Penrose Limits and Spacetime Singularities

Abstract

We give a covariant characterisation of the Penrose plane wave limit: the plane wave profile matrix $A(u)$ 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 $A(u)\sim u^{-2}$, the scale invariance of the latter reflecting the power-law behaviour of the singularities.

9 pages, LaTeX2e; v2: additional references and cosmetic corrections

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Cited by in corpus (40)

• The G_2 spinorial geometry of supersymmetric IIB backgrounds
• The Causal Structure of QED in Curved Spacetime: Analyticity and the Refractive Index
• Cosmologies with Null Singularities and their Gauge Theory Duals
• Fermi Coordinates and Penrose Limits
• The Universality of Penrose Limits near Space-Time Singularities
• Penrose limits of homogeneous spaces
• The Refractive Index of Curved Spacetime II: QED, Penrose Limits and Black Holes
• Memory effect, conformal symmetry and gravitational plane waves
• Homogeneity and plane-wave limits
• String spectra near some null cosmological singularities
• From polarized gravitational waves to analytically solvable electromagnetic beams
• Niederer's transformation, time-dependent oscillators and polarized gravitational waves
• String Propagation through a Big Crunch/Big Bang Transition
• Can free strings propagate across plane wave singularities?
• Scalar Field Probes of Power-Law Space-Time Singularities
• Null cosmological singularities and free strings: II
• Exact Parallel Waves in General Relativity
• Killing tensors in pp-wave spacetimes
• Light-like Big Bang singularities in string and matrix theories
• On the Hagedorn Behaviour of Singular Scale-Invariant Plane Waves
• Ringdown nonlinearities in the eikonal regime
• Power-law singularities in string theory and M-theory
• Null cosmological singularities and free strings
• Penrose Limits vs String Expansions
• Memory Effect of Gravitational Wave Pulses in PP-Wave Spacetimes
• Observer dependent D-brane for strings propagating in pp-wave time dependent background
• A New Twist on the Geometry of Gravitational Plane Waves
• Electromagnetic memory in arbitrary curved space-times
• Asymptotic behaviour of curvature and matter in the Penrose limit
• String Excitation by Initial Singularity of Inflation
• pp-Waves and the Hidden Symmetries of Black Hole Quasinormal Modes
• Gravitational Waves from Thurston Geometries
• Separability, plane wave limits and black holes
• Tidal Forces in Kerr-AdS and Grey Galaxies
• Aspects of Plane Wave (Matrix) String Dynamics
• Holography and Cosmological Singularities
• Equivalence of a harmonic oscillator to a free particle and Eisenhart lift
• Free string evolution across plane wave singularities
• Test gravitational waves in sandwich wave background
• Penrose Limit and Non-relativistic geometries