scholarly journals Bounds on the Bondi energy by a flux of curvature

2016 ◽  
Vol 18 (9) ◽  
pp. 2045-2106
Author(s):  
Spyros Alexakis ◽  
Arick Shao
Keyword(s):  
Bondi Energy

scholarly journals Static Bondi energy in the teleparallel equivalent of general relativity

1999 ◽  
Vol 40 (3) ◽  
pp. 1490-1503 ◽  
Author(s):  
J. W. Maluf ◽  
J. F. da Rocha-Neto
Keyword(s):  
General Relativity ◽  
Bondi Energy

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 A new look at the Bondi-Sachs energy-momentum

2021 ◽  
Author(s):  
Jörg Frauendiener ◽  
Chris Stevens
Keyword(s):  
Unit Sphere ◽  
Gauss Curvature ◽  
Null Infinity ◽  
Conformally Invariant ◽  
Lorentzian Metric ◽  
Correct Definition ◽  
Ghp Formalism ◽  
Bondi Mass ◽  
Definition Of ◽  
Bondi Energy

Abstract How does one compute the Bondi mass on an arbitrary cut of null infinity I when it is not presented in a Bondi system? What then is the correct definition of the mass aspect? How does one normalise an asymptotic translation computed on a cut which is not equipped with the unit-sphere metric? These are questions which need to be answered if one wants to calculate the Bondi-Sachs energy-momentum for a space-time which has been determined numerically. Under such conditions there is not much control over the presentation of I so that most of the available formulations of the Bondi energy-momentum simply do not apply. The purpose of this article is to provide the necessary background for a manifestly conformally invariant and gauge independent formulation of the Bondi energy-momentum. To this end we introduce a conformally invariant version of the GHP formalism to rephrase all the well-known formulae. This leads us to natural definitions for the space of asymptotic translations with its Lorentzian metric, for the Bondi news and the mass-aspect. A major role in these developments is played by the “co-curvature”, a naturally appearing quantity closely related to the Gauß curvature on a cut of I.

Positivity of the Bondi energy

1984 ◽  
Vol 25 (4) ◽  
pp. 1004-1008 ◽  
Author(s):  
O. Reula ◽  
K. P. Tod
Keyword(s):  
Bondi Energy
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