Positive energy theorem (original) (raw)
En la relatividad general, la conjetura de masa positiva o teorema de la energía positiva establece que, asumiendo la condición de energía dominante, la masa de un espacio-tiempo asintóticamente plano no es negativo; además, la masa es cero solo para el espacio-tiempo de Minkowski. Es un de curvatura escalar, con condiciones de contorno asintóticas y una declaración correspondiente de geométrica .
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| dbo:abstract | En la relatividad general, la conjetura de masa positiva o teorema de la energía positiva establece que, asumiendo la condición de energía dominante, la masa de un espacio-tiempo asintóticamente plano no es negativo; además, la masa es cero solo para el espacio-tiempo de Minkowski. Es un de curvatura escalar, con condiciones de contorno asintóticas y una declaración correspondiente de geométrica . (es) The positive energy theorem (also known as the positive mass theorem) refers to a collection of foundational results in general relativity and differential geometry. Its standard form, broadly speaking, asserts that the gravitational energy of an isolated system is nonnegative, and can only be zero when the system has no gravitating objects. Although these statements are often thought of as being primarily physical in nature, they can be formalized as mathematical theorems which can be proven using techniques of differential geometry, partial differential equations, and geometric measure theory. Richard Schoen and Shing-Tung Yau, in 1979 and 1981, were the first to give proofs of the positive mass theorem. Edward Witten, in 1982, gave the outlines of an alternative proof, which were later filled in rigorously by mathematicians. Witten and Yau were awarded the Fields medal in mathematics in part for their work on this topic. An imprecise formulation of the Schoen-Yau / Witten positive energy theorem states the following: Given an asymptotically flat initial data set, one can define the energy-momentum of each infinite region as an element of Minkowski space. Provided that the initial data set is geodesically complete and satisfies the dominant energy condition, each such element must be in the causal future of the origin. If any infinite region has null energy-momentum, then the initial data set is trivial in the sense that it can be geometrically embedded in Minkowski space. The meaning of these terms is discussed below. There are alternative and non-equivalent formulations for different notions of energy-momentum and for different classes of initial data sets. Not all of these formulations have been rigorously proven, and it is currently an open problem whether the above formulation holds for initial data sets of arbitrary dimension. (en) 在广义相对论里，正能量定理（在微分几何裡常被称为正质量猜想）被表述为：假设主能量條件即的质量为非负，而且仅在闵可夫斯基時空裡质量为零。在渐进边界条件下这个定理是数量曲率，相当于几何刚度的表述。1979年理查德·舍恩和丘成桐使用变分法完成这个定理对于ADM質量的原始证明。1981年爱德华·威滕受超重力环境下的正能量定理启发，采用旋量给出一个简化的证明。馬爾科姆·路德維森和等给出这个定理在Bondi质量的扩展。和史蒂芬·霍金等把这个定理扩展到渐进反德西特空間和爱因斯坦-麦克斯韦理论。 (zh) |
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| rdfs:comment | En la relatividad general, la conjetura de masa positiva o teorema de la energía positiva establece que, asumiendo la condición de energía dominante, la masa de un espacio-tiempo asintóticamente plano no es negativo; además, la masa es cero solo para el espacio-tiempo de Minkowski. Es un de curvatura escalar, con condiciones de contorno asintóticas y una declaración correspondiente de geométrica . (es) 在广义相对论里，正能量定理（在微分几何裡常被称为正质量猜想）被表述为：假设主能量條件即的质量为非负，而且仅在闵可夫斯基時空裡质量为零。在渐进边界条件下这个定理是数量曲率，相当于几何刚度的表述。1979年理查德·舍恩和丘成桐使用变分法完成这个定理对于ADM質量的原始证明。1981年爱德华·威滕受超重力环境下的正能量定理启发，采用旋量给出一个简化的证明。馬爾科姆·路德維森和等给出这个定理在Bondi质量的扩展。和史蒂芬·霍金等把这个定理扩展到渐进反德西特空間和爱因斯坦-麦克斯韦理论。 (zh) The positive energy theorem (also known as the positive mass theorem) refers to a collection of foundational results in general relativity and differential geometry. Its standard form, broadly speaking, asserts that the gravitational energy of an isolated system is nonnegative, and can only be zero when the system has no gravitating objects. Although these statements are often thought of as being primarily physical in nature, they can be formalized as mathematical theorems which can be proven using techniques of differential geometry, partial differential equations, and geometric measure theory. (en) |
| rdfs:label | Conjetura de masa positiva (es) Positive energy theorem (en) 正能量定理 (zh) |
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