-existence of zeros of the Killing vector at degenerate horizons. A
problem with yet another Lemma is pointed out; this problem does not arise if
one assumes analyticity of the metric. An alternative solution, that does not
require analyticity, has been given in arXiv:1004.0513 [gr-qc] under
appropriate global condition
Uniqueness Theorem of Static Degenerate and Non-degenerate Charged Black Holes in Higher Dimensions
We prove the uniqueness theorem for static higher dimensional charged black
holes spacetime containing an asymptotically flat spacelike hypersurface with
compact interior and with both degenerate and non-degenerate components of the
event horizon.Comment: 9 pages, RevTex, to be published in Phys.Rev.D1
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