Topic
Tensor field
About: Tensor field is a research topic. Over the lifetime, 3699 publications have been published within this topic receiving 87216 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this article, the second-order Euler-Lagrange tensors are derived from a Lagrangian which is at most of second order in the derivatives of the field functions.
Abstract: Lagrange scalar densities which are concomitants of a pseudo-Riemannian metric-tensor, a scalar field and their derivatives of arbitrary order are considered. The most general second-order Euler-Lagrange tensors derivable from such a Lagrangian in a four-dimensional space are constructed, and it is shown that these Euler-Lagrange tensors may be obtained from a Lagrangian which is at most of second order in the derivatives of the field functions.
3,247 citations
TL;DR: In this paper, the boundary stress tensor associated with a gravitating system in asymptotically anti-de Sitter space is computed, and the conformal anomalies in two and four dimensions are recovered.
Abstract: We propose a procedure for computing the boundary stress tensor associated with a gravitating system in asymptotically anti-de Sitter space. Our definition is free of ambiguities encountered by previous attempts, and correctly reproduces the masses and angular momenta of various spacetimes. Via the AdS/CFT correspondence, our classical result is interpretable as the expectation value of the stress tensor in a quantum conformal field theory. We demonstrate that the conformal anomalies in two and four dimensions are recovered. The two dimensional stress tensor transforms with a Schwarzian derivative and the expected central charge. We also find a nonzero ground state energy for global AdS5, and show that it exactly matches the Casimir energy of the dual super Yang–Mills theory on S
3×R.
2,803 citations
TL;DR: In this article, the authors studied toroidal compactification of Matrix theory, using ideas and results of non-commutative geometry, and argued that they correspond in supergravity to tori with constant background three-form tensor field.
Abstract: We study toroidal compactification of Matrix theory, using ideas and results of non-commutative geometry. We generalize this to compactification on the noncommutative torus, explain the classification of these backgrounds, and argue that they correspond in supergravity to tori with constant background three-form tensor field. The paper includes an introduction for mathematicians to the IKKT formulation of Matrix theory and its relation to the BFSS Matrix theory.
1,681 citations
Book•
8 Mar 1996
TL;DR: In this paper, the Riemannian themes in Lorentzian geometry connections and curvature of curvature are discussed and the splitting problem in global geodesic geometry is discussed.
Abstract: Introduction - Riemannian themes in Lorentzian geometry connections and curvature Lorentzian manifolds and causality Lorentzian distance examples of space-times completness and extendibility stability of completeness and incompleteness maximal geodesics and causally disconnected space-times the Lorentzian cut locus Morse index theory on Lorentzian manifolds some results in global Lorentzian geometry singularities gravitational plane wave space-times the splitting problem in global Lorentzian geometry. Appendices: Jacobi Fields and Toponogov's theorem for Lorentzian manifolds from the Jacobi, to a Riccati, to the Raychaudhuri equation - Jacobi Tensor Fields and the exponential map revisited.
1,523 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 1 |
| 2025 | 39 |
| 2024 | 44 |
| 2023 | 81 |
| 2022 | 287 |
| 2021 | 101 |