scholarly journals The Minimal Geometric Deformation Approach: A Brief Introduction

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
J. Ovalle ◽  
R. Casadio ◽  
A. Sotomayor
Keyword(s):  
Perfect Fluid ◽  
Brane World ◽  
Geometric Deformation ◽  
General Relativistic ◽  
Deformation Approach

We review the basic elements of the Minimal Geometric Deformation approach in detail. This method has been successfully used to generate brane-world configurations from general relativistic perfect fluid solutions.

scholarly journals Anisotropic Tolman VII solution by gravitational decoupling

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Sudipta Hensh ◽  
Zdeněk Stuchlík
Keyword(s):  
Perfect Fluid ◽  
Compact Objects ◽  
Effective Density ◽  
Fluid Solution ◽  
Coupling Constant ◽  
Tangential Pressure ◽  
Geometric Deformation ◽  
Two Fluid ◽  
Deformation Approach

Abstract Using the gravitational decoupling by the minimal geometric deformation approach, we build an anisotropic version of the well-known Tolman VII solution, determining an exact and physically acceptable interior two-fluid solution that can represent behavior of compact objects. Comparison of the effective density and density of the perfect fluid is demonstrated explicitly. We show that the radial and tangential pressure are different in magnitude giving thus the anisotropy of the modified Tolman VII solution. The dependence of the anisotropy on the coupling constant is also shown.

scholarly journals Minimal geometric deformation in a Reissner–Nordström background

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Ángel Rincón ◽  
Luciano Gabbanelli ◽  
Ernesto Contreras ◽  
Francisco Tello-Ortiz
Keyword(s):  
Black Hole Solution ◽  
Effective Density ◽  
Schwarzschild Black Hole ◽  
Exact Analytical Solutions ◽  
Geometric Deformation ◽  
New Material ◽  
Free Parameters ◽  
Scalar Invariants ◽  
Deformation Approach ◽  
Do So

Abstract This article is devoted to the study of new exact analytical solutions in the background of Reissner–Nordström space-time by using gravitational decoupling via minimal geometric deformation approach. To do so, we impose the most general equation of state, relating the components of the $$\theta $$θ-sector in order to obtain the new material contributions and the decoupler function f(r). Besides, we obtain the bounds on the free parameters of the extended solution to avoid new singularities. Furthermore, we show the finitude of all thermodynamic parameters of the solution such as the effective density $${\tilde{\rho }}$$ρ~, radial $${\tilde{p}}_{r}$$p~r and tangential $${\tilde{p}}_{t}$$p~t pressure for different values of parameter $$\alpha $$α and the total electric charge Q. Finally, the behavior of some scalar invariants, namely the Ricci R and Kretshmann $$R_{\mu \nu \omega \epsilon }R^{\mu \nu \omega \epsilon }$$RμνωϵRμνωϵ scalars are analyzed. It is also remarkable that, after an appropriate limit, the deformed Schwarzschild black hole solution always can be recovered.

scholarly journals Durgapal IV model considering the minimal geometric deformation approach

2020 ◽  
Vol 44 (10) ◽  
pp. 105102
Author(s):  
Francisco Tello-Ortiz ◽  
Ángel Rincón ◽  
Piyali Bhar ◽  
Y. Gomez-Leyton
Keyword(s):  
Geometric Deformation ◽  
Iv Model ◽  
Deformation Approach

On the classical and quantum irrotational motions of a relativistic perfect fluid I. Classical theory

1985 ◽  
Vol 401 (1820) ◽  
pp. 53-66 ◽  
Keyword(s):  
Perfect Fluid ◽  
Vacuum State ◽  
Background Field ◽  
Field Configuration ◽  
Spontaneous Breaking ◽  
Sound Waves ◽  
Action Functional ◽  
Fluid Equation ◽  
Goldstone Bosons ◽  
General Relativistic

Some aspects of perfect-fluid general-relativistic hydrodynamics under the assumptions of irrotationality and isentropicity are analysed. A new derivation of the known fact that the Lagrangian for these fluids is just the pressure is given. Then we study the fluctuations around a given background field configuration, extracting a rule that connects the order at which a Taylor expansion of the action functional possibly stops with the fluid equation of state. From a classical invariance of the action we deduce the conserved Noether current. Because of the spontaneous breaking of such an invariance on the vacuum state Goldstone bosons arise, which turn out to be just phonons (quantized sound waves). Some useful results concerning the linear theory of sound waves are also given.

