First and Second Order Perturbations of Hypersurfaces

Abstract

In this paper we find the first and second order perturbations of the induced metric and the extrinsic curvature of a non-degenerate hypersurface $\Sigma$ in a spacetime $(M,g)$, when the metric $g$ is perturbed arbitrarily to second order and the hypersurface itself is allowed to change perturbatively (i.e. to move within spacetime) also to second order. The results are fully general and hold in arbitrary dimensions and signature. An application of these results for the perturbed matching theory between spacetimes is presented.

31 pages, no figures. To be published in Classical and Quantum Gravity

References in corpus (4)

• Non-Gaussianity from Inflation: Theory and Observations
• Effect of inhomogeneities on the expansion rate of the Universe
• Unified treatment of cosmological perturbations from super-horizon to small scales
• Gauge-Invariant Temperature Anisotropies and Primordial Non-Gaussianity

Cited by in corpus (25)

• Second and higher-order perturbations of a spherical spacetime
• Phenomenological Relations for Axial Quasi-normal Modes of Neutron Stars with Realistic Equations of State
• Review on exact and perturbative deformations of the Einstein-Straus model: uniqueness and rigidity results
• Revisiting Hartle's model using perturbed matching theory to second order: amending the change in mass
• Completion of the universal I-Love-Q relations in compact stars including the mass
• Linear perturbations of matched spacetimes: the gauge problem and background symmetries
• Slowly rotating homogeneous masses revisited
• High-order perturbations of a spherical collapsing star
• Stationary axisymmetric exteriors for perturbations of isolated bodies in general relativity, to second order
• First order perturbations of the Einstein-Straus and Oppenheimer-Snyder models
• Thin Shell Dynamics and Equations of State
• Slowly rotating Tolman VII solution
• A revised formalism for slowly-rotating superfluid neutron stars in general relativity
• Gauge fixing and regularity of axially symmetric and axistationary second order perturbations around spherical backgrounds
• A generalization of the Zerilli master variable for a dynamical spherical spacetime
• Transverse expansion of the metric at null hypersurfaces I. Uniqueness and application to Killing horizons
• On the mass of rotating stars in Newtonian gravity and GR
• Supertranslations: redundancies of horizon data, and global symmetries at null infinity
• Existence and uniqueness of compact rotating configurations in GR in second order perturbation theory
• Slowly rotating ultracompact Schwarzschild star in the gravastar limit
• First order perturbations of hypersurfaces of arbitrary causal character
• Review on the matching conditions for the tidal problem: towards the application to more general contexts
• Collapsing Layers on Schwarzschild-Lemaitre Geodesics
• Covariant higher order perturbations of branes in curved spacetime
• Hartle's model within the general theory of perturbative matchings: the change in mass