Space-time singularities in Weyl manifolds

Abstract

We extend one of the Hawking-Penrose singularity theorems in general relativity to the case of some scalar-tensor gravity theories in which the scalar field has a geometrical character and space-time has the mathematical structure of a Weyl integrable space-time (WIST). We adopt an invariant formalism, so that the extended version of theorem does not depend on a particular frame.

16 pages

References in corpus (6)

• The 1965 Penrose singularity theorem
• Einstein and Jordan frames reconciled: a frame-invariant approach to scalar-tensor cosmology
• Invariant quantities in the scalar-tensor theories of gravitation
• Inducing the cosmological constant from five-dimensional Weyl space
• Wesson's IMT with a Weylian bulk
• On the embedding of spacetime in five-dimensional Weyl spaces

Cited by in corpus (15)

• Selected topics in scalar-tensor theories and beyond
• Energy conditions in $f(Q,T)$ gravity
• Weyl Connections and their Role in Holography
• The Raychaudhuri equation in spacetimes with torsion and non-metricity
• Local conformal symmetry in non-Riemannian geometry and the origin of physical scales
• Cosmological models in Weyl geometrical scalar-tensor theory
• Gauge invariant fluctuations of the metric during inflation from new scalar-tensor Weyl-Integrable gravity model
• A generalized Weyl structure with arbitrary non-metricity
• An Invariant Approach to Weyl's unified field theory
• A brief review of a modified relativity that explains cosmological constant
• Kinematics in Metric-Affine Geometry
• Dynamical analysis and cosmological evolution in Weyl integrable gravity
• On the physical interpretation of non-metricity in Brans-Dicke gravity
• Weyl frames and canonical transformations in geometrical scalar-tensor theories of gravity
• Lagrangian Formulation of the Raychaudhuri Equation in Non-Riemannian Geometry