Axially symmetric and static solutions of Einstein equations with self-gravitating scalar field

Abstract

The exact axisymmetric and static solution of the Einstein equations coupled to axisymmetric and static gravitating scalar (or phantom) field is presented. The spacetimes modified by the scalar field are explicitly given for the so called $\gamma$-metric and Erez-Rosen metric with quadrupole moment $q$, influence of the additional deformation parameters ${\gamma }_{\ast }$ and $q_{\ast }$ generated by the scalar field is studied. It is shown that the null energy condition is satisfied for the phantom field, but it is not satisfied for the standard scalar field. The test particle motion in the both modified $\gamma$-metric and Erez-Rosen quadrupole metric is studied; the circular geodesics are determined, and near-circular trajectories are explicitly presented for characteristic values of the spacetime parameters. It is also demonstrated that the parameters ${\gamma }_{\ast }$ and $q_{\ast }$ have no influence on the test particle motion in the equatorial plane.

arXiv comment16 pages, 9 figures

References in corpus (15)

• Rotating Charged Black Hole Solution in Heterotic String Theory
• Rotating Regular Black Hole Solution
• Janis-Newman-Winicour and Wyman solutions are the same
• Circular geodesics and accretion disks in Janis-Newman-Winicour and Gamma metric
• Static and slowly rotating neutron stars in scalar-tensor theory with self-interacting massive scalar field
• Non-spherical sources of static gravitational fields: investigating the boundaries of the no-hair theorem
• Weyl metrics and wormholes
• Static and Dynamic Hairy Planar Black Holes
• Comparison of Vacuum Static Quadrupolar Metrics
• Electrically-Charged Lifshitz Spacetimes, and Hyperscaling Violations
• Charged Black Holes in Colored Lifshitz Spacetimes
• Stationary cylindrically symmetric spacetimes with a massless scalar field and a non-positive cosmological constant
• Generating Solutions to the Einstein Field Equations
• On the equivalence of approximate stationary axially symmetric solutions of Einstein field equations
• Global monopoles and scalar fields as the electrogravity dual of Schwarzschild spacetime

Cited by in corpus (15)

• Black hole mimicker hiding in the shadow: Optical properties of the $\gamma$-metric
• Hairy black holes in DHOST theories: Exploring disformal transformation as a solution-generating method
• On Rotating Black Holes in DHOST Theories
• Test particle motion around black hole in Einstein-Maxwell-scalar theory
• Spherically symmetric static vacuum solutions in hybrid metric-Palatini gravity
• Three parameter metrics in the presence of a scalar field in four and higher dimensions
• Generating Rotating Spacetime in Ricci-Based Gravity: Naked Singularity as a Black Hole Mimicker
• A family of scalar-Einstein and vacuum Brans-Dicke axisymmetric solutions
• Effects of Electromagnetic Field on the Structure of Massive Compact Objects
• Black hole and naked singularity geometries supported by three-form fields
• A class of rotating metrics in the presence of a scalar field
• A class of Taub-NUT-scalar metrics via Ehlers transformations
• Nonspherically-symmetric black hole in Einstein-massless scalar theory
• A quadrupolar generalization of the Erez-Rosen coordinates
• A Generalized Class of Taub-NUT-Scalar Metrics