Scalar-tensor gravity and conformal continuations
arXiv:gr-qc/0204001 · doi:10.1063/1.1519667
Abstract
Global properties of vacuum static, spherically symmetric configurations are studied in a general class of scalar-tensor theories (STT) of gravity in various dimensions. The conformal mapping between the Jordan and Einstein frames is used as a tool. Necessary and sufficient conditions are found for the existence of solutions admitting a conformal continuation (CC). The latter means that a singularity in the Einstein-frame manifold maps to a regular surface S_(trans) in the Jordan frame, and the solution is then continued beyond this surface. S_(trans) can be an ordinary regular sphere or a horizon. In the second case, S_(trans) proves to connect two epochs of a Kantowski-Sachs type cosmology. It is shown that, in an arbitrary STT, with arbitrary potential functions , the list of possible types of causal structures of vacuum space-times is the same as in general relativity with a cosmological constant. This is true even for conformally continued solutions. It is found that when S_(trans) is an ordinary sphere, one of the generic structures appearing as a result of CC is a traversable wormhole. Two explicit examples are presented: a known solution illustrating the emergence of singularities and wormholes, and a nonsingular 3-dimensional model with an infinite sequence of CCs.
Latex2e, 13 pages, 3 bezier figures
References in corpus (2)
Cited by in corpus (28)
- Possible wormholes in a brane world
- Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology
- Wormholes without exotic matter in Einstein-Cartan theory
- Notes on wormhole existence in scalar-tensor and F(R) gravity
- Invariant quantities in the scalar-tensor theories of gravitation
- No realistic wormholes from ghost-free scalar-tensor phantom dark energy
- Wormholes and black universes without phantom fields in Einstein-Cartan theory
- Scalar fields as sources for wormholes and regular black holes
- Self-stabilization of extra dimensions
- Cold black holes and conformal continuations
- Transformation properties and general relativity regime in scalar-tensor theories
- Induced gravity, and minimally and conformally coupled scalar fields in Bianchi-I cosmological models
- Spherically symmetric static vacuum solutions in hybrid metric-Palatini gravity
- Duality between static spherically or hyperbolically symmetric solutions and cosmological solutions in scalar-tensor gravity
- Spherically symmetric black holes and wormholes in hybrid metric-Palatini gravity
- Hybrid metric-Palatini gravity: black holes, wormholes, singularities and instabilities
- Scalar fields in multidimensional gravity. No-hair and other no-go theorems
- Black hole and naked singularity geometries supported by three-form fields
- Regular Bouncing Solutions, Energy Conditions and the Brans-Dicke Theory
- Field redefinitions, Weyl invariance, and nature of mavericks
- Quantum and classical cosmology in the Brans-Dicke theory
- Spherically symmetric space-times in generalized hybrid metric-Palatini gravity
- Conformal and kinetic couplings as two Jordan frames of the same theory
- Arbitrary static, spherically symmetric space-times as solutions of scalar-tensor gravity
- Conformal frames and D-dimensional gravity
- On the stability of electrovacuum space-times in scalar-tensor gravity
- On the stability of spherically symmetric space-times in scalar-tensor gravity
- Stationary Points of Scalar Fields Coupled to Gravity