Commits April 2012

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New changesets in Carpet Mercurial
by Carpet mercurial repositories 04 Apr '12

04 Apr '12

changeset: 3507:e970c8c56a63 tag: tip user: Erik Schnetter <schnetter(a)gmail.com> date: Wed Apr 04 15:54:40 2012 -0400 summary: Carpet: Do not count ghost zones when calculating speed

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[svn:einsteintoolkit] Workshop_Spring_2012/supercomputing/ (Rev. 57)
by jfaber＠einsteintoolkit.org 04 Apr '12

04 Apr '12

User: jfaber Date: 2012/04/04 01:43 PM Added: /supercomputing/ supercomputing.aux, supercomputing.log, supercomputing.nav, supercomputing.out, supercomputing.pdf, supercomputing.snm, supercomputing.tex, supercomputing.toc Log: Contributions to the notes on supercomputing/Xsede resources File Changes: Directory: /supercomputing/ =========================== File [added]: supercomputing.aux Delta lines: <Unavailable> File [added]: supercomputing.log Delta lines: <Unavailable> File [added]: supercomputing.nav Delta lines: <Unavailable> File [added]: supercomputing.out Delta lines: <Unavailable> File [added]: supercomputing.pdf Delta lines: <Unavailable> File [added]: supercomputing.snm Delta lines: <Unavailable> File [added]: supercomputing.tex Delta lines: <Unavailable> File [added]: supercomputing.toc Delta lines: <Unavailable>

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[svn:einsteintoolkit] Workshop_Spring_2012/example_wavetoy/Cactus/arrangements/Introduction/WaveToy/ (Rev. 56)
by roland.haas＠physics.gatech.edu 04 Apr '12

04 Apr '12

User: rhaas Date: 2012/04/04 01:22 PM Modified: /example_wavetoy/Cactus/arrangements/Introduction/WaveToy/ interface.ccl, schedule.ccl /example_wavetoy/Cactus/arrangements/Introduction/WaveToy/src/ WaveToy.c Log: add routines to compute wave energy to wavetoy example File Changes: Directory: /example_wavetoy/Cactus/arrangements/Introduction/WaveToy/ ===================================================================== File [modified]: interface.ccl Delta lines: +2 -0 =================================================================== --- example_wavetoy/Cactus/arrangements/Introduction/WaveToy/interface.ccl 2012-04-04 18:04:36 UTC (rev 55) +++ example_wavetoy/Cactus/arrangements/Introduction/WaveToy/interface.ccl 2012-04-04 18:22:04 UTC (rev 56) @@ -8,7 +8,9 @@ phi } "The evolved scalar field" +CCTK_REAL energy TYPE=gf TIMELEVELS=3 "Energy in wave" + CCTK_INT FUNCTION Boundary_SelectVarForBC(CCTK_POINTER_TO_CONST IN GH, \ CCTK_INT IN faces, CCTK_INT IN boundary_width, CCTK_INT IN table_handle, \ CCTK_STRING IN var_name, CCTK_STRING IN bc_name) File [modified]: schedule.ccl Delta lines: +6 -1 =================================================================== --- example_wavetoy/Cactus/arrangements/Introduction/WaveToy/schedule.ccl 2012-04-04 18:04:36 UTC (rev 55) +++ example_wavetoy/Cactus/arrangements/Introduction/WaveToy/schedule.ccl 2012-04-04 18:22:04 UTC (rev 56) @@ -1,4 +1,4 @@ -STORAGE: scalarevolve[3] +STORAGE: scalarevolve[3] energy[3] SCHEDULE WaveToy_InitialData AT CCTK_INITIAL { @@ -11,6 +11,11 @@ SYNC: scalarevolve } "Evolution of 3D wave equation" +SCHEDULE WaveToy_Energy AT CCTK_EVOL AFTER WaveToy_Evolution +{ + LANG: C +} "Compute wave energy" + SCHEDULE WaveToy_Boundaries AT CCTK_EVOL AFTER WaveToy_Evolution { LANG: C Directory: /example_wavetoy/Cactus/arrangements/Introduction/WaveToy/src/ ========================================================================= File [modified]: WaveToy.c Delta lines: +19 -0 =================================================================== --- example_wavetoy/Cactus/arrangements/Introduction/WaveToy/src/WaveToy.c 2012-04-04 18:04:36 UTC (rev 55) +++ example_wavetoy/Cactus/arrangements/Introduction/WaveToy/src/WaveToy.c 2012-04-04 18:22:04 UTC (rev 56) @@ -70,7 +70,26 @@ } } +/* + * Routine to compute energy + */ +void WaveToy_Energy(CCTK_ARGUMENTS) { + DECLARE_CCTK_ARGUMENTS; + /* Energy density is just square of wave */ + for (int k=1; k<cctk_lsh[2]-1; k++) { + for (int j=1; j<cctk_lsh[1]-1; j++) { + for (int i=1; i<cctk_lsh[0]-1; i++) { + energy[CCTK_GFINDEX3D(cctkGH,i,j,k)] = + SQ(phi[CCTK_GFINDEX3D(cctkGH,i,j,k)]) * + CCTK_DELTA_SPACE(0) * CCTK_DELTA_SPACE(1) * + CCTK_DELTA_SPACE(2); + } + } + } +} + + /* * Select boundary condition */

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[svn:einsteintoolkit] Workshop_Spring_2012/example_tov/ (Rev. 55)
by knarf＠cct.lsu.edu 04 Apr '12

