Classical tests of general relativity: Brane-world Sun from minimal geometric deformation

Abstract

-We consider a solution of the effective four-dimensional brane-world equations, obtained from the General Relativistic Schwarzschild metric via the principle of Minimal Geometric Deformation, and investigate the corresponding signatures stemming from the possible existence of a warped extra-dimension. In particular, we derive bounds on an extradimensional parameter, closely related with the fundamental gravitational length, from the experimental results of the classical tests of General Relativity in the Solar system.Introduction. -Brane-world (BW) models [1] represent a well-known branch of contemporary highenergy physics, inspired and supported by string theory. These models are indeed a straightforward 5D phenomenological realisation of the Hořava-Witten supergravity solutions [2], when the hidden brane is moved to infinity along one extra-dimension, and the moduli effects from the remaining compact extra-dimensions may be neglected [3]. The brane self-gravity, encoded in the brane tension σ, is one of the fundamental parameters appearing in all BW models, with σ

The Minimal Geometric Deformation Approach: A Brief Introduction

“…with given by the standard GR expression (35) and * the minimal geometric deformation in (43). Moreover, (43) implies that * ( ) ≥ 0,…”

“…In addition, the effective four-dimensional Einstein equations are not a closed system, due to the extradimensional effects resulting in terms undetermined by the four-dimensional equations. Despite these complications, the MGD has proven to be useful, among other things, to derive exact and physically acceptable interior solutions for spherically symmetric and nonuniform stellar distributions [24,25]; to express the tidal charge in the metric found in [26] 2 Advances in High Energy Physics in terms of the usual Arnowitt-Deser-Misner (ADM) mass [27]; to study microscopic black holes [28]; to clarify the role of exterior Weyl stresses acting on compact stellar distributions [29]; to generate other physically acceptable inner stellar solutions [30,31]; to extend the concept of variable tension introduced in [32] by analysing the shape of the black string in the extra dimension [33]; to prove, contrary to previous claims, the consistency of a Schwarzschild exterior [34] for a spherically symmetric self-gravitating system made of regular matter in the brane-world; to derive bounds on extra-dimensional parameters [35] from the observational results of the classical tests of GR in the solar system; to investigate the gravitational lensing phenomena beyond GR [36]; to determine the critical stability region for BoseEinstein condensates in gravitational systems [37]; to study Dark SU( ) glueball stars on fluid branes [38] as well as the correspondence between sound waves in a de Laval propelling nozzle and quasinormal modes emitted by braneworld black holes [39].…”

Black hole acoustics in the minimal geometric deformation of a de Laval nozzle

“…[17]. Besides, the most recent brane tension bound σ 3.2×10 −6 GeV 4 has been obtained by the informational entropy of the minimal geometrically deformed Bose-Einstein condensate of gravitons [32].…”

“…The ς parameter in (3) regards the Weyl fluid in the bulk and its induced deformation of the brane 4D vacuum [17]. The region inner to the stellar distribution is regular at the origin.…”

“…This approach has been comprehensively and successfully constrained by experimental and observational bounds, provided by the perihelion precession of Mer-cury, the deflection of light by the Sun, the gravitational redshift and the radar echo delay, recently obtained in Ref. [17]. Besides, observational lensing effects by minimal geometrically deformed black holes have a typical signature that may soon be probed by the European Space Agency satellite mission [18].…”