The Newman–Penrose (NP) formalism is a set of notation developed by Ezra T. Newman and Roger Penrose for general relativity (GR). Their notation is an effort to treat general relativity in terms of spinor notation, which introduces complex forms of the usual variables used in GR. The NP formalism is itself a special case of the tetrad formalism, where the tensors of the theory are projected onto a complete vector basis at each point in spacetime. Usually this vector basis is chosen to reflect some symmetry of the spacetime, leading to simplified expressions for physical observables. In the case of the NP formalism, the vector basis chosen is a : a set of four null vectors—two real, and a complex-conjugate pair. The two real members asymptotically point radially inward and radially outward,
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| - Newman–Penrose formalism (en)
- Formalismo de Newman-Penrose (pt)
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| - The Newman–Penrose (NP) formalism is a set of notation developed by Ezra T. Newman and Roger Penrose for general relativity (GR). Their notation is an effort to treat general relativity in terms of spinor notation, which introduces complex forms of the usual variables used in GR. The NP formalism is itself a special case of the tetrad formalism, where the tensors of the theory are projected onto a complete vector basis at each point in spacetime. Usually this vector basis is chosen to reflect some symmetry of the spacetime, leading to simplified expressions for physical observables. In the case of the NP formalism, the vector basis chosen is a : a set of four null vectors—two real, and a complex-conjugate pair. The two real members asymptotically point radially inward and radially outward, (en)
- O formalismo de Newman-Penrose (NP) é um conjunto de notação desenvolvido por Ezra T. Newman e Roger Penrose para a relatividade geral (RG). Sua notação é um esforço para tratar a relatividade geral em termos de notação de espinores, que introduz formas complexas de variáveis habituais utilizadas na RG. O formalismo NP é por si só um caso especial do , onde os tensores da teoria são projetados sobre uma base vetorial completa em cada ponto no espaço-tempo. Normalmente, esta base vetorial é escolhida para refletir alguma simetria do espaço-tempo, levando a simplificar expressões para observáveis físicos. No caso do formalismo NP, a base escolhida é um vetor de : um conjunto de quatro vetores nulos — dois reais, e um par complexo-conjugado. Os dois membros reais assintoticamente apontam ra (pt)
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| - The Newman–Penrose (NP) formalism is a set of notation developed by Ezra T. Newman and Roger Penrose for general relativity (GR). Their notation is an effort to treat general relativity in terms of spinor notation, which introduces complex forms of the usual variables used in GR. The NP formalism is itself a special case of the tetrad formalism, where the tensors of the theory are projected onto a complete vector basis at each point in spacetime. Usually this vector basis is chosen to reflect some symmetry of the spacetime, leading to simplified expressions for physical observables. In the case of the NP formalism, the vector basis chosen is a : a set of four null vectors—two real, and a complex-conjugate pair. The two real members asymptotically point radially inward and radially outward, and the formalism is well adapted to treatment of the propagation of radiation in curved spacetime. The Weyl scalars, derived from the Weyl tensor, are often used. In particular, it can be shown that one of these scalars— in the appropriate frame—encodes the outgoing gravitational radiation of an asymptotically flat system. Newman and Penrose introduced the following functions as primary quantities using this tetrad:
* Twelve complex spin coefficients (in three groups) which describe the change in the tetrad from point to point: .
* Five complex functions encoding Weyl tensors in the tetrad basis: .
* Ten functions encoding Ricci tensors in the tetrad basis: (real); (complex). In many situations—especially algebraically special spacetimes or vacuum spacetimes—the Newman–Penrose formalism simplifies dramatically, as many of the functions go to zero. This simplification allows for various theorems to be proven more easily than using the standard form of Einstein's equations. In this article, we will only employ the tensorial rather than spinorial version of NP formalism, because the former is easier to understand and more popular in relevant papers. One can refer to ref. for a unified formulation of these two versions. (en)
- O formalismo de Newman-Penrose (NP) é um conjunto de notação desenvolvido por Ezra T. Newman e Roger Penrose para a relatividade geral (RG). Sua notação é um esforço para tratar a relatividade geral em termos de notação de espinores, que introduz formas complexas de variáveis habituais utilizadas na RG. O formalismo NP é por si só um caso especial do , onde os tensores da teoria são projetados sobre uma base vetorial completa em cada ponto no espaço-tempo. Normalmente, esta base vetorial é escolhida para refletir alguma simetria do espaço-tempo, levando a simplificar expressões para observáveis físicos. No caso do formalismo NP, a base escolhida é um vetor de : um conjunto de quatro vetores nulos — dois reais, e um par complexo-conjugado. Os dois membros reais assintoticamente apontam radialmente para dentro e radialmente para fora, e o formalismo está bem adaptado ao tratamento de propagação da radiação no espaço-tempo curvo. As variáveis mais frequentemente utilizadas no formalismo são os , derivados do tensor de Weyl. Em particular, pode ser mostrado que um destes escalares — no quadro apropriado — codifica a radiação gravitacional de saída de um sistema assintoticamente plano. (pt)
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