scholarly journals Junction conditions and thin shells in perfect-fluid f(R,T) gravity

2021 ◽  
Vol 103 (10) ◽  
Author(s):  
João Luís Rosa
Keyword(s):  
Perfect Fluid ◽  
Thin Shells ◽  
Junction Conditions

scholarly journals Kodama-Schwarzschild versus Gaussian Normal Coordinates Picture of Thin Shells

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Mikhail Z. Iofa
Keyword(s):  
Spherical Shell ◽  
Coordinate Transformation ◽  
Time Dependent ◽  
Thin Shells ◽  
Junction Conditions ◽  
Coordinate Systems ◽  
Normal Coordinate ◽  
Normal Coordinates

Geometry of the spacetime with a spherical shell embedded in it is studied in two coordinate systems: Kodama-Schwarzschild coordinates and Gaussian normal coordinates. We find explicit coordinate transformation between the Kodama-Schwarzschild and Gaussian normal coordinate systems. We show that projections of the metrics on the surface swept by the shell in the 4D spacetime in both cases are identical. In the general case of time-dependent metrics we calculate extrinsic curvatures of the shell in both coordinate systems and show that the results are identical. Applications to the Israel junction conditions are discussed.

scholarly journals Rotating thin shells in (2 + 1)-dimensional asymptotically AdS spacetimes: Mechanical properties, machian effects, and energy conditions

2015 ◽  
Vol 24 (09) ◽  
pp. 1542022 ◽  
Author(s):  
José P. S. Lemos ◽  
Francisco J. Lopes ◽  
Masato Minamitsuji
Keyword(s):  
Energy Momentum Tensor ◽  
Energy Condition ◽  
Momentum Tensor ◽  
Energy Conditions ◽  
Thin Shells ◽  
Dominant Energy Condition ◽  
Junction Conditions ◽  
Rest Energy ◽  
Inertial Frames ◽  
Ads Spacetime

In this paper, a rotating thin shell in a (2 + 1)-dimensional asymptotically AdS spacetime is studied. The spacetime exterior to the shell is the rotating BTZ spacetime and the interior is the empty spacetime with a cosmological constant. Through the Einstein equation in (2 + 1) dimensions and the corresponding junction conditions we calculate the dynamical relevant quantities, namely, the rest energy–density, the pressure, and the angular momentum flux density. We also analyze the matter in a frame where its energy–momentum tensor has a perfect fluid form. In addition, we show that Machian effects, such as the dragging of inertial frames, also occur in rotating (2 + 1)-dimensional spacetimes. The weak and the dominant energy condition for these shells are discussed.

scholarly journals Junction conditions in quadratic gravity: thin shells and double layers

2016 ◽  
Vol 33 (10) ◽  
pp. 105008 ◽  
Author(s):  
Borja Reina ◽  
José M M Senovilla ◽  
Raül Vera
Keyword(s):  
Double Layers ◽  
Thin Shells ◽  
Junction Conditions ◽  
Quadratic Gravity

scholarly journals Cosmological Milestones and Gravastars - Topics in General Relativity

2021 ◽  
Author(s):  
◽  
Celine Cattoen
Keyword(s):  
General Relativity ◽  
Perfect Fluid ◽  
Thin Shells ◽  
Generalized Power Series ◽  
Friedmann Equations ◽  
Usual Concept ◽  
Transverse Stresses ◽  
Necessary And Sufficient ◽  
Differential Curvature ◽  
Fluid Spheres

<p>In this thesis, we consider two different problems relevant to general relativity. Overthe last few years, opinions on physically relevant singularities occurring in FRWcosmologies have considerably changed. We present an extensive catalogue of suchcosmological milestones using generalized power series both at the kinematical anddynamical level. We define the notion of “scale factor singularity” and explore its relationto polynomial and differential curvature singularities. We also extract dynamicalinformation using the Friedmann equations and derive necessary and sufficient conditionsfor the existence of cosmological milestones such as big bangs, big crunches, bigrips, sudden singularities and extremality events. Specifically, we provide a completecharacterization of cosmological milestones for which the dominant energy conditionis satisfied. The second problem looks at one of the very small number of seriousalternatives to the usual concept of an astrophysical black hole, that is, the gravastarmodel developed by Mazur and Mottola. By considering a generalized class of similarmodels with continuous pressure (no infinitesimally thin shells) and negative centralpressure, we demonstrate that gravastars cannot be perfect fluid spheres: anisotropcpressures are unavoidable. We provide bounds on the necessary anisotropic pressureand show that these transverse stresses that support a gravastar permit a higher compactnessthan is given by the Buchdahl–Bondi bound for perfect fluid stars. We alsocomment on the qualitative features of the equation of state that such gravastar-likeobjects without any horizon must have.</p>

Dynamics of perfect fluid collapse in f(𝒢,T) gravity

2019 ◽  
Vol 28 (03) ◽  
pp. 1950054 ◽  
Author(s):  
M. Sharif ◽  
M. Zeeshan Gul
Keyword(s):  
Energy Density ◽  
Perfect Fluid ◽  
Junction Conditions ◽  
Conformally Flat ◽  
Dynamical Equations ◽  
Spherical Collapse ◽  
Exterior Regions ◽  
Correction Terms ◽  
Weyl Scalar ◽  
Collapse Rate

This paper investigates the dynamics of perfect fluid spherical collapse in curvature-matter coupled gravity. Using Darmois junction conditions, we derive smooth matching of both interior and exterior regions. The dynamical equations are formulated through Misner–Sharp formalism that give the collapse rate for both general and constant curvature terms. Finally, we formulate a relationship between correction terms, Weyl scalar and matter variables. For constant value of [Formula: see text], it is found that the metric is conformally flat if and only if energy density of the collapsing system is homogeneous while the positive correction terms decrease the collapse rate.

scholarly journals EFFECTS OF ELECTROMAGNETIC FIELD ON GRAVITATIONAL COLLAPSE

2009 ◽  
Vol 24 (31) ◽  
pp. 2551-2563 ◽  
Author(s):  
M. SHARIF ◽  
G. ABBAS
Keyword(s):  
Electromagnetic Field ◽  
Cosmological Constant ◽  
Perfect Fluid ◽  
Gravitational Collapse ◽  
Physical Significance ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
Positive Cosmological Constant ◽  
Symmetric Spacetimes ◽  
Apparent Horizons

In this paper, the effect of electromagnetic field has been investigated on the spherically symmetric gravitational collapse with the perfect fluid in the presence of positive cosmological constant. Junction conditions between the static exterior and non-static interior spherically symmetric spacetimes are discussed. We study the apparent horizons and their physical significance. It is found that electromagnetic field reduces the bound of cosmological constant by reducing the pressure and hence collapsing process is faster as compared to the perfect fluid case. This work gives the generalization of the perfect fluid case to the charged perfect fluid. Results for the perfect fluid case are recovered.

Five-dimensional spherical symmetric perfect fluid collapse in f(R, T) gravity

2019 ◽  
Vol 97 (6) ◽  
pp. 637-643
Author(s):  
M. Jamil Amir ◽  
Sadia Sattar
Keyword(s):  
Black Hole ◽  
Perfect Fluid ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
Field Equations ◽  
Interior Region ◽  
Exterior Region ◽  
Modified Theory Of Gravity ◽  
Apparent Horizons ◽  
Modified Theory

This paper contains the study of spherically symmetric perfect fluid collapse in the framework of f(R, T) modified theory of gravity using five-dimensional background. We consider the five-dimensional spherical symmetric metric as the interior region and a five-dimensional Schwarzschild metric as an exterior region. The Darmois junction conditions between exterior and interior regions are discussed. By taking the particular f(R, T) model, the corresponding field equations are evaluated for both marginally bound L(r) = 1 and non-marginally bound L(r) ≠ 1 cases. We find the gravitational mass of the collapsing system and discuss the apparent horizons and their time formation for different possible cases. Also, the cosmological and black hole horizons have been discussed. It has been concluded that the term involving λ plays a double role: it accelerates the collapse in the region where ρ0 < 4p0 and it slows down the collapsing of matter when ρ0 > 4p0. Further, it is noted that our results reduce to the results found by Sharif and Ahmad (J. Korean Phys. Soc. 52, 980 (2008). doi: 10.3938/jkps.52.980) in general relativity for λ = 0.

scholarly journals Cosmological Milestones and Gravastars - Topics in General Relativity

2021 ◽  
Author(s):  
◽  
Celine Cattoen
Keyword(s):  
General Relativity ◽  
Perfect Fluid ◽  
Thin Shells ◽  
Generalized Power Series ◽  
Friedmann Equations ◽  
Usual Concept ◽  
Transverse Stresses ◽  
Necessary And Sufficient ◽  
Differential Curvature ◽  
Fluid Spheres

<p>In this thesis, we consider two different problems relevant to general relativity. Overthe last few years, opinions on physically relevant singularities occurring in FRWcosmologies have considerably changed. We present an extensive catalogue of suchcosmological milestones using generalized power series both at the kinematical anddynamical level. We define the notion of “scale factor singularity” and explore its relationto polynomial and differential curvature singularities. We also extract dynamicalinformation using the Friedmann equations and derive necessary and sufficient conditionsfor the existence of cosmological milestones such as big bangs, big crunches, bigrips, sudden singularities and extremality events. Specifically, we provide a completecharacterization of cosmological milestones for which the dominant energy conditionis satisfied. The second problem looks at one of the very small number of seriousalternatives to the usual concept of an astrophysical black hole, that is, the gravastarmodel developed by Mazur and Mottola. By considering a generalized class of similarmodels with continuous pressure (no infinitesimally thin shells) and negative centralpressure, we demonstrate that gravastars cannot be perfect fluid spheres: anisotropcpressures are unavoidable. We provide bounds on the necessary anisotropic pressureand show that these transverse stresses that support a gravastar permit a higher compactnessthan is given by the Buchdahl–Bondi bound for perfect fluid stars. We alsocomment on the qualitative features of the equation of state that such gravastar-likeobjects without any horizon must have.</p>

ON A PERFECT FLUID K¨ AHLER SPACETIME

2016 ◽  
Vol 12 (3) ◽  
pp. 4350-4355
Author(s):  
VIBHA SRIVASTAVA ◽  
P. N. PANDEY
Keyword(s):  
Field Equation ◽  
Perfect Fluid ◽  
Sectional Curvature ◽  
Einstein Field Equation ◽  
Cosmological Term ◽  
Conformal Killing ◽  
Killing Vectors ◽  
Projectively Flat ◽  
Conformal Killing Vectors

The object of the present paper is to study a perfect fluid K¨ahlerspacetime. A perfect fluid K¨ahler spacetime satisfying the Einstein field equation with a cosmological term has been studied and the existence of killingand conformal killing vectors have been discussed. Certain results related to sectional curvature for pseudo projectively flat perfect fluid K¨ahler spacetime have been obtained. Dust model for perfect fluid K¨ahler spacetime has also been studied.

Maysel's formula generalized for piezoelectric vibrations - Application to thin shells of revolution

1996 ◽  
Author(s):  
Hans Irschik ◽  
Franz Ziegler ◽  
Hans Irschik ◽  
Franz Ziegler
Keyword(s):  
Thin Shells ◽  
Shells Of Revolution
Sign in / Sign up

Export Citation Format

Share Document