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On the Energy-Momentum Tensor of the Scalar Field in Scalar--Tensor Theories of Gravity
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We study the dynamical description of gravity, the appropriate definition of the scalar field energy-momentum tensor, and the interrelation between them in scalar-tensor theories of gravity. We show that the quantity which one would naively identify as the energy-momentum tensor of the scalar field is not appropriate because it is spoiled by a part of the dynamical description of gravity. A new connection can be defined in terms of which the full dynamical description of gravity is explicit, and the correct scalar field energy-momentum tensor can be immediately identified. Certain inequalities must be imposed on the two free functions (the coupling function and the potential) that define a particular scalar-tensor theory, to ensure that the scalar field energy density never becomes negative. The correct dynamical description leads naturally to the Einstein frame formulation of scalar-tensor gravity which is also studied in detail.
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Singularity theorems and the inclusion of torsion in affine theories of gravity
The authors prove new focusing and singularity theorems for Lorentzian manifolds with torsion, covering accelerated time-like and null curves, perfect fluids, and scalar fields.
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