On the causal geometry of spacetime: Some applications to cosmology

1986 ◽  
Vol 122 (2) ◽  
pp. 219-229
Author(s):  
Anastassios Kartsaklis
Keyword(s):  
Causal Geometry

scholarly journals New tensorial estimates in Besov spaces for time-dependent (2 + 1)-dimensional problems

2014 ◽  
Vol 11 (04) ◽  
pp. 821-908
Author(s):  
Arick Shao
Keyword(s):  
Primary Objective ◽  
Null Cone ◽  
Trace Theorems ◽  
Einstein Vacuum ◽  
Bondi Mass ◽  
Vacuum Spacetime ◽  
Bondi Energy ◽  
Funct Anal ◽  
Invent Math ◽  
Causal Geometry

In this paper, we consider various tensorial estimates in geometric Besov-type norms on a one-parameter foliation of surfaces with evolving geometries. Moreover, we wish to accomplish this with only very weak control on these geometries. Several of these estimates were proved in [S. Klainerman and I. Rodnianski, Causal geometry of Einstein-vacuum spacetimes with finite curvature flux, Invent. Math. 159 (2005) 437–529; S. Klainerman and I. Rodnianski, Sharp trace theorems for null hypersurfaces on Einstein metrics with finite curvature flux, Geom. Funct. Anal. 16(3) (2006) 164–229], but in very specific settings. A primary objective of this paper is to significantly simplify and make more robust the proofs of the estimates. Another goal is to generalize these estimates to more abstract settings. In [S. Alexakis and A. Shao, On the geometry of null cones to infinity under curvature flux bounds, Class. Quantum Grav. 31 (2014) 195012], we will apply these estimates in order to consider a variant of the problem in [S. Klainerman and I. Rodnianski, Causal geometry of Einstein-vacuum spacetimes with finite curvature flux, Invent. Math. 159 (2005) 437–529], that of a truncated null cone in an Einstein-vacuum spacetime extending to infinity. This analysis will then be used in [S. Alexakis and A. Shao, Bounds on the Bondi energy by a flux of curvature, to appear in J. Eur. Math. Soc.] to study and to control the Bondi mass and the angular momentum under minimal conditions.

scholarly journals Causal Geometry

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 24
Author(s):  
Pavel Chvykov ◽  
Erik Hoel
Keyword(s):  
Causal Relationship ◽  
Causal Model ◽  
Information Geometry ◽  
Scientific Models ◽  
Coarse Grained ◽  
Model Parameters ◽  
Coarse Grained Model ◽  
Fundamental Part ◽  
The Impact ◽  
Causal Geometry

Information geometry has offered a way to formally study the efficacy of scientific models by quantifying the impact of model parameters on the predicted effects. However, there has been little formal investigation of causation in this framework, despite causal models being a fundamental part of science and explanation. Here, we introduce causal geometry, which formalizes not only how outcomes are impacted by parameters, but also how the parameters of a model can be intervened upon. Therefore, we introduce a geometric version of “effective information”—a known measure of the informativeness of a causal relationship. We show that it is given by the matching between the space of effects and the space of interventions, in the form of their geometric congruence. Therefore, given a fixed intervention capability, an effective causal model is one that is well matched to those interventions. This is a consequence of “causal emergence,” wherein macroscopic causal relationships may carry more information than “fundamental” microscopic ones. We thus argue that a coarse-grained model may, paradoxically, be more informative than the microscopic one, especially when it better matches the scale of accessible interventions—as we illustrate on toy examples.

The causal geometry of twistor space

1990 ◽  
Vol 31 (4) ◽  
pp. 863-867 ◽  
Author(s):  
Robert J. Low
Keyword(s):  
Twistor Space ◽  
Causal Geometry

scholarly journals Causal geometry of Einstein-Vacuum spacetimes with finite curvature flux

2004 ◽  
Vol 159 (3) ◽  
pp. 437-529 ◽  
Author(s):  
Sergiu Klainerman ◽  
Igor Rodnianski
Keyword(s):  
Einstein Vacuum ◽  
Causal Geometry
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