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32
Homogeneous Plane Waves
, 2002
"... Motivated by the search for potentially exactly solvable timedependent string backgrounds, we determine all homogeneous plane wave (HPW) metrics in any dimension and find one family of HPWs with geodesically complete metrics and another with metrics with null singularities. The former generalises b ..."
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Cited by 22 (2 self)
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Motivated by the search for potentially exactly solvable timedependent string backgrounds, we determine all homogeneous plane wave (HPW) metrics in any dimension and find one family of HPWs with geodesically complete metrics and another with metrics with null singularities. The former generalises both the CahenWallach (constant Aij) metrics to timedependent HPWs, Aij(t), and the OzsvathSchücking antiMach metric to arbitrary dimensions. The latter is a generalisation of the known homogeneous metrics with Aij ∼ 1/t2 to a more complicated timedependence. We display these metrics in various coordinate systems, show how to embed them into string theory, and determine the isometry algebra of a general HPW and the associated conserved charges. We review the LewisRiesenfeld theory of invariants of timedependent harmonic oscillators and show how it can be deduced from the geometry of plane waves. We advocate the use of the invariant associated with the extra (timelike) isometry of HPWs for lightcone quantisation, and illustrate the procedure in some examples.
String theory and the classical stability of plane waves,” Phys
 Rev. D
, 2003
"... The presence of fields with negative mass–squared typically leads to some form of instability in standard field theories. The observation that, at least in the light–cone gauge, strings propagating in plane wave spacetimes can have worldsheet scalars with such tachyon–like masses suggests that the s ..."
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Cited by 20 (1 self)
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The presence of fields with negative mass–squared typically leads to some form of instability in standard field theories. The observation that, at least in the light–cone gauge, strings propagating in plane wave spacetimes can have worldsheet scalars with such tachyon–like masses suggests that the supergravity background may itself be unstable. To address this issue, we perform a perturbative analysis around the type IIB vacuum plane wave, the solution which most obviously generates worldsheet scalars with negative mass–squared. We argue that this background is perturbatively stable. 1 1
Causal inheritance in plane wave quotients
, 2003
"... We investigate the appearance of closed timelike curves in quotients of plane waves along spacelike isometries. First we formulate a necessary and sufficient condition for a quotient of a general spacetime to preserve stable causality. We explicitly show that the plane waves are stably causal; in pa ..."
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Cited by 19 (3 self)
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We investigate the appearance of closed timelike curves in quotients of plane waves along spacelike isometries. First we formulate a necessary and sufficient condition for a quotient of a general spacetime to preserve stable causality. We explicitly show that the plane waves are stably causal; in passing, we observe that some ppwaves are not even distinguishing. We then consider the classification of all quotients of the maximally supersymmetric tendimensional plane wave under a spacelike isometry, and show that the quotient will lead to closed timelike curves iff the isometry involves a translation along the u direction. The appearance of these closed timelike curves is thus connected to the special properties of the light cones in plane wave spacetimes. We show that all other quotients preserve stable causality.
The Causal Boundary of spacetimes revisited
, 2007
"... We present a new development of the causal boundary of spacetimes, originally introduced by Geroch, Kronheimer and Penrose. Given a strongly causal spacetime (or, more generally, a chronological set), we reconsider the GKP ideas to construct a family of completions with a chronology and topology ext ..."
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Cited by 11 (4 self)
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We present a new development of the causal boundary of spacetimes, originally introduced by Geroch, Kronheimer and Penrose. Given a strongly causal spacetime (or, more generally, a chronological set), we reconsider the GKP ideas to construct a family of completions with a chronology and topology extending the original ones. Many of these completions present undesirable features, like those appeared in previous approaches by other authors. However, we show that all these deficiencies are due to the attachment of an “excessively big ” boundary. In fact, a notion of “completion with minimal boundary ” is then introduced in our family such that, when we restrict to these minimal completions, which always exist, all previous objections disappear. The optimal character of our construction is illustrated by a number of satisfactory properties and examples.
Causal structures and causal boundaries
, 2005
"... We give an uptodate perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications, and the definition and construction of causal boundaries and of ..."
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Cited by 11 (0 self)
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We give an uptodate perspective with a general overview of the theory of causal properties, the derived causal structures, their classification and applications, and the definition and construction of causal boundaries and of
The causal boundary of wavetype spacetimes
 J. High Energy Phys
"... Abstract. A complete and systematic approach to compute the causal boundary of wavetype spacetimes is carried out. The case of a 1dimensional boundary is specially analyzed and its critical appearance in ppwave type spacetimes is emphasized. In particular, the corresponding results obtained in th ..."
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Cited by 10 (4 self)
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Abstract. A complete and systematic approach to compute the causal boundary of wavetype spacetimes is carried out. The case of a 1dimensional boundary is specially analyzed and its critical appearance in ppwave type spacetimes is emphasized. In particular, the corresponding results obtained in the framework of the AdS/CFT correspondence for holography on the boundary, are reinterpreted and very widely generalized. Technically, a recent new definition of causal boundary is used and stressed. Moreover, a set of mathematical tools is introduced (analytical functional approach, SturmLiouville theory, Fermattype arrival time, Busemanntype functions).
On the maximal superalgebras of supersymmetric backgrounds
"... Abstract. In this note we give a precise definition of the notion of a maximal superalgebra of certain types of supersymmetric supergravity backgrounds, including the Freund–Rubin backgrounds, and propose a geometric construction extending the wellknown construction of its Killing superalgebra. We ..."
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Cited by 7 (3 self)
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Abstract. In this note we give a precise definition of the notion of a maximal superalgebra of certain types of supersymmetric supergravity backgrounds, including the Freund–Rubin backgrounds, and propose a geometric construction extending the wellknown construction of its Killing superalgebra. We determine the structure of maximal Lie superalgebras and show that there is a finite number of isomorphism classes, all related via contractions from an orthosymplectic Lie superalgebra. We use the structure theory to show that maximally supersymmetric waves do not possess such a maximal superalgebra, but that the maximally supersymmetric Freund–Rubin backgrounds do. We perform the explicit geometric construction of the maximal superalgebra of AdS4 ×S 7 and find that is isomorphic to osp(132). We propose an algebraic construction of the maximal superalgebra of any background asymptotic to AdS4 ×S 7 and we test this proposal by computing the maximal superalgebra of the M2brane in its two maximally supersymmetric limits, finding agreement. Contents