MGD-decoupled black holes, anisotropic fluids and holographic entanglement entropy
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Regular Article - Theoretical Physics
MGD-decoupled black holes, anisotropic fluids and holographic entanglement entropy Roldão da Rocha1,a , Anderson A. Tomaz2,3,b 1
Center of Mathematics, Federal University of ABC, Santo André, Brazil Center for Natural and Human Sciences, Federal University of ABC, Santo André, Brazil 3 Institute of Physics, Fluminense Federal University, Niterói, Brazil
2
Received: 6 May 2020 / Accepted: 27 August 2020 © The Author(s) 2020
Abstract The holographic entanglement entropy (HEE) is investigated for a black hole under the minimal geometric deformation (MGD) procedure, created by gravitational decoupling via an anisotropic fluid, in an AdS/CFT on the brane setup. The respective HEE corrections are computed and confronted to the corresponding corrections for both the standard MGD black holes and the Schwarzschild ones.
1 Introduction The method of geometric deformation (MGD) consists of a protocol to derive compact stellar configurations of the effective Einstein’s field equations on the brane [1–8]. The MGD is a well succeeded theory that allows the study of nonlinear gravity in braneworlds, whose effective action can be obtained at low energies. There is a precise and intrinsic relationship between Gauss–Codazzi-like geometrical methods and AdS/CFT, as comprehensively paved in Refs. [9,10]. This approach also includes dark radiation, that naturally arises as homogeneous solutions. In this setup, the bulk gravity is dual to CFT on the brane, providing a holographic interpretation of braneworld scenarios as underlying apparatuses to MGD [9,10]. The MGD, and its extensions [1,4,11,12], comprise high precision phenomenological bounds that physically regulate their inherent parameters. The strictest bounds on the brane tension were derived in Refs. [13–15]. In addition, hydrodynamical analog systems, that emulate MGD black holes in the laboratory, were studied in Ref. [16]. Besides, MGD black strings were proposed in Ref. [17]. Refs. [18–36] include and study anisotropic solutions of quasi-Einstein’s equations, in the context of the MGD procedure [37]. Besides, anisotropic a e-mail:
[email protected] (corresponding author)
b e-mails:
[email protected]; [email protected]
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MGD-decoupled solutions were obtained by gravitational decoupling methods [38–43]. The MGD was also studied in the context of the strong gravitational lensing [44], whereas MGD glueball stars were scrutinized in Refs. [45,46]. In addition, MGD black holes in the GUP context were studied in Ref. [47], and relativistic anisotropic compact stellar configurations have been recently derived in [48]. The MGD-decoupling method was later introduced when one iteratively produces, from a source of gravity, more intricate, weakly-coupled, gravitational sources, that still preserve spherical symmetry [3]. Once the MGD decoupling is introduced by a perfect fluid via the brane effective Einstein’s equations, additional sources that are weaklycoupled to gravity induce anisotropy.
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