Adding initial data - Revision history

Rhaas: /* param.ccl */

2021-04-07T14:52:54Z

‎param.ccl

Rhaas: update link to pdf file about Kruskal coordinates

2018-08-07T12:09:02Z

update link to pdf file about Kruskal coordinates

Twright: adding initial data moved to Adding initial data: Capitalize titles; Newer MediaWiki will orphan pages with lowercase title names

2018-08-06T16:50:31Z

adding initial data moved to Adding initial data: Capitalize titles; Newer MediaWiki will orphan pages with lowercase title names

141.142.42.12: use Media instead of Image for downloads.

2017-08-11T18:51:38Z

use Media instead of Image for downloads.

141.142.42.12: minor wikitext issues

2017-08-11T18:50:38Z

minor wikitext issues

Noncct zhichao-zhao: /* Example */

2017-02-22T03:15:05Z

‎Example

Eschnett: /* Running an Example */

2010-04-19T18:00:35Z

‎Running an Example

Eschnett: /* schedule.ccl */

2010-04-19T17:57:58Z

‎schedule.ccl

Eschnett: /* param.ccl */

2010-04-19T17:55:26Z

‎param.ccl

Eschnett: /* CCL Files: Cactus Declarations */

2010-04-19T17:45:23Z

‎CCL Files: Cactus Declarations

@@ Line 182: / Line 182: @@
 We also set a few parameters of our own:
-PRIVATE:
+ PRIVATE:
   BOOLEAN calculate_Schwarzschild_radius "Calculate the Schwarzschild radius?"

@@ Line 12: / Line 12: @@
 ==Example==
-Let us assume, for the sake of simplicity, that we are going to set up initial data for the spacetime only.  Let us pick a concrete example: the Kruskal coordinates.  The Kruskal coordinates describe a single, static black hole (the Schwarzschild spacetime), and their advantage over many other coordinate systems is that they cover the whole, extended Schwarzschild spacetime (i.e. including both asymptotically flat ends, the worm hole, the black and white hole horizons), and that they do not introduce coordinate singularities.  Of course there are curvature singularities inside the white and black holes, but there are no "artificial" singularities, e.g. at the horizons.  The Kruskal coordinates are beautifully described in Sean M. Carroll's "A No-Nonsense Introduction to General Relativity", 2001, at http://pancake.uchicago.edu/~carroll/notes/grtinypdf.pdf .
+Let us assume, for the sake of simplicity, that we are going to set up initial data for the spacetime only.  Let us pick a concrete example: the Kruskal coordinates.  The Kruskal coordinates describe a single, static black hole (the Schwarzschild spacetime), and their advantage over many other coordinate systems is that they cover the whole, extended Schwarzschild spacetime (i.e. including both asymptotically flat ends, the worm hole, the black and white hole horizons), and that they do not introduce coordinate singularities.  Of course there are curvature singularities inside the white and black holes, but there are no "artificial" singularities, e.g. at the horizons.  The Kruskal coordinates are beautifully described in Sean M. Carroll's "A No-Nonsense Introduction to General Relativity", 2001, at https://preposterousuniverse.com/wp-content/uploads/2015/08/grtinypdf.pdf .
 To make things a bit more interesting, we are also going to apply a coordinate transformation to the Kruskal coordinates, so that we can evaluate them on arbitrary slices.  Of course that means that the actual coordinates are not the Kruskal coordinates.  This means that the slicing can in principle be chosen arbitrarily within the extended Schwarzschild spacetime.  Other coordinates (e.g. ingoing Eddington-Finkelstein coordinates) are regular only a in part of the spacetime.  This will allow us to examine arbitrary slicings of Schwarzschild -- even slicings that are not spherically symmetric -- which is very interesting when one studies trapped surfaces or apparent horizons.

@@ Line 25: / Line 25: @@
 ==Kruskal Solution==
-As mentioned above, we begin by implementing a Fortran module that evaluates the Kruskal solution at a particular event (t,x,y,z).  How to do this is outside the scope of this tutorial; one example implementation is here: [[Image:kruskal.F90]].
+As mentioned above, we begin by implementing a Fortran module that evaluates the Kruskal solution at a particular event (t,x,y,z).  How to do this is outside the scope of this tutorial; one example implementation is here: [[Media:kruskal.F90]].
 This module contains a routine that has as its input arguments 4 real numbers t, x, y, and z, describing the spacetime event where the four-metric needs to be evaluated.  Its output arguments are alpha, beta^i, and g_ij, which this routine has to fill in.  For convenience, this routine also sets the two arguments u and v to the Kruskal coordinates of this event, and two other arguments st and sr to its Schwarzschild coordinates.  (Since the metric is spherically symmetric, angular coordinates can be omitted.)
@@ Line 151: / Line 151: @@
   } "Schwarzschild radius"
-The complete file is here: [[Image:interface.ccl.txt]]
+The complete file is here: [[Media:interface.ccl.txt]]
 ===param.ccl===
@@ Line 205: / Line 205: @@
   } 1.0e-6
-The complete file is here: [[Image:param.ccl.txt]]
+The complete file is here: [[Media:param.ccl.txt]]
 ===schedule.ccl===
@@ Line 234: / Line 234: @@
 Scheduling the initial data routine takes no options, leaving all schedule options at their default values.  This means e.g. that this routine is called once for each refinement level (corresponding to "OPTIONS=local").  Also, no grid functions need to be synchronised since all grid points are set, including boundary and ghost points.
-The complete file is here: [[Image:schedule.ccl.txt]]
+The complete file is here: [[Media:schedule.ccl.txt]]
 ==Setting up and Running an Example==
-You can obtain a tarball of the complete thorn here: [[Image:Kruskal.tar.gz]].
+You can obtain a tarball of the complete thorn here: [[Media:Kruskal.tar.gz]].
 This section is missing.  There are example parameter files in the par subdirectory.  It is particularly interesting to run "kruskal-wald-iyer.par", which shows that "numerical apparent horizons" are found after all, although true apparent horizons do not exist.  Speak about http://prd.aps.org/abstract/PRD/v73/i2/e021502 .

@@ Line 128: / Line 128: @@
              end if
-For reference, the complete initial data routine is here: [[Image:InitialData.F90]]
+For reference, the complete initial data routine is here: [[Media:InitialData.F90]]
 ==CCL Files: Cactus Declarations==

@@ Line 12: / Line 12: @@
 ==Example==
-Let us assume, for the sake of simplicity, that we are going to set up initial data for the spacetime only.  Let us pick a concrete example: the Kruskal coordinates.  The Kruskal coordinates describe a single, static black hole (the Schwarzschild spacetime), and their advantage over many other coordinate systems is that they cover the whole, extended Schwarzschild spacetime (i.e. including both asymptotically flat ends, the worm hole, the black and white hole horizons), and that they do not introduce coordinate singularities.  Of course there are curvature singularities inside the white and black holes, but there are no "artificial" singularities, e.g. at the horizons.  The Krukal coordinates are beautifully described in Sean M. Carroll's "A No-Nonsense Introduction to General Relativity", 2001, at http://pancake.uchicago.edu/~carroll/notes/grtinypdf.pdf .
+Let us assume, for the sake of simplicity, that we are going to set up initial data for the spacetime only.  Let us pick a concrete example: the Kruskal coordinates.  The Kruskal coordinates describe a single, static black hole (the Schwarzschild spacetime), and their advantage over many other coordinate systems is that they cover the whole, extended Schwarzschild spacetime (i.e. including both asymptotically flat ends, the worm hole, the black and white hole horizons), and that they do not introduce coordinate singularities.  Of course there are curvature singularities inside the white and black holes, but there are no "artificial" singularities, e.g. at the horizons.  The Kruskal coordinates are beautifully described in Sean M. Carroll's "A No-Nonsense Introduction to General Relativity", 2001, at http://pancake.uchicago.edu/~carroll/notes/grtinypdf.pdf .
 To make things a bit more interesting, we are also going to apply a coordinate transformation to the Kruskal coordinates, so that we can evaluate them on arbitrary slices.  Of course that means that the actual coordinates are not the Kruskal coordinates.  This means that the slicing can in principle be chosen arbitrarily within the extended Schwarzschild spacetime.  Other coordinates (e.g. ingoing Eddington-Finkelstein coordinates) are regular only a in part of the spacetime.  This will allow us to examine arbitrary slicings of Schwarzschild -- even slicings that are not spherically symmetric -- which is very interesting when one studies trapped surfaces or apparent horizons.

←Older revision	Revision as of 16:50, 6 August 2018
(No difference)

←Older revision		Revision as of 17:57, 19 April 2010
Line 235:		Line 235:

	The complete file is here: [[Image:schedule.ccl.txt]]		The complete file is here: [[Image:schedule.ccl.txt]]
		+
		+	==Running an Example==
		+
		+	This section is missing. There are example parameter files in the par subdirectory. It is particularly interesting to run "kruskal-wald-iyer.par", which shows that "numerical apparent horizons" are found after all, although true apparent horizons do not exist. Speak about http://prd.aps.org/abstract/PRD/v73/i2/e021502 .

@@ Line 183: / Line 183: @@
 PRIVATE:
   CCTK_REAL mass "Black hole mass"
@@ Line 202: / Line 206: @@
 The complete file is here: [[Image:param.ccl.txt]]

←Older revision		Revision as of 17:45, 19 April 2010
Line 131:		Line 131:

	==CCL Files: Cactus Declarations==		==CCL Files: Cactus Declarations==
		+
		+	In the last step (now that all the hard work is done), we describe to Cactus how this torn is called, what its variables are, what parameters it takes, and when its routines need to be called.
		+
		+	===interface.ccl===
		+
		+	This thorn is called "Kruskal", and it implements an interface that we also call "Kruskal" (for the lack of a better idea).
		+	IMPLEMENTS: Kruskal
		+
		+	This thorn requires access to a few other variables, in particular the grid points' coordinates, and the ADMBase variables which it calculates:
		+	INHERITS: ADMBase StaticConformal grid
		+
		+	It also calculates and stores the Kruskal and Schwarzschild coordinates of every grid point for convenience, so we define grid functions for these:
		+	CCTK_REAL Schwarzschild_radius TYPE=gf
		+	{
		+	schw_radius
		+	schw_time
		+	kruskal_u
		+	kruskal_v
		+	} "Schwarzschild radius"
		+
		+	The complete file is here: [[Image:interface.ccl.txt]]
		+
		+	===param.ccl===
		+
		+	There are two kinds of parameters that we have to deal with:
		+	* Parameters that choose which kind of initial data should be set up (which we extend to include "Kruskal")
		+	* Parameters for ourselves, where e.g. the ADM mass of the Schwarzschild spacetime is set, and the slicing is chosen
		+
		+	Let's begin with the initial data choice parameters, which are defined in ADMBase. We obtain access to them, and extend their range (the set of allowed values) to include "Kruskal"). We can do this because ADMBase allows us to do so -- private parameters could not be extended.
		+
		+	SHARES: ADMBase
		+
		+	EXTENDS KEYWORD initial_lapse
		+	{
		+	"Kruskal" :: "Kruskal lapse"
		+	}
		+
		+	EXTENDS KEYWORD initial_shift
		+	{
		+	"Kruskal" :: "Kruskal shift"
		+	}
		+
		+	EXTENDS KEYWORD initial_data
		+	{
		+	"Kruskal" :: "Kruskal metric"
		+	}
		+
		+	USES KEYWORD metric_type
		+
		+	We also set a few parameters of our own:
		+
		+	PRIVATE:
		+
		+	CCTK_REAL mass "Black hole mass"
		+	{
		+	0:* :: ""
		+	} 1.0
		+
		+	KEYWORD slicing "Choice of slicing"
		+	{
		+	"Kruskal" :: "v = t"
		+	"Schwarzschild" :: "v = u tanh (t / 4M)"
		+	"Wald-Iyer" :: "v = t cos theta"
		+	} "Kruskal"
		+
		+	CCTK_REAL delta "Finite differencing distance"
		+	{
		+	(0:* :: ""
		+	} 1.0e-6
		+
		+	The complete file is here: [[Image:param.ccl.txt]]