Article

# Born-Infeld Theory and Stringy Causality

Physical Review D (impact factor: 4.56). 02/2001; 63(6):064006. DOI:10.1103/PhysRevD.63.064006 pp.064006
Source: arXiv

ABSTRACT Fluctuations around a non-trivial solution of Born-Infeld theory have a limiting speed given not by the Einstein metric but the Boillat metric. The Boillat metric is S-duality invariant and conformal to the open string metric. It also governs the propagation of scalars and spinors in Born-Infeld theory. We discuss the potential clash between causality determined by the closed string and open string light cones and find that the latter never lie outside the former. Both cones touch along the principal null directions of the background Born-Infeld field. We consider black hole solutions in situations in which the distinction between bulk and brane is not sharp such as space filling branes and find that the location of the event horizon and the thermodynamic properties do not depend on whether one uses the closed or open string metric. Analogous statements hold in the more general context of non-linear electrodynamics or effective quantum-corrected metrics. We show how Born-Infeld action to second order might be obtained from higher-curvature gravity in Kaluza-Klein theory. Finally we point out some intriguing analogies with Einstein-Schr\"odinger theory.

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##### Article:Riemann problem for the Born-Infeld system without differential constraints
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ABSTRACT: We consider the Born-Infeld system without differential constraints. Such a situation occurs as soon as the differential constraints are not satisfied at the initial time. In such a case, the Poynting vector is not a conservative variable and the technique of enlargement of systems cannot be applied. In one space dimension the resulting system consists of five conservative equations for which only one Riemann invariant exists. It is fully linearly degenerate but not strictly hyperbolic, nor is it rich. Under a smallness condition on the initial datum of one variable, we prove that the Riemann problem has a unique entropy solution having discontinuities with three separated speeds. It is surprising that the result holds even for initial data lied in non hyperbolic regions.
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##### Article:Bi-refringence versus bi-metricity
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ABSTRACT: In this article we carefully distinguish the notion of bi-refringence (a polarization-dependent doubling in photon propagation speeds) from that of bi-metricity (where the two photon polarizations see'' two distinct metrics). We emphasise that these notions are logically distinct, though there are special symmetries in ordinary (3+1)-dimensional nonlinear electrodynamics which imply the stronger condition of bi-metricity. To illustrate this phenomenon we investigate a generalized version of (3+1)-dimensional nonlinear electrodynamics, which permits the inclusion of arbitrary inhomogeneities and background fields. [For example dielectrics (a la Gordon), conductors (a la Casimir), and gravitational fields (a la Landau--Lifshitz).] It is easy to demonstrate that the generalized theory is bi-refringent: In (3+1) dimensions the Fresnel equation, the relationship between frequency and wavenumber, is always quartic. It is somewhat harder to show that in some cases (eg, ordinary nonlinear electrodynamics) the quartic factorizes into two quadratics thus providing a bi-metric theory. Sometimes the quartic is a perfect square, implying a single unique effective metric. We investigate the generality of this factorization process.
05/2002;
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##### Article:Derivation of particle, string, and membrane motions from the Born–Infeld electromagnetism
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ABSTRACT: We derive classical particle, string and membrane motion equations from a rigorous asymptotic analysis of the Born-Infeld nonlinear electromagnetic theory. We first add to the Born-Infeld equations the corresponding energy-momentum conservation laws and write the resulting system as a non-conservative symmetric 10 × 10 system of first-order PDEs. Then, we show that four rescaled versions of the system have smooth solutions existing in the (finite) time interval where the corresponding limit problems have smooth solutions. Our analysis is based on a continuation principle previously formulated by the second author for (singular) limit problems.

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### Keywords

Analogous statements

background Born-Infeld field

black hole solutions

Born-Infeld action

Born-Infeld theory

branes

closed string

cones touch

effective quantum-corrected metrics

event horizon

intriguing analogies

non-linear electrodynamics

non-trivial solution

open string light cones

open string metric

potential clash

principal null directions

second order

spinors

thermodynamic properties