Gravitational decoupling in $2+1$ dimensional space--times with cosmological term

Abstract

In this work we implement the Minimal Geometric Deformation method to obtain the isotropic sector and the decoupler matter content of any anisotropic solution of the Einstein field equations with cosmological constant in $2+1$ dimensional space--times. We obtain that the solutions of both sectors can be expressed analytically in terms of the metric functions of the original anisotropic solutions instead of formal integral as in its $3+1$ counterpart. As a particular example we study a regular black hole solution and we show that, depending on the sign of the cosmological constant, the solutions correspond to regular black holes violating the null energy condition or to a non--regular black hole without exotic hair. The exotic/non--exotic and the regular/non--regular black hole dualities are discussed.

References in corpus (6)

• Searching Exact Solutions for Compact Stars in Braneworld: a conjecture
• Brane-world stars with solid crust and vacuum exterior
• Stability of the graviton Bose-Einstein condensate in the brane-world
• Classical Tests of General Relativity: Brane-World Sun from Minimal Geometric Deformation
• Non-uniform Braneworld Stars: an Exact Solution
• The Schwarzschild's Braneworld Solution

Cited by in corpus (9)

• Gravitational decoupling for axially symmetric systems and rotating black holes
• A causal Schwarzschild-de Sitter interior solution by gravitational decoupling
• An anisotropic version of Tolman VII solution in $f(R,T)$ gravity via Gravitational Decoupling MGD Approach
• Anisotropic 2+1 dimensional black holes by gravitational decoupling
• Energy exchange between relativistic fluids: the polytropic case
• Regularity condition on the anisotropy induced by gravitational decoupling in the framework of MGD
• MGD-decoupled black holes, anisotropic fluids and holographic entanglement entropy
• Gravitational decoupling and superfluid stars
• Gravitational decoupling for hairy black holes in asymptotically AdS spacetimes