A way of decoupling the gravitational bulk field equations of regular braneworld black holes to suppress the bulk singularities

Abstract

We provide a methodology for decoupling the bulk gravitational field equations of braneworld black holes to suppress the bulk singularities. Thus, we provide a regular braneworld black hole setup. To achieve this, we apply a Minimal Geometric Deformation (MGD) with respect to a coupling constant $\alpha$ to the $4D$ Minkowski spacetime embedded in an extra dimension. This results in a gravitational decoupling into a system $\mathcal{A}$ with equations of motion of order ${\alpha }^0$ and a system $\mathcal{B}$, related to the so-called Quasi-Einstein equations of order $\alpha$. This methodology allows for the construction of a regular geometry everywhere. We outline the necessary constraints for eliminating singularities and provide a recipe for solving the equations of motion. Both the warp factor, the scalar field, and the potential obtained are smooth and free from Dirac delta singularities. A control parameter is introduced such that, in the limit $b\to 0$, the Randall-Sundrum (RS) setup is recovered, resulting in a transition from a thick brane to a thin brane. The asymptotic behavior of the curvature invariant $\underset{y\to \pm \infty }{\lim }{R}_{5D}(r,y)$ is positive near the de Sitter core (for small $r$), asymptotically negative for finite $r>r_{\ast }$, and asymptotically flat at the $4D$ boundary as $r\to \infty$. Although this work aims to suppress bulk singularities, it is expected that our methodology may be useful for future investigations related to the embedding of gravitational objects within other braneworld contexts.

Accepted for publication in Fortschritte der Physik - Progress of Physics

References in corpus (18)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• Gravitational decoupling for axially symmetric systems and rotating black holes
• The Curious Case of ASASSN-20hx: A Slowly-Evolving, UV and X-ray Luminous, Ambiguous Nuclear Transient
• Regular hairy black holes through Minkowski deformation
• Hunting extra dimensions in the shadow of Sgr A*
• Constraining extra dimensions using observations of black hole quasi-normal modes
• Quantum anomaly detection in the latent space of proton collision events at the LHC
• Gravitational decoupling of generalized Horndeski hybrid stars
• Looking for extra dimensions in the observed quasi-periodic oscillations of black holes
• Impact of compactlike and asymmetric configurations of thick branes on the scalar-tensor representation of $f\left(R,T\right)$ gravity
• Bridging Dimensions: General Embedding Algorithm and Field-Theory Reconstruction in 5D Braneworld Models
• Resummed inclusive cross-section in Randall-Sundrum model at NNLO+NNLL
• Localized brane-world black hole analytically connected to an AdS${}_5$ boundary
• Braneworld Black Bounce to Transversable Wormhole
• Five-dimensional regular black holes in a brane world
• Z2-Symmetric Thick Brane with Specific Warp Function
• Thick branes via higher order field theory models with exponential and power-law tails

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