4,100 research outputs found

### On Pairs of Difference Operators Satisfying: [P,Q] = Id

Different finite difference replacements for the derivative are analyzed in
the context of the Heisenberg commutation relation. The type of the finite
difference operator is shown to be tied to whether one can naturally consider
$P$ and $X$ to be self-adjoint and skew self-adjoint or whether they have to be
viewed as creation and annihilation operators. The first class, generalizing
the central difference scheme, is shown to give unitary equivalent
representations. For the second case we construct a large class of examples,
generalizing previously known difference operator realizations of $[P,X]=Id$.Comment: 32 pages, plain Te

### Gravitation as a Many Body Problem

The idea of viewing gravitation as a many body phenomenon is put forward here. Physical arguments supporting this idea are briefly reviewed. The basic mathematical object of the new gravitational mechanics is a matrix of operators. Striking similarity of the method of R-matrix (QISM) to the mathematical formulation of the new gravitational mechanics is pointed out. The s-wave difference Schrodinger equation describing a process of emission of radiation by a gravitating particle is shown to be analogous to the Baxter equation of the QISM

### Charging a Double Kerr Solution in 5D Einstein--Maxwell--Kalb--Ramond Theory

We consider the low-energy effective action of the 5D
Einstein-Maxwell-Kalb-Ramond theory. After compactifying this truncated model
on a two-torus and switching off the U(1) vector fields of this theory, we
recall a formulation of the resulting three-dimensional action as a double
Ernst system coupled to gravity. Further, by applying the so-called normalized
Harrison transformation on a generic solution of this double Ernst system we
recover the U(1) vector field sector of the theory. Afterward, we compute the
field content of the generated charged configuration for the special case when
the starting Ernst potentials correspond to a pair of interacting Kerr black
holes, obtaining in this way an exact field configuration of the 5D
Einstein-Maxwell-Kalb-Ramond theory endowed with effective Coulomb and dipole
terms with momenta. Some physical properties of this object are analyzed as
well as the effect of the normalized Harrison transformation on the double Kerr
seed solution.Comment: 15 pages in latex, revised versio

### 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

### Are There Topological Black Hole Solitons in String Theory?

We point out that the celebrated Hawking effect of quantum instability of
black holes seems to be related to a nonperturbative effect in string theory.
Studying quantum dynamics of strings in the gravitational background of black
holes we find classical instability due to emission of massless string
excitations. The topology of a black hole seems to play a fundamental role in
developing the string theory classical instability due to the effect of sigma
model instantons. We argue that string theory allows for a qualitative
description of black holes with very small masses and it predicts topological
solitons with quantized spectrum of masses. These solitons would not decay into
string massless excitations but could be pair created and may annihilate also.
Semiclassical mass quantization of topological solitons in string theory is
based on the argument showing existence of nontrivial zeros of beta function of
the renormalization group.Comment: 12 pages, TeX, requires phyzzx.tex, published in Gen. Rel. Grav. 19
(1987) 1173; comment added on December 18, 199

### Limit structure of Future Null Infinity tangent -topology of the event horizon and gravitational wave tail-

We investigated the relation between the behavior of gravitational wave at
late time and the limit structure of future null infinity tangent which will
determine the topology of the event horizon far in the future. In the present
article, we mainly consider a spacetime with two black holes. Although in most
of cases, the black holes coalesce and its event horizon is topologically a
single sphere far in the future, there are several possibilities that the black
holes never coalesce and such exact solutions as examples. In our formulation,
the tangent vector of future null infinity is, under conformal embedding,
related to the number of black holes far in the future through the
Poincar\'e-Hopf's theorem. Under the conformal embedding, the topology of event
horizon far in the future will be affected by the geometrical structure of the
future null infinity. In this article, we related the behavior of Weyl
curvature to this limit behavior of the generator vector of the future null
infinity. We show if Weyl curvature decays sufficiently slowly at late time in
the neighborhood of future null infinity, two black holes never coalesce.Comment: 20 pages, 3 figures, accepted for publication in Class. Quant. Gra

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