989 research outputs found

### Graphene and the Zermelo Optical Metric of the BTZ Black Hole

It is well known that the low energy electron excitations of the curved
graphene sheet $\Sigma$ are solutions of the massless Dirac equation on a 2+1
dimensional ultra-static metric on ${\Bbb R} \times \Sigma$. An externally
applied electric field on the graphene sheet induces a gauge potential which
could be mimicked by considering a stationary optical metric of the Zermelo
form, which is conformal to the BTZ black hole when the sheet has a constant
negative curvature. The Randers form of the metric can model a magnetic field,
which is related by a boost to an electric one in the Zermelo frame. We also
show that there is fundamental geometric obstacle to obtaining a model that
extends all the way to the black hole horizon.Comment: 10 pages Latex, no figures, substantial revisions, relation between
magnetic and electric fields and Randers and Zermelo forms clarifie

### Dilaton Black Holes Near the Horizon

Generic $U(1)^2$ 4-d black holes with unbroken $N=1$ supersymmetry are shown
to tend to a Robinson-Bertotti type geometry with a linear dilaton and doubling
of unbroken supersymmetries near the horizon. Purely magnetic dilatonic black
holes, which have unbroken $N=2$ supersymmetry, behave near the horizon as a
2-d linear dilaton vacuum $\otimes \, S^2$. This geometry is invariant under 8
supersymmetries, i.e. half of the original $N=4$ supersymmetries are unbroken.
The supersymmetric positivity bound, which requires the mass of the 4-d dilaton
black holes to be greater than or equal to the central charge, corresponds to
positivity of mass for a class of stringy 2-d black holes.Comment: 10 pages, SU-ITP-92-2

### Cones, Tri-Sasakian Structures and Superconformal Invariance

In this note we show that rigid N=2 superconformal hypermultiplets must have
target manifolds which are cones over tri-Sasakian metrics. We comment on the
relation of this work to cone-branes and the AdS/CFT correspondence.Comment: 10 pages, Latex2

### SL(2,R) Invariance of Non-Linear Electrodynamics Coupled to An Axion and a Dilaton

The most general Lagrangian for non-linear electrodynamics coupled to an
axion $a$ and a dilaton $\phi$ with SL(2,\mbox{\elevenmsb R}) invariant
equations of motion is -\half\left(\nabla\phi\right)^2 - \half
e^{2\phi}\left(\nabla a\right)^2 + \fraction{1}{4}aF_{\mu\nu}\star F^{\mu\nu} +
L_{\rm inv}(g_{\mu\nu},e^{-\frac{1}{2}\phi}F_{\rho\sigma}) where $L_{\rm
inv}(g_{\mu\nu},F_{\rho\sigma})$ is a Lagrangian whose equations of motion are
invariant under electric-magnetic duality rotations. In particular there is a
unique generalization of Born-Infeld theory admitting SL(2,\mbox{\elevenmsb
R}) invariant equations of motion.Comment: 9 pages, LaTe

### Fixed Scalars and Suppression of Hawking Evaporation

For an extreme charged black hole some scalars take on a fixed value at the
horizon determined by the charges alone. We call them fixed scalars. We find
the absorption cross section for a low frequency wave of a fixed scalar to be
proportional to the square of the frequency. This implies a strong suppression
of the Hawking radiation near extremality. We compute the coefficient of
proportionality for a specific model.Comment: 10 pages, late

### Topology, Entropy and Witten Index of Dilaton Black Holes

We have found that for extreme dilaton black holes an inner boundary must be
introduced in addition to the outer boundary to give an integer value to the
Euler number. The resulting manifolds have (if one identifies imaginary time)
topology $S^1 \times R \times S^2$ and Euler number $\chi = 0$ in contrast to
the non-extreme case with $\chi=2$. The entropy of extreme $U(1)$ dilaton black
holes is already known to be zero. We include a review of some recent ideas due
to Hawking on the Reissner-Nordstr\"om case. By regarding all extreme black
holes as having an inner boundary, we conclude that the entropy of {\sl all}
extreme black holes, including $[U(1)]^2$ black holes, vanishes. We discuss the
relevance of this to the vanishing of quantum corrections and the idea that the
functional integral for extreme holes gives a Witten Index. We have studied
also the topology of ``moduli space'' of multi black holes. The quantum
mechanics on black hole moduli spaces is expected to be supersymmetric despite
the fact that they are not HyperK\"ahler since the corresponding geometry has
torsion unlike the BPS monopole case. Finally, we describe the possibility of
extreme black hole fission for states with an energy gap. The energy released,
as a proportion of the initial rest mass, during the decay of an
electro-magnetic black hole is 300 times greater than that released by the
fission of an ${}^{235} U$ nucleus.Comment: 51 pages, 4 figures, LaTeX. Considerably extended version. New
sections include discussion of the Witten index, topology of the moduli
space, black hole sigma model, and black hole fission with huge energy
releas

### The geometry of sound rays in a wind

We survey the close relationship between sound and light rays and geometry.
In the case where the medium is at rest, the geometry is the classical geometry
of Riemann. In the case where the medium is moving, the more general geometry
known as Finsler geometry is needed. We develop these geometries ab initio,
with examples, and in particular show how sound rays in a stratified atmosphere
with a wind can be mapped to a problem of circles and straight lines.Comment: Popular review article to appear in Contemporary Physic

### Spinning particles in Taub-NUT space

The geodesic motion of pseudo-classical spinning particles in Euclidean
Taub-NUT space is analysed. The constants of motion are expressed in terms of
Killing-Yano tensors. Some previous results from the literature are corrected.Comment: LaTeX, 8 page

### On the Obstructions to non-Cliffordian Pin Structures

We derive the topological obstructions to the existence of non-Cliffordian
pin structures on four-dimensional spacetimes. We apply these obstructions to
the study of non-Cliffordian pin-Lorentz cobordism. We note that our method of
derivation applies equally well in any dimension and in any signature, and we
present a general format for calculating obstructions in these situations.
Finally, we interpret the breakdown of pin structure and discuss the relevance
of this to aspects of physics.Comment: 31 pages, latex, published in Comm. Math. Phys. 164, No. 1, pages
65-87 (1994

### Black-Hole-Wave Duality in String Theory

Extreme 4-dimensional dilaton black holes embedded into 10-dimensional
geometry are shown to be dual to the gravitational waves in string theory. The
corresponding gravitational waves are the generalization of pp-fronted waves,
called supersymmetric string waves. They are given by Brinkmann metric and the
two-form field, without a dilaton. The non-diagonal part of the metric of the
dual partner of the wave together with the two-form field correspond to the
vector field in 4-dimensional geometry of the charged extreme black holes.Comment: 12 pages, LaTeX, preprint UG-3/94, SU-ITP-94-11, QMW-PH-94-1

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