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2013

Scalar-tensor gravitation and the Bakry-Emery-Ricci tensor

Woolgar, E

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Understand

The Bakry-Emery generalized Ricci tensor arises in scalar-tensor gravitation theories in the conformal gauge known as the Jordan frame.

Recent results from the mathematics literature show that standard singularity and splitting theorems that hold when an energy condition is applied in general relativity also hold when that energy condition is applied to the Bakry-Emery tensor.
We show here that a direct consequence is that the Hawking-Penrose singularity theorem and the timelike splitting theorem hold for scalar-tensor theory in the Jordan frame.
As examples, we consider dilaton gravity (including totally anti-symmetric torsion) and the Brans-Dicke family of scalar-tensor theories.

Scalar-tensor gravitation and the Bakry-Emery-Ricci tensor · Around

Built on

C Brans and RH Dicke, Mach’s principle and a relativistic theory of gravitation
1961
Earlier work this paper cites.
J O’Hanlon and BOJ Tupper, Vacuum-field solutions in the Brans-Dicke theory
1972
Earlier work this paper cites.
SW Hawking and GFR Ellis, The large scale structure of space-time
1973
Earlier work this paper cites.
CM Will, Theory and experiment in gravitational physics
1981
Earlier work this paper cites.

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Then

J Lott, Some geometric properties of the Bakry-Émery-Ricci tensor
2003
Later among the works it cites.
C Villani, Optimal transport
2009
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JS Case, Singularity theorems and the Lorentzian splitting theorem for the Bakry-Emery-Ricci tensor
2010
Later among the works it cites.

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