Strategy to Construct Exact Solutions in Einstein-Scalar Gravities

Abstract

In this article we propose a new efficient strategy to construct exact solutions of Einstein gravities with a minimally coupled self-interacting scalar field. The strategy is to use the symmetry of the equations of motion (EOMs) to give a proper ansatz for scalar field first, then derive the metric and the corresponding scalar potential later. Using this strategy we give a simple example of constructing exact circular solutions in three dimensional gravities, these solutions contain the HMTZ black holes as a special case and some other new solutions. We also talk about thermodynamics of these exact solutions. This strategy also works for other metrics and in higher dimensional spacetime if their EOMs admit a scalar invariance.

Typos fixed, more solutions added including some hairy solitons in three dimensions and hairy black holes in higher dimensions

References in corpus (6)

• Asymptotic behavior and Hamiltonian analysis of anti-de Sitter gravity coupled to scalar fields
• Mass of asymptotically anti-de Sitter hairy spacetimes
• Static and Dynamic Hairy Planar Black Holes
• Hairy black holes in N=2 gauged supergravity
• The Non-integrable Mass and the Scalar Charge
• Charged Black Holes with Scalar Hair

Cited by in corpus (15)

• Thermodynamics of Charged Black Holes in Einstein-Horndeski-Maxwell Theory
• Hairy Black Holes and Duality in an Extended Supergravity Model
• Oscillons in hyperbolic models
• Constructing black holes in Einstein-Maxwell-scalar theory
• Collisions of kinks in deformed ${\phi }^4$ and ${\phi }^6$ models
• Kink scattering in hyperbolic models
• Hairy AdS Solitons
• On the thermodynamics of hairy black holes
• On black holes with scalar hairs
• Exact holographic RG flows in extended SUGRA
• The Non-integrable Mass and the Scalar Charge
• Scattering of kinks in scalar-field models with higher-order self-interactions
• Entropy of black holes coupled to a scalar field
• Charged Black Holes with Scalar Hair
• Agujeros Negros con Pelo y Dualidad AdS/CFT