356 research outputs found
Distorted Black Holes with Charge
We present new solutions to the Einstein-Maxwell equations representing a
class of charged distorted black holes. These solutions are static-axisymmetric
and are generalizations of the distorted black hole solutions studied by Geroch
and Hartle. Physically, they represent a charged black hole distorted by
external matter fields. We discuss the zeroth and first law for these black
holes. The first law is proved in two different forms, one motivated by the
isolated horizon framework and the other using normalizations at infinity.Comment: 18 pages, LaTe
Matrix Ernst Potentials and Orthogonal Symmetry for Heterotic String in Three Dimensions
A new matrix representation for low-energy limit of heterotic string theory
reduced to three dimensions is considered. The pair of matrix Ernst Potentials
uniquely connected with the coset matrix is derived. The action of the symmetry
group on the Ernst potentials is established.Comment: 10 pages in LaTe
Extremal Problems for Roman Domination
A Roman dominating function of a graph G is a labeling f: V(G) →{0,1,2} such that every vertex with a label 0 has a neighbor with label 2. The Roman domination number γR(G) of G is the minimum of ∑ʋϵV(G)f(v) over such functions. Let G be a connected n-vertex graph. We prove that γR(G) ≤ 4n/5, and we characterize the graphs achieving equality. We obtain sharp upper and lower bounds for γR(G) + γR(Ḡ) and γR(G)γR(Ḡ), improving known results for domination number. We prove that γR(G) ≤ 8n/11 when ᵟ(G) ≥ 2 and n ≥ 9, and this is sharp
Symplectic Gravity Models in Four, Three and Two Dimensions
A class of the gravity models describing a coupled system of
Abelian vector fields and the symmetric matrix generalizations of
the dilaton and Kalb-Ramond fields is considered. It is shown that the
Pecci-Quinn axion matrix can be entered and the resulting equations of motion
possess the symmetry in four dimensions. The stationary case is
studied. It is established that the theory allows a -model
representation with a target space which is invariant under the
group of isometry transformations. The chiral matrix of the coset is constructed. A K\"ahler formalism based on the use of the Ernst
complex symmetric matrix is developed. The stationary
axisymmetric case is considered. The Belinsky-Zakharov chiral matrix depending
on the original field variables is obtained. The Kramer-Neugebauer
transformation, which algebraically maps the original variables into the target
space ones, is presented.Comment: 21 pages, RevTex, no figurie
Static axisymmetric spacetimes with non-generic world-line SUSY
The conditions for the existence of Killing-Yano tensors, which are closely
related to the appearance of non-generic world-line SUSY, are presented for
static axisymmetric spacetimes. Imposing the vacuum Einstein equation, the set
of solutions admitting Killing-Yano tensors is considered. In particular, it is
shown that static, axisymmetric and asymptotically flat vacuum solutions
admitting Killing-Yano tensors are only the Schwarzschild solution.Comment: 10 pages (RevTeX), TIT/HEP-253/COSMO-4
Higher Spin Field Equation in a Virtual Black Hole Metric
In a quantum theory of gravity, fluctuations about the vacuum may be
considered as Planck scale virtual black holes appearing and annihilating in
pairs. Incident fields scattering from such fluctuations would lose quantum
coherence.
In a recent paper (hep-th/9705147), Hawking and Ross obtained an estimate for
the magnitude of this loss in the case of a scalar field. Their calculation
exploited the separability of the conformally invariant scalar wave equation in
the electrovac C metric background, which is justified as a sufficiently good
description of a virtual black hole pair in the limit considered.
In anticipation of extending this result, the Teukolsky equations for
incident fields of higher spin are separated on the vacuum C metric background
and solved in the same limit. With the exception of spin 2 fields, these
equations are shown in addition to be valid on the electrovac C metric
background. The angular solutions are found to reduce to the spin- weighted
spherical harmonics, and the radial solutions are found to approach
hypergeometrics close to the horizons.
By defining appropriate scattering boundary conditions, these solutions are
then used to estimate the transmission and reflection coefficients for an
incident field of spin s. The transmission coefficient is required in order to
estimate the loss of quantum coherence of an incident field through scattering
off virtual black holes.Comment: 23 pages, 3 figures, LaTeX, minor typo correcte
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