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.

arXiv commentAccepted for publication in Fortschritte der Physik - Progress of Physics

References in corpus (49)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• A Large Mass Hierarchy from a Small Extra Dimension
• An Alternative to Compactification
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• Formation and evaporation of non-singular black holes
• The Einstein Equations on the 3-Brane World
• Black Strings and p-Branes are Unstable
• Non-conventional cosmology from a brane-universe
• Brane-World Black Holes
• Decoupling gravitational sources in general relativity: from perfect to anisotropic fluids
• Anisotropic solutions by gravitational decoupling
• Localized Gravitons, Gauge Bosons and Chiral Fermions in Smooth Spaces Generated by a Bounce
• Black holes by gravitational decoupling
• Hairy black holes by gravitational decoupling
• Charged Brane-World Black Holes
• A new family of analytical anisotropic solutions by gravitational decoupling
• Gravitational Decoupled Charged Anisotropic Spherical Solutions
• Gravitational decoupling for axially symmetric systems and rotating black holes
• Black string instabilities in anti-de Sitter space
• Brane-world extra dimensions in light of GW170817
• Brane-world stars and (microscopic) black holes
• Quest for Localized 4-D Black Holes in Brane Worlds
• Bulk shape of brane-world black holes
• The Gravitational decoupling method: the higher dimensional case to find new analytic solutions
• A way of decoupling gravitational sources in pure Lovelock gravity
• The Curious Case of ASASSN-20hx: A Slowly-Evolving, UV and X-ray Luminous, Ambiguous Nuclear Transient
• Stable Black Strings in Anti-de Sitter Space
• A novel braneworld model with a bulk scalar field
• Regular hairy black holes through Minkowski deformation
• Quest for Localized 4-D Black Holes in Brane Worlds. II : Removing the bulk singularities
• Constraining extra dimensions using observations of black hole quasi-normal modes
• Hunting extra dimensions in the shadow of Sgr A*
• Quantum anomaly detection in the latent space of proton collision events at the LHC
• Regular black holes from semi-classical down to Planckian size
• Gravitational decoupling of generalized Horndeski hybrid stars
• Braneworld Gravity under gravitational decoupling
• 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
• Extra dimensions in CERN LHC via mini-black holes: effective Kerr-Newman brane-world effects
• Schwarzschild Black Branes and Strings in higher-dimensional Brane Worlds
• Resummed inclusive cross-section in Randall-Sundrum model at NNLO+NNLL
• Bridging Dimensions: General Embedding Algorithm and Field-Theory Reconstruction in 5D Braneworld Models
• Braneworld Black Bounce to Transversable Wormhole
• Localized brane-world black hole analytically connected to an AdS${}_5$ boundary
• Five-dimensional regular black holes in a brane world
• Z2-Symmetric Thick Brane with Specific Warp Function
• Stability of a tachyon braneworld
• Thick branes via higher order field theory models with exponential and power-law tails

Cited by in corpus (2)

• Localized five-dimensional rotating brane-world black hole Analytically Connected to an to an AdS${}_5$ boundary
• Embedding Wormholes and Dyonic Black Strings in Warped Braneworlds via Local Sum Rules