Causal symmetries

Causal symmetries

Based on the recent work \cite{PII} we put forward a new type of transformation for Lorentzian manifolds characterized by mapping every causal future-directed vector onto a causal future-directed vector. The set of all such transformations, which we call causal symmetries, has the structure of a submonoid which contains as its maximal subgroup the set of conformal transformations. We find the necessary and sufficient conditions for a vector field $\xiv$ to be the infinitesimal generator of a one-parameter submonoid of pure causal symmetries. We speculate about possible applications to gravitat…

General study and basic properties of causal symmetries

We fully develop the concept of causal symmetry introduced in Class. Quant. Grav. 20 (2003) L139. A causal symmetry is a transformation of a Lorentzian manifold (V,g) which maps every future-directed vector onto a future-directed vector. We prove that the set of all causal symmetries is not a group under the usual composition operation but a submonoid of the diffeomorphism group of V. Therefore, the infinitesimal generating vector fields of causal symmetries --causal motions-- are associated to local one-parameter groups of transformations which are causal symmetries only for positive values o…

Causal Relations and their applications

In this work we define and study the relations between Lorentzian Manifolds given by the diffeomorphisms which map causal future directed vectors onto causal future directed vectors. This class of diffeomorphisms, called proper causal relations, contains as a subset the well-known group of conformal relations and are deeply linked to the so-called causal tensors. If two given Lorentzian manifolds are in mutual proper causal relation then they are said to be causally isomorphic: they are indistinguishable from the causal point of view. Finally, the concept of causal transformations for Lorentzi…

因果集是否具有对称性？

Do causal sets have symmetries?

本文研究因果集是否具有对称性，通过分析有限偏序集的自同构群来系统识别和分类其对称性，并将一般偏序集与撒点因果集的局部对称性进行比较，以寻找可作为离散时空模型的偏序集。

Symmetries, charges and conservation laws at causal diamonds in general relativity

We study the covariant phase space of vacuum general relativity at the null boundary of causal diamonds. The past and future components of such a null boundary each have an infinite-dimensional symmetry algebra consisting of diffeomorphisms of the $2$-sphere and boost supertranslations corresponding to angle-dependent rescalings of affine parameter along the null generators. Associated to these symmetries are charges and fluxes obtained from the covariant phase space formalism using the prescription of Wald and Zoupas. By analyzing the behavior of the spacetime metric near the corners of the c…

定向球模型非平衡动力学中的动力学对称性

Dynamical symmetries in the non-equilibrium dynamics of the directed spherical model

本文研究淬火定向球模型的非平衡弛豫动力学，发现新的弹道及各向异性弹道标度区域，并用meta-Schrödinger不变性和meta-共形不变性刻画其动力学对称性。