Topic
Lanczos tensor
About: Lanczos tensor is a research topic. Over the lifetime, 803 publications have been published within this topic receiving 17158 citations. The topic is also known as: Lanczos potential.
Papers published on a yearly basis
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Papers
TL;DR: In this article, the authors considered the problem of a small particle falling in a Schwarzschild background ("black hole") and examined its spectrum in the high-frequency limit, in terms of the traceless transverse tensor harmonics called electric and magnetic by Mathews.
Abstract: We are concerned with the pulse of gravitational radiation given off when a star falls into a "black hole" near the center of our galaxy. We look at the problem of a small particle falling in a Schwarzschild background ("black hole") and examine its spectrum in the high-frequency limit. In formulating the problem it is essential to pose the correct boundary condition: gravitational radiation not only escaping to infinity but also disappearing down the hole. We have examined the problem in the approximation of linear perturbations from a Schwarzschild background geometry, utilizing the decomposition into the tensor spherical harmonics given by Regge and Wheeler (1957) and by Mathews (1962). The falling particle contributes a $\ensuremath{\delta}$-function source term (geodesic motion in the background Schwarzschild geometry) which is also decomposed into tensor harmonics, each of which "drives" the corresponding perturbation harmonic. The power spectrum radiated in infinity is given in the high-frequency approximation in terms of the traceless transverse tensor harmonics called "electric" and "magnetic" by Mathews.
1,036 citations
TL;DR: In this paper, a covariant formulation of the outgoing radiation condition for gravitational fields is proposed, based on a detailed examination of the geometry of null lines and of the algebraic and differential properties of the Riemann tensor.
Abstract: A covariant formulation of the outgoing radiation condition for gravitational fields is proposed. The condition is based on a detailed examination of the geometry of null lines and of the algebraic and differential properties of the Riemann tensor. It relates the absence of incoming radiation, in a gravitational field with bounded sources and Euclidean topology, to the asymptotic behaviour of the Riemann tensor. Fields that are algebraically special in the Petrov classification are highly special examples of fields obeying the suggested condition.
740 citations
TL;DR: In this article, a calculus for general relativity is developed in which the basic role of tensors is taken over by spinors, and the Riemann-Christoffel tensor is written in a spinor form according to a scheme of Witten.
648 citations
11 Jul 1989
TL;DR: It is proved that computing the rank of a three-dimensional tensor over any finite field is NP-complete and over the rational numbers the problem isNP-hard.
Abstract: We prove that computing the rank of a three-dimensional tensor over any finite field is NP-complete. Over the rational numbers the problem is NP-hard.
553 citations
TL;DR: In this paper, the authors review and give the theory of experiments and Gedanken experiments in relation to various expressions for the electromagnetic energy-momentum tensor and discuss the electrostriction effect, mainly in electrostatic experiments.
521 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 1 |
| 2024 | 2 |
| 2023 | 9 |
| 2022 | 30 |
| 2021 | 3 |
| 2020 | 6 |