Global structure of static spherically symmetric solutions surrounded by quintessence

Abstract

We investigate all static spherically symmetric solutions in the context of general relativity surrounded by a minimally-coupled quintessence field, using dynamical system analysis. Applying the 1+1+2 formalism and introducing suitable normalized variables involving the Gaussian curvature, we were able to reformulate the field equations as first order differential equations. In the case of a massless canonical scalar field we recovered all known black hole results, such as the Fisher solution, and we found that apart from the Schwarzschild solution all other solutions are naked singularities. Additionally, we identified the symmetric phase space which corresponds to the white hole part of the solution and in the case of a phantom field, we were able to extract the conditions for the existence of wormholes and define all possible class of solutions such as Cold Black holes, singular spacetimes and wormholes like Ellis wormhole, for example. For an exponential potential, we found that the black hole solution which is asymptotically flat is unique and it is the Schwarzschild spacetime, while all other solutions are naked singularities. Furthermore, we found solutions connecting to a white hole through a maximum radius, and not a minimum radius (throat) such as wormhole solutions, therefore violating the flare-out condition. Finally, we have found a necessary and sufficient condition on the form of the potential to have an asymptotically AdS spacetime along with a necessary condition for the existence of asymptotically flat black holes.

37 pages, 5 figures; Accepted for publication in Class. Quantum Grav

References in corpus (6)

• Massive Gravity
• Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunneling
• Cold, clumpy accretion onto an active supermassive black hole
• A covariant approach for perturbations of rotationally symmetric spacetimes
• Astrophysical Black Hole horizons in a cosmological context: Nature and possible consequences on Hawking Radiation
• Global structure of Black Holes via dynamical system

Cited by in corpus (13)

• New rotating black holes in non-linear Maxwell $f(\mathcal{R})$ gravity
• Cosmological dynamics of brane gravity: A global dynamical system perspective
• Static spherically symmetric configurations with N non-linear scalar fields: global and asymptotic properties
• Global dynamics in Einstein-Gauss-Bonnet scalar field cosmology with matter
• Time-averaging axion-like interacting scalar fields models
• Generalized Scalar Field Cosmologies: A Global Dynamical Systems Formulation
• Generalized scalar field cosmologies: theorems on asymptotic behavior
• Averaging Generalized Scalar Field Cosmologies I: Locally Rotationally Symmetric Bianchi III and open Friedmann-Lemaître-Robertson-Walker models
• Dynamics and exact Bianchi I spacetimes in Einstein-aether scalar field theory
• Covariant formulation of refracted gravity
• Some Specific Wormhole Solutions in Extended $f(R,G,T)$ Gravity
• Phase space of static wormholes sustained by an isotropic perfect fluid
• Dynamical systems approach to stellar modelling in $f(G,B)$ gravity