Holographic entanglement entropy under the minimal geometric deformation and extensions

Abstract

The holographic entanglement entropy (HEE) of the minimal geometrical deformation (MGD) procedure and extensions (EMGD), is scrutinized within the membrane paradigm of AdS/CFT. The HEE corrections of the Schwarzschild and Reissner-Nordström solutions, due to a finite fluid brane tension, are then derived and discussed in the context of the MGD and the EMGD.The AdS/CFT duality generally states that weakly-coupled gravity in (d + 1)-dimensional antide Sitter (AdS) space is dual to a strongly-coupled conformal field theory (CFT), whose underlying hydrodynamical limit corresponds to the Navier-Stokes equations -at the d-dimensional AdS space boundary [1][2][3]. The membrane paradigm is usually deployed into the fluid/gravity correspondence, as a low-energy regime of AdS/CFT [4]. In the membrane paradigm setup, black holes were studied in the infrared (IR) limit [5][6][7]. In addition, the seminal Refs. [8-10] present important features of this duality. For a N number of colours, indexing a SU(N ) (gauge) theory, AdS/CFT duality asserts that N = 4 superconformal Yang-Mills theory in 4D is dual to type IIB string theory on AdS 5 × S 5 . In the original setup, the AdS 5 boundary is a 4D Minkowski spacetime, and the D 3 -brane near horizon geometry is AdS 5 , whereas the far away brane geometry remains flat.In the membrane paradigm of AdS/CFT, and beyond the general relativity (GR), the so called method of geometrical deformation (MGD) places itself as an important procedure to generate new solutions of the effective Einstein's field equations on the brane [5,7,[11][12][13][14][15], including anisotropic solutions, describing compact stellar distributions, in a AdS bulk Weyl fluid flow [16,17]. The MGD and its extensions take into account the brane Einstein's field equations [18,19], where the effective stress-energy tensor has additional terms, in particular regarding the Gauss-Codazzi equations from the bulk stress-energy tensor projected onto the brane [8]. Important terms, constituting the effective brane stress-tensor, are the bulk dark radiation, the bulk dark pressure, the electric part of the Weyl tensor and quadratic terms on the brane stress-energy tensor. This last one is derived for regimes of energy that are beyond the (finite) brane tension in the theory. Being our universe described by a brane with tension σ, the MGD leads to a deformation of the Schwarzschild metric proportional to a positive length scale ∼ σ −1 [7,11,12].The MGD and its extensions [5] have been recently equipped with experimental, phenomenological, and observational very precise bounds, physically constraining their running parameters.MGD gravitational lensing effects were explored in Ref. [20] and the classical tests of GR imposed bounds on the brane tension in Ref. [17]. The most precise values of the brane tension range were obtained in Refs. [21,22]. In fact, in these references, the information entropy was used to provide account for the critical stellar densities, in the MGD and EMGD setups, deriving analogue of the Chandrasekhar's...

MGD-decoupled black holes, anisotropic fluids and holographic entanglement entropy

“…Just for the current goal, one stopped at the second order. As it was demonstrated in [67,68], Eq. 38is solved -order by order -employing g 1 (y) and g 2 (y) in Eq.…”

“…Based on Ref. [66], which defines the HEE in asymptotically flat spacetimes, the aim of this work consists to implement the procedure established in [67,68] to compute the HEE for a spacetime obtained by the MGD gravitational decoupling protocol, using an additional anisotropic fluid in the stress-energy tensor [53]. Into this incursion, one intends to verify how two ways of positioning the boundaries -either far from or almost on the horizon -affects the HEE, up to the second-order in an expanded solution.…”

“…Into this incursion, one intends to verify how two ways of positioning the boundaries -either far from or almost on the horizon -affects the HEE, up to the second-order in an expanded solution. This can answer if the first law of black hole thermodynamics still holds, as well as how to fit each order of the HEE correction when compared with HEE corrections arising from the standard MGD spacetime and the Schwarzschild one [68].…”

Braneworld Gravity under gravitational Decoupling

“…In these cases, the anisotropy generated by the new source can be interpreted in many ways, depending on the main goal of each author, and in general it will be different from the one considered here, which came from the contributions of the bulk into the brane. Other solutions obtained using the MGD decoupling method come from the analysis of theories beyond GR like , and gravity, pure Lovelock gravity, AdS/CFT, for mention some of them, where the source has a different interpretation with the presented here. For more recent applications of the MGD‐decoupling method see for instance refs.…”

MGD Dirac Stars

“…As a natural step in the membrane paradigm of AdS/CFT [13,14], the holographic entanglement entropy of MGD black holes was computed in Ref. [15]. The MGD has observational bounds, derived in Refs.…”