Einstein Equations via Null Surfaces

Iyer, Savitri V.; Newman, Ezra T.; Kozameh, Carlos N.

doi:10.12693/aphyspola.85.647

Cited by 2 publications

(2 citation statements)

References 8 publications

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“…Though there has been a considerable amount of technical material written on this program already 1,2,3,4 , recent developments considerably simplify the earlier work and suggest that a new complete presentation would be worthwhile. The discussion here is intended to be essentially self-contained.…”

Section: Introductionmentioning

confidence: 99%

“…The formulation is in terms of two functions, Ω(x, S 2 ) and Z(x, S 2 ), of the space-time points, x a , and parametrized by points on the sphere, i.e., by functions on the sphere-bundle over a space-time manifold, functions on R 4 xS 2 . The first of the functions Ω, is to be considered as a conformal factor for a sphere's worth of conformal metrics -the factor turning the conformal metrics into Einstein metrics -while the second function, Z, describes, at each space-time point, a sphere's worth of characteristic surfaces.…”

Section: Introductionmentioning

confidence: 99%

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GR via characteristic surfaces

Frittelli

Kozameh

Newman

1995

Journal of Mathematical Physics

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We reformulate the Einstein equations as equations for families of surfaces on a four-manifold. These surfaces eventually become characteristic surfaces for an Einstein metric (with or without sources). In particular they are formulated in terms of two functions on R 4 xS 2 , i.e. the sphere bundle over space-time,-one of the functions playing the role of a conformal factor for a family of associated conformal metrics, the other function describing an S 2 's worth of surfaces at each space-time point. It is from these families of surfaces themselves that the conformal metric-conformal to an Einstein metric-is constructed; the conformal factor turns them into Einstein metrics. The surfaces are null surfaces with respect to this metric.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

GR via characteristic surfaces

Frittelli

Kozameh

Newman

1995

Journal of Mathematical Physics

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Solution for the null-surface formulation in 2+1 dimensions with radiation source

Harriott,

Williams

2024

Can. J. Phys.

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The null-surface formulation (NSF) of general relativity has three coupled and highly nonlinear eld equations whose solution determines (a family of) null surfaces indicated by the variable u. This variable is one of a set of intrinsic coordinates that are defined in terms of the surfaces. The first of the three field equations is called the main metricity condition, and it is by far the most complicated. This work considers the NSF in 2+1 dimensions and presents a solution that is founded on the following strategy: Simplify the main metricity condition by requiring the uu-component of the metric tensor to be zero and then search for an additively separable solution formed from a sum of separate terms, each term being linked with a term in a certain differential operator ∂ so as to cause a convenient cancellation. The main motivation for this approach is that it may suggest how to find a solution in higher dimensions, where the role of ∂ is played by the eth operator of Newman and Penrose.

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Einstein Equations via Null Surfaces

Cited by 2 publications

References 8 publications

GR via characteristic surfaces

GR via characteristic surfaces

Solution for the null-surface formulation in 2+1 dimensions with radiation source

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