General Relativistic Polytropic Fluid Spheres.

1964 ◽  
Vol 140 ◽  
pp. 434 ◽  
Author(s):  
Robert F. Tooper
Keyword(s):  
General Relativistic ◽  
Fluid Spheres

General relativistic fluid spheres with variable polytropic index

1966 ◽  
Vol 6 (2) ◽  
pp. 139-147
Author(s):  
R. van der Borght
Keyword(s):  
General Relativity ◽  
Compressible Fluid ◽  
Fluid Sphere ◽  
Polytropic Index ◽  
Field Equations ◽  
Relativistic Fluid ◽  
General Relativistic ◽  
Temperature And Pressure ◽  
Fluid Spheres

AbstractIn this paper we derive solutions of the field equations of general relativity for a compressible fluid sphere which obeys density-temperature and pressure-temperature relations which allow for a variation of the polytropic index throughout the sphere.

General Relativistic Fluid Spheres

1959 ◽  
Vol 116 (4) ◽  
pp. 1027-1034 ◽  
Author(s):  
H. A. Buchdahl
Keyword(s):  
Relativistic Fluid ◽  
General Relativistic ◽  
Fluid Spheres

scholarly journals BUCHDAHL-LIKE TRANSFORMATIONS FOR PERFECT FLUID SPHERES

2008 ◽  
Vol 17 (01) ◽  
pp. 135-163 ◽  
Author(s):  
PETARPA BOONSERM ◽  
MATT VISSER
Keyword(s):  
Perfect Fluid ◽  
Functional Form ◽  
Polar Coordinates ◽  
Coordinate Systems ◽  
Large Classes ◽  
Isotropic Coordinates ◽  
General Relativistic ◽  
Algorithmic Techniques ◽  
Isothermal Coordinates ◽  
Fluid Spheres

In two previous articles [Phys. Rev. D71 (2005) 124307 (gr-qc/0503007) and Phys. Rev. D76 (2006) 0440241 (gr-qc/0607001)] we have discussed several "algorithmic" techniques that permit one (in a purely mechanical way) to generate large classes of general-relativistic static perfect fluid spheres. Working in Schwarzschild curvature coordinates, we used these algorithmic ideas to prove several "solution-generating theorems" of varying levels of complexity. In the present article we consider the situation in other coordinate systems. In particular, in general diagonal coordinates we shall generalize our previous theorems, in isotropic coordinates we shall encounter a variant of the so-called "Buchdahl transformation," and in other coordinate systems (such as Gaussian polar coordinates, Synge isothermal coordinates, and Buchdahl coordinates) we shall find a number of more complex "Buchdahl-like transformations" and "solution-generating theorems" that may be used to investigate and classify the general-relativistic static perfect fluid sphere. Finally, by returning to general diagonal coordinates and making a suitable ansatz for the functional form of the metric components, we place the Buchdahl transformation in its most general possible setting.

Beyond the Schwarzschild Metric

2018 ◽  
Author(s):  
David M. Wittman
Keyword(s):  
Black Holes ◽  
General Relativity ◽  
Gravitational Waves ◽  
Test Particle ◽  
Direct Detection ◽  
Relativistic Effects ◽  
Big Bang ◽  
Clusters Of Galaxies ◽  
General Relativistic ◽  
The Universe

General relativity explains much more than the spacetime around static spherical masses.We briefly assess general relativity in the larger context of physical theories, then explore various general relativistic effects that have no Newtonian analog. First, source massmotion gives rise to gravitomagnetic effects on test particles.These effects also depend on the velocity of the test particle, which has substantial implications for orbits around black holes to be further explored in Chapter 20. Second, any changes in the sourcemass ripple outward as gravitational waves, and we tell the century‐long story from the prediction of gravitational waves to their first direct detection in 2015. Third, the deflection of light by galaxies and clusters of galaxies allows us to map the amount and distribution of mass in the universe in astonishing detail. Finally, general relativity enables modeling the universe as a whole, and we explore the resulting Big Bang cosmology.

On the Possibility of the Nonexplosive Core Contraction of Massive Stars. II. General Relativistic Analysis

1999 ◽  
Vol 521 (1) ◽  
pp. 376-381 ◽  
Author(s):  
Atsuyuki Hayashi ◽  
Yoshiharu Eriguchi ◽  
Masa‐aki Hashimoto
Keyword(s):  
Massive Stars ◽  
General Relativistic ◽  
Relativistic Analysis
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