ترغب بنشر مسار تعليمي؟ اضغط هنا

Painleve-Gullstrand Coordinates for the Kerr Solution

105   0   0.0 ( 0 )
 نشر من قبل Jose Natario
 تاريخ النشر 2014
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Jose Natario




اسأل ChatGPT حول البحث

We construct a coordinate system for the Kerr solution, based on the zero angular momentum observers dropped from infinity, which generalizes the Painleve-Gullstrand coordinate system for the Schwarzschild solution. The Kerr metric can then be interpreted as describing space flowing on a (curved) Riemannian 3-manifold. The stationary limit arises as the set of points on this manifold where the speed of the flow equals the speed of light, and the horizons as the set of points where the radial speed equals the speed of light. A deeper analysis of what is meant by the flow of space reveals that the acceleration of free-falling objects is generally not in the direction of this flow. Finally, we compare the new coordinate system with the closely related Doran coordinate system.



قيم البحث

اقرأ أيضاً

96 - Yuki Kanai , Masaru Siino , 2010
We construct an exact solution for the spherical gravitational collapse in a single coordinate patch. To describe the dynamics of collapse, we use a generalized form of the Painleve-Gullstrand coordinates in the Schwarzschild spacetime. The time coor dinate of the form is the proper time of a free-falling observer so that we can describe the collapsing star not only outside but also inside the event horizon in a single coordinate patch. We show the both solutions corresponding to the gravitational collapse from infinity and from a finite radius.
149 - J. Ziprick , G. Kunstatter 2008
We perform a numerical study of black hole formation from the spherically symmetric collapse of a massless scalar field. The calculations are done in Painleve-Gullstrand (PG) coordinates that extend across apparent horizons and allow the numerical ev olution to proceed until the onset of singularity formation. We generate spacetime maps of the collapse and illustrate the evolution of apparent horizons and trapping surfaces for various initial data. We also study the critical behaviour and find the expected Choptuik scaling with universal values for the critical exponent and echoing period consistent with the accepted values of $gamma=0.374$ and $Delta = 3.44$, respectively. The subcritical curvature scaling exhibits the expected oscillatory behaviour but the form of the periodic oscillations in the supercritical mass scaling relation, while universal with respect to initial PG data, is non-standard: it is non-sinusoidal with large amplitude cusps.
94 - C. A. Brannen 2009
We derive the exact equations of motion (in Newtonian, F=ma, form) for test masses in Schwarzschild and Gullstrand-Painleve coordinates. These equations of motion are simpler than the usual geodesic equations obtained from Christoffel tensors in that the affine parameter is eliminated. The various terms can be compared against tests of gravity. In force form, gravity can be interpreted as resulting from a flux of superluminal particles (gravitons). We show that the first order relativistic correction to Newtons gravity results from a two graviton interaction.
We present a simple exact solution for the interior of a rotating star. The interpretation of the stress energy tensor as that of a fluid requires the existence of a high viscosity, which is quite expected for a rotating fluid. In spite of the negati ve stresses, energy conditions are in fact all satisfied.
We derive the second-order post-Minkowskian solution for the small-deflection motion of test particles in the external field of the Kerr-Newman black hole via an iterative method. The analytical results are exhibited in the coordinate system constitu ted by the particles initial velocity unit vector, impact vector, and their cross-product. The achieved formulas explicitly give the dependences of the particles trajectory and velocity on the time once their initial position and velocity are specified, and can be applied not only to a massive particle, but also to a photon as well.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا