Junction Conditions and local Spacetimes in General Relativity

Abstract

In the present work, a theoretical framework focussing on local geometric deformations is introduced in order to cope with the problem of how to join spacetimes with different geometries and physical properties. Using this framework, it is shown that two Lorentzian manifolds can be matched in agreement with the well-known Darmois-Israel junction conditions by locally deforming the associated spacetime metrics in relation to each other. Based on the insight that metrics can be suitably matched in this way, it is shown that the underlying geometric approach allows the characterization of local spacetimes in General Relativity. In addition, it is shown that this approach allows the treatment of problems that cannot be treated by using standard gluing techniques.

arXiv comment36 pages, matches published version

References in corpus (19)

• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Analog gravity from Bose-Einstein condensates
• Geometry of General Hypersurfaces in Spacetime: Junction Conditions
• On Gravitational Shock Waves in Curved Spacetimes
• Acoustic geometry for general relativistic barotropic irrotational fluid flow
• Relativistic Bose-Einstein Condensates: a new system for analogue models of gravity
• Initial Data and Coordinates for Multiple Black Hole Systems
• Is the gravitational action additive?
• Solving the Initial Value Problem of two Black Holes
• Junction conditions in quadratic gravity: thin shells and double layers
• Physics and Initial Data for Multiple Black Hole Spacetimes
• The large central charge limit of conformal blocks
• Double layers in gravity theories
• Equations for general shells
• Building SO(10) models from F-theory
• Analogue Gravity Models From Conformal Rescaling
• Kerr-Schild type initial data for black holes with angular momenta
• A simple method of constructing binary black hole initial data
• Distributional Metrics and the Action Principle of Einstein-Hilbert Gravity

Cited by in corpus (6)

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• Junction conditions for LRS spacetimes in the $1+1+2$ covariant formalism
• Hidden Killing Fields, Geometric Symmetries and Black Hole Mergers
• The gravitational Field of a massless Particle on the Horizon of a stationary Black Hole
• General Shells and Generalized Functions
• Dynamical Horizons and Black Hole Soft Hair