04 Apr '12

User: knarf Date: 2012/04/04 01:04 PM Added: /example_tov/ fast_tov.par Log: fast tov parameter file File Changes: Directory: /example_tov/ ======================== File [added]: fast_tov.par Delta lines: +221 -0 =================================================================== --- example_tov/fast_tov.par (rev 0) +++ example_tov/fast_tov.par 2012-04-04 18:04:36 UTC (rev 55) @@ -0,0 +1,221 @@ +## mclachlan tov_static +ActiveThorns = "Time MoL" +ActiveThorns = "Coordbase CartGrid3d Boundary StaticConformal" +ActiveThorns = "SymBase ADMBase TmunuBase HydroBase InitBase ADMCoupling ADMMacros" +ActiveThorns = "IOUtil Formaline" +ActiveThorns = "SpaceMask CoordGauge Constants LocalReduce aeilocalinterp LoopControl" +ActiveThorns = "Carpet CarpetLib CarpetReduce CarpetRegrid2 CarpetInterp" +ActiveThorns = "CarpetIOASCII CarpetIOScalar CarpetIOHDF5 CarpetIOBasic" + +ActiveThorns = "ADMConstraints NaNChecker" + +# grid parameters +CartGrid3D::type = "coordbase" +CartGrid3D::domain = "full" +CartGrid3D::avoid_origin = "no" +CoordBase::xmin = 0.0 +CoordBase::ymin = 0.0 +CoordBase::zmin = 0.0 +CoordBase::xmax = 15.0 +CoordBase::ymax = 15.0 +CoordBase::zmax = 15.0 +CoordBase::dx = 1 +CoordBase::dy = 1 +CoordBase::dz = 1 + +CoordBase::boundary_size_x_lower = 3 +CoordBase::boundary_size_y_lower = 3 +CoordBase::boundary_size_z_lower = 3 +CoordBase::boundary_size_x_upper = 3 +CoordBase::boundary_size_y_upper = 3 +CoordBase::boundary_size_z_upper = 3 +CoordBase::boundary_shiftout_x_lower = 1 +CoordBase::boundary_shiftout_y_lower = 1 +CoordBase::boundary_shiftout_z_lower = 1 +CoordBase::boundary_shiftout_x_upper = 0 +CoordBase::boundary_shiftout_y_upper = 0 +CoordBase::boundary_shiftout_z_upper = 0 + + + + +ActiveThorns = "ReflectionSymmetry" + +ReflectionSymmetry::reflection_x = "yes" +ReflectionSymmetry::reflection_y = "yes" +ReflectionSymmetry::reflection_z = "yes" +ReflectionSymmetry::avoid_origin_x = "no" +ReflectionSymmetry::avoid_origin_y = "no" +ReflectionSymmetry::avoid_origin_z = "no" + + + +TmunuBase::stress_energy_storage = yes +TmunuBase::stress_energy_at_RHS = yes +TmunuBase::timelevels = 1 +TmunuBase::prolongation_type = none + +HydroBase::timelevels = 3 + +ADMMacros::spatial_order = 4 + +ADMBase::metric_type = "physical" + +ADMConstraints::bound = "static" +ADMConstraints::constraints_timelevels = 3 +ADMConstraints::constraints_persist = yes + +SpaceMask::use_mask = "yes" + +Cactus::terminate = "time" +Cactus::cctk_final_time = 1000 + +Carpet::domain_from_coordbase = "yes" +Carpet::enable_all_storage = no +Carpet::use_buffer_zones = "yes" + +Carpet::poison_new_timelevels = "yes" +Carpet::check_for_poison = "no" +Carpet::poison_value = 113 + +Carpet::init_3_timelevels = no +Carpet::init_fill_timelevels = "yes" + +CarpetLib::poison_new_memory = "yes" +CarpetLib::poison_value = 114 + +# system specific Carpet paramters +Carpet::max_refinement_levels = 10 +driver::ghost_size = 3 +Carpet::prolongation_order_space = 3 +Carpet::prolongation_order_time = 2 + +CarpetRegrid2::regrid_every = 0 +CarpetRegrid2::num_centres = 1 + +CarpetRegrid2::num_levels_1 = 1 +CarpetRegrid2::radius_1[1] = 15.0 + + +time::dtfac = 0.25 +MoL::ODE_Method = "rk4" +MoL::MoL_Intermediate_Steps = 4 +MoL::MoL_Num_Scratch_Levels = 1 + +# check all physical variables for NaNs +NaNChecker::check_every = 1 +NaNChecker::action_if_found = "just warn" #"terminate", "just warn", "abort" +NaNChecker::check_vars = "ADMBase::metric ADMBase::lapse ADMBase::shift HydroBase::rho HydroBase::eps HydroBase::press HydroBase::vel" + +## Lapse Condition: \partial_t alpha = - alpha K +## Shift Condition: \partial_t beta^i = 0 + +# Hydro paramters +ActiveThorns = "EOS_Omni" +ActiveThorns = "GRHydro" + +HydroBase::evolution_method = "GRHydro" + +GRHydro::riemann_solver = "Marquina" +GRHydro::GRHydro_eos_type = "Polytype" +GRHydro::GRHydro_eos_table = "2D_Polytrope" +GRHydro::recon_method = "ppm" +GRHydro::GRHydro_stencil = 3 +GRHydro::bound = "none" +GRHydro::rho_abs_min = 1.e-10 +#GRHydro::GRHydro = 18 # Tmunu(10), rho,press,eps,w_lorentz,vel, tau +#GRHydro::GRHydro = 10 # gij(6), alpha, beta(3) + + +ActiveThorns = "GenericFD NewRad" +ActiveThorns = "ML_BