Equations for general shells

Abstract

The complete set of (field) equations for shells of arbitrary, even changing, causal character are derived in arbitrary dimension. New equations that seem to have never been considered in the literature emerge, even in the traditional cases of everywhere non-null, or everywhere null, shells. In the latter case there arise field equations for some degrees of freedom encoded exclusively in the distributional part of the Weyl tensor. For non-null shells the standard Israel equations are recovered but not only, the additional relations containing also relevant information. The results are applicable to a widespread literature on domain walls, branes and braneworlds, gravitational layers, impulsive gravitational waves, and the like. Moreover, they are of a geometric nature, and thus they can be used in any theory based on a Lorentzian manifold.

32 pages, no figures. New paragraph and new footnote, plus some added references. Version to be published

References in corpus (9)

• Gravitational action with null boundaries
• The use of Generalised Functions and Distributions in General Relativity
• Boundary terms of the Einstein-Hilbert action
• Lorentzian and signature changing branes
• Generalized Israel Junction Conditions for a Fourth-Order Brane World
• Bel-Debever criteria for the classification of the Weyl tensors in higher dimensions
• Is the accelerated expansion evidence of a forthcoming change of signature on the brane?
• Double layers in gravity theories
• Area deficits and the Bel-Robinson tensor

Cited by in corpus (14)

• A consistent model of non-singular Schwarzschild black hole in loop quantum gravity and its quasinormal modes
• Junction conditions in scalar-tensor theories
• Null shells: general matching across null boundaries and connection with cut-and-paste formalism
• Double layer from least action principle
• Junction Conditions and local Spacetimes in General Relativity
• General matching across Killing horizons of zero order
• Energy conditions for non-timelike thin shells
• On weak solutions in Einstein theory and beyond
• Variational formalism for generic shells in general relativity
• Lightlike singular hypersurfaces in quadratic gravity
• Junction conditions in a general field theory
• Black holes and their horizons in semiclassical and modified theories of gravity
• Solutions of the Einstein field equations for a bounded and finite discontinuous source, and its generalization: Metric matching conditions and jumping effects
• General Shells and Generalized Functions