scholarly journals The minimal geometric deformation approach extended

2015 ◽  
Vol 32 (21) ◽  
pp. 215020 ◽  
Author(s):  
R Casadio ◽  
J Ovalle ◽  
Roldão da Rocha
Keyword(s):  
Geometric Deformation ◽  
Deformation Approach

A NONSINGULAR PERFECT FLUID CLASSICAL LEPTON MODEL OF ARBITRARILY SMALL RADIUS

2013 ◽  
Vol 22 (14) ◽  
pp. 1350088 ◽  
Author(s):  
THOMAS E. KIESS
Keyword(s):  
Electric Field ◽  
Perfect Fluid ◽  
Small Radius ◽  
Spherically Symmetric ◽  
Model Based ◽  
Perfect Fluids ◽  
General Relativistic ◽  
Relativistic Models ◽  
Lepton Model

We exhibit a classical lepton model based on a perfect fluid that reproduces leptonic charges and masses in arbitrarily small volumes without metric singularities or pressure discontinuities. This solution is the first of this kind to our knowledge, because to date the only classical general relativistic models that have reproduced leptonic charges and masses in arbitrarily small volumes are based on imperfect (anisotopic) fluids or perfect fluids with electric field discontinuities. We use a Maxwell–Einstein exact metric for a spherically symmetric static perfect fluid in a region in which the pressure vanishes at a boundary, beyond which the metric is of the Reissner–Nordström form. This construction models lepton mass and charge in the limit as the boundary → 0.

scholarly journals Shear-free conditions of a Chaplygin-gas-dominated universe

2021 ◽  
pp. 2150192
Author(s):  
Amare Abebe ◽  
Mudhahir Al Ajmi ◽  
Maye Elmardi ◽  
Hemwati Nandan ◽  
Noor ul Sabah
Keyword(s):  
General Relativity ◽  
Perfect Fluid ◽  
Chaplygin Gas ◽  
Current Investigation ◽  
Free Condition ◽  
General Relativistic ◽  
Relativistic Framework ◽  
Fluid Spacetimes

In this work, we revisit the shear-free conjecture of general relativity and study the well-known shear-free condition in the context of the Chaplygin-gas cosmology. It had been shown in previous investigations that, in the general relativistic framework, the matter congruences of shear-free perfect fluid spacetimes should be either expansion-free or rotation-free. Our current investigation, however, indicates that a universe dominated by a Chaplygin-gas can allow a simultaneous expansion and rotation of the fluid provided that certain non-trivial conditions, which we derive and describe in what follows, are met. We also show that, in the appropriate limiting cases, our results reduce to the expected results of dust spacetimes which can only expand or rotate, but not both, at the same time.

scholarly journals Ultracompact stars with polynomial complexity by gravitational decoupling

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
M. Carrasco-Hidalgo ◽  
E. Contreras
Keyword(s):  
Differential Equations ◽  
Polynomial Complexity ◽  
System Of Differential Equations ◽  
Geometric Deformation ◽  
Star Configuration ◽  
Deformation Approach

AbstractIn this work we construct an ultracompact star configuration in the framework of Gravitational Decoupling by the Minimal Geometric Deformation approach. We use the complexity factor as a complementary condition to close the system of differential equations. It is shown that for a polynomial complexity the resulting solution can be matched with two different modified-vacuum geometries.

scholarly journals Regularity condition on the anisotropy induced by gravitational decoupling in the framework of MGD

2020 ◽  
Vol 80 (2) ◽  
Author(s):  
G. Abellán ◽  
V. A. Torres-Sánchez ◽  
E. Fuenmayor ◽  
E. Contreras
Keyword(s):  
Standard Method ◽  
Regularity Condition ◽  
Physical Characteristics ◽  
Compact Objects ◽  
Anisotropy Factor ◽  
Einstein Equations ◽  
Anisotropic Fluid ◽  
Acceptable Solution ◽  
Geometric Deformation ◽  
Deformation Approach

Abstract We use gravitational decoupling to establish a connection between the minimal geometric deformation approach and the standard method for obtaining anisotropic fluid solutions. Motivated by the relations that appear in the framework of minimal geometric deformation, we give an anisotropy factor that allows us to solve the quasi–Einstein equations associated to the decoupling sector. We illustrate this by building an anisotropic extension of the well known Tolman IV solution, providing in this way an exact and physically acceptable solution that represents the behavior of compact objects. We show that, in this way, it is not necessary to use the usual mimic constraint conditions. Our solution is free from physical and geometrical singularities, as expected. We have presented the main physical characteristics of our solution both analytically and graphically and verified the viability of the solution obtained by studying the usual criteria of physical acceptability.

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