Search results for "Cauchy surface"

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Diffeomorphisms, Noether charges, and the canonical formalism in two-dimensional dilaton gravity

1995

We carry out a parallel study of the covariant phase space and the conservation laws of local symmetries in two-dimensional dilaton gravity. Our analysis is based on the fact that the Lagrangian can be brought to a form that vanishes on-shell giving rise to a well-defined covariant potential for the symplectic current. We explicitly compute the symplectic structure and its potential and show that the requirement to be finite and independent of the Cauchy surface restricts the asymptotic symmetries.

AstrofísicaPhysicsGravitacióSymplectic representationsymbols.namesakeSymplectic vector spaceCauchy surfaceClassical mechanicssymbolsDilatonNoether's theoremSymplectomorphismMathematics::Symplectic GeometrySymplectic geometryMathematical physicsSymplectic manifoldPhysical Review D
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The Light Ray transform in Stationary and Static Lorentzian geometries

2019

Given a Lorentzian manifold, the light ray transform of a function is its integrals along null geodesics. This paper is concerned with the injectivity of the light ray transform on functions and tensors, up to the natural gauge for the problem. First, we study the injectivity of the light ray transform of a scalar function on a globally hyperbolic stationary Lorentzian manifold and prove injectivity holds if either a convex foliation condition is satisfied on a Cauchy surface on the manifold or the manifold is real analytic and null geodesics do not have cut points. Next, we consider the light ray transform on tensor fields of arbitrary rank in the more restrictive class of static Lorentzia…

Mathematics - Differential GeometryGeodesicinverse problems010102 general mathematicsMathematical analysislight ray transform01 natural sciencesRayFoliationManifoldinversio-ongelmatTensor field010101 applied mathematicsCauchy surfaceMathematics - Analysis of PDEsDifferential geometryDifferential Geometry (math.DG)FOS: Mathematicswave equationGeometry and TopologyMathematics::Differential Geometry0101 mathematicsScalar fieldMathematicsAnalysis of PDEs (math.AP)
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