scholarly journals Spherically symmetric dissipative anisotropic fluids: A general study

2004 ◽  
Vol 69 (8) ◽  
Author(s):  
L. Herrera ◽  
A. Di Prisco ◽  
J. Martin ◽  
J. Ospino ◽  
N. O. Santos ◽  
...  
Keyword(s):  
Spherically Symmetric ◽  
General Study ◽  
Anisotropic Fluids

Evolution of expansion-free spherically symmetric self-gravitating non-dissipative fluids and some analytical solutions

2018 ◽  
Vol 15 (04) ◽  
pp. 1850058 ◽  
Author(s):  
Rajesh Kumar ◽  
Sudhir Kumar Srivastava
Keyword(s):  
Analytical Models ◽  
Fluid Distribution ◽  
Junction Condition ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
Minkowski Space Time ◽  
Spherically Symmetric Metric ◽  
Anisotropic Fluids ◽  
Vacuum Cavity ◽  
Dissipative Fluids

We consider the distribution of spherically symmetric self-gravitating non-dissipative (but anisotropic) fluids under the expansion-free condition which requires the existence of vacuum cavity within the fluid distribution. The Darmois junction condition is investigated for matching the spherically symmetric metric to an internal vacuum cavity (Minkowski space-time). We have studied some analytical models, total of three family of solutions out of which two satisfy the junction conditions over both the hypersurfaces. The models are investigated under some known dynamical assumptions which further provide analytical solution in each family.

scholarly journals All static spherically symmetric anisotropic solutions for general relativistic polytropes

2020 ◽  
Vol 29 (12) ◽  
pp. 2050082
Author(s):  
G. Abellán ◽  
P. Bargueño ◽  
E. Contreras ◽  
E. Fuenmayor
Keyword(s):  
Perfect Fluid ◽  
Generating Function ◽  
Generating Functions ◽  
Interesting Case ◽  
Spherically Symmetric ◽  
Conformally Flat ◽  
Class 1 ◽  
General Relativistic ◽  
Anisotropic Fluids

In this work, we develop an algorithm to construct all static spherically symmetric anisotropic solutions for general relativistic polytropes. To this end, we follow the strategy presented by K. Lake in Phys. Rev. D 67 (2003) 104015 to obtain all static spherically symmetric perfect fluid solutions and then extended by L. Herrera el al., Phys. Rev. D 77 (2008) 027502 to the interesting case of locally anisotropic fluids. The formalism here developed requires the knowledge of only one function to generate all possible solutions. To illustrate the method, we obtain formal expressions for the generating functions of known polytopic solutions. Additionally, we obtain the generating function for both the conformally flat and class 1 polytropes.

scholarly journals Nonlocal equation of state in anisotropic static fluid spheres in general relativity

2004 ◽  
Vol 82 (1) ◽  
pp. 29-51 ◽  
Author(s):  
H Hernández ◽  
L A Núñez
Keyword(s):  
Equation Of State ◽  
Radial Pressure ◽  
Spherically Symmetric ◽  
Density Profiles ◽  
Physical Conditions ◽  
Tangential Stresses ◽  
Nonlocal Equation ◽  
Static Fluid ◽  
Anisotropic Fluids ◽  
Fluid Spheres

We show that it is possible to obtain, at least certain regions within spherically symmetric static matter configurations, credible anisotropic fluids satisfying a nonlocal equation of state. This particular type of equation of state provides, at a given point, the radial pressure not only as a function of the density at that point, but its functional throughout the enclosed distribution. To establish the physical plausibility of the proposed family of solutions satisfying a nonlocal equation of state, we study the constraints imposed by the junction, energy, and some intuitive physical conditions. We show that these static fluids having this particular equation of state are "naturally" anisotropic in the sense that they satisfy, identically, the anisotropic Tolman–Oppenheimer–Volkov equation. We also show that it is possible to obtain physically plausible static anisotropic spherically symmetric matter configurations starting from known density profiles, and also for configurations where tangential pressures vanish. This very particular type of relativistic sphere with vanishing tangential stresses is inspired by some of the models proposed to describe extremely magnetized neutron stars (magnetars) during the transverse quantum collapse.

The two-body problem: an effective-one-body approach

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Body Problem ◽  
Equations Of Motion ◽  
Reaction Force ◽  
Kerr Black Hole ◽  
Radiation Reaction ◽  
Spherically Symmetric ◽  
Geodesic Motion ◽  
Two Body Problem ◽  
Symmetric Spacetime ◽  
Radiation Reaction Force

This chapter presents the basics of the ‘effective-one-body’ approach to the two-body problem in general relativity. It also shows that the 2PN equations of motion can be mapped. This can be done by means of an appropriate canonical transformation, to a geodesic motion in a static, spherically symmetric spacetime, thus considerably simplifying the dynamics. Then, including the 2.5PN radiation reaction force in the (resummed) equations of motion, this chapter provides the waveform during the inspiral, merger, and ringdown phases of the coalescence of two non-spinning black holes into a final Kerr black hole. The chapter also comments on the current developments of this approach, which is instrumental in building the libraries of waveform templates that are needed to analyze the data collected by the current gravitational wave detectors.

Spherically Symmetric Gravitational Fields

1965 ◽  
Vol 6 (1) ◽  
pp. 1-5 ◽  
Author(s):  
P. G. Bergmann ◽  
M. Cahen ◽  
A. B. Komar
Keyword(s):  
Spherically Symmetric ◽  
Gravitational Fields
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