8,632 research outputs found
Penrose Limits and Spacetime Singularities
We give a covariant characterisation of the Penrose plane wave limit: the
plane wave profile matrix is the restriction of the null geodesic
deviation matrix (curvature tensor) of the original spacetime metric to the
null geodesic, evaluated in a comoving frame. We also consider the Penrose
limits of spacetime singularities and show that for a large class of black
hole, cosmological and null singularities (of Szekeres-Iyer ``power-law
type''), including those of the FRW and Schwarzschild metrics, the result is a
singular homogeneous plane wave with profile , the scale
invariance of the latter reflecting the power-law behaviour of the
singularities.Comment: 9 pages, LaTeX2e; v2: additional references and cosmetic correction
The Refractive Index of Curved Spacetime II: QED, Penrose Limits and Black Holes
This work considers the way that quantum loop effects modify the propagation
of light in curved space. The calculation of the refractive index for scalar
QED is reviewed and then extended for the first time to QED with spinor
particles in the loop. It is shown how, in both cases, the low frequency phase
velocity can be greater than c, as found originally by Drummond and Hathrell,
but causality is respected in the sense that retarded Green functions vanish
outside the lightcone. A "phenomenology" of the refractive index is then
presented for black holes, FRW universes and gravitational waves. In some
cases, some of the polarization states propagate with a refractive index having
a negative imaginary part indicating a potential breakdown of the optical
theorem in curved space and possible instabilities.Comment: 62 pages, 14 figures, some signs corrected in formulae and graph
Goedel, Penrose, anti-Mach: extra supersymmetries of time-dependent plane waves
We prove that M-theory plane waves with extra supersymmetries are necessarily
homogeneous (but possibly time-dependent), and we show by explicit construction
that such time-dependent plane waves can admit extra supersymmetries. To that
end we study the Penrose limits of Goedel-like metrics, show that the Penrose
limit of the M-theory Goedel metric (with 20 supercharges) is generically a
time-dependent homogeneous plane wave of the anti-Mach type, and display the
four extra Killings spinors in that case. We conclude with some general remarks
on the Killing spinor equations for homogeneous plane waves.Comment: 20 pages, LaTeX2
On solvable models of type IIB superstring in NS-NS and R-R plane wave backgrounds
We consider type IIB string in the two plane-wave backgrounds which may be
interpreted as special limits of the AdS_3 x S^3 metric supported by either the
NS-NS or R-R 3-form field. The NS-NS plane-wave string model is equivalent to a
direct generalization of the Nappi-Witten model, with its spectrum being
similar to that of strings in constant magnetic field. The R-R model can be
solved in the light-cone gauge, where the Green-Schwarz action describes 4
massive and 4 massless copies of free bosons and fermions. We find the spectra
of the two string models and study the asymptotic density of states. We also
discuss a more general class of exactly solvable plane-wave models with reduced
supersymmetry which is obtained by adding twists in two spatial 2-planes.Comment: 36 pages, harvmac. v2: discussion of equivalence of the supergravity
parts of the spectra of the NS-NS and R-R models added in sect.5.3; v3: added
remark on periodicity of the NS-NS spectrum; v4: minor correction in sect.6.
A Representation of Symmetry Generators for the Type IIB Superstring on a Plane Wave in the U(4) Formalism
We calculate the symmetry currents for the type IIB superstring on a
maximally supersymmetric plane wave background using the N=(2,2)
superconformally covariant U(4) formulation developed by Berkovits, Maldacena
and Maoz. An explicit realization of the U(4) generators together with 16
fermionic generators is obtained in terms of the N=(2,2) worldsheet fields.
Because the action is no longer quadratic, we use a light-cone version to
display the currents in terms of the covariant worldsheet variables.Comment: 9 pages, harvmac, Corrected some typographical errors, Added
reference
The Conformal Penrose Limit and the Resolution of the pp-curvature Singularities
We consider the exact solutions of the supergravity theories in various
dimensions in which the space-time has the form M_{d} x S^{D-d} where M_{d} is
an Einstein space admitting a conformal Killing vector and S^{D-d} is a sphere
of an appropriate dimension. We show that, if the cosmological constant of
M_{d} is negative and the conformal Killing vector is space-like, then such
solutions will have a conformal Penrose limit: M^{(0)}_{d} x S^{D-d} where
M^{(0)}_{d} is a generalized d-dimensional AdS plane wave. We study the
properties of the limiting solutions and find that M^{(0)}_{d} has 1/4
supersymmetry as well as a Virasoro symmetry. We also describe how the
pp-curvature singularity of M^{(0)}_{d} is resolved in the particular case of
the D6-branes of D=10 type IIA supergravity theory. This distinguished case
provides an interesting generalization of the plane waves in D=11 supergravity
theory and suggests a duality between the SU(2) gauged d=8 supergravity of
Salam and Sezgin on M^{(0)}_{8} and the d=7 ungauged supergravity theory on its
pp-wave boundary.Comment: 20 pages, LaTeX; typos corrected, journal versio
All spacetimes with vanishing curvature invariants
All Lorentzian spacetimes with vanishing invariants constructed from the
Riemann tensor and its covariant derivatives are determined. A subclass of the
Kundt spacetimes results and we display the corresponding metrics in local
coordinates. Some potential applications of these spacetimes are discussed.Comment: 24 page
Kaigorodov spaces and their Penrose limits
Kaigorodov spaces arise, after spherical compactification, as near horizon
limits of M2, M5, and D3-branes with a particular pp-wave propagating in a
world volume direction. We show that the uncompactified near horizon
configurations K\times S are solutions of D=11 or D=10 IIB supergravity which
correspond to perturbed versions of their AdS \times S analogues. We derive the
Penrose-Gueven limits of the Kaigorodov space and the total spaces and analyse
their symmetries. An Inonu-Wigner contraction of the Lie algebra is shown to
occur, although there is a symmetry enhancement. We compare the results to the
maximally supersymmetric CW spaces found as limits of AdS\times S spacetimes:
the initial gravitational perturbation on the brane and its near horizon
geometry remains after taking non-trivial Penrose limits, but seems to
decouple. One particuliar limit yields a time-dependent homogeneous plane-wave
background whose string theory is solvable, while in the other cases we find
inhomogeneous backgrounds.Comment: latex2e, 24 page
N=(4,4) Type IIA String Theory on PP-Wave Background
We construct IIA GS superstring action on the ten-dimensional pp-wave
background, which arises as the compactification of eleven-dimensional pp-wave
geometry along the isometry direction. The background geometry has 24 Killing
spinors and among them, 16 components correspond to the non-linearly realized
kinematical supersymmetry in the string action. The remaining eight components
are linearly realized and shown to be independent of x^+ coordinate, which is
identified with the world-sheet time coordinate of the string action in the
light-cone gauge. The resultant dynamical N=(4,4) supersymmetry is
investigated, which is shown to be consistent with the field contents of the
action containing two free massive supermultiplets.Comment: latex, 15 pages; v2: typos corrected, polished, references adde
Vector Supersymmetry of 2D Yang-Mills Theory
The vector supersymmetry of the 2D topological BF model is extended to 2D
Yang-Mills. The consequences of the corresponding Ward identity on the
ultraviolet behavior of the theory are analyzed.Comment: Some references adde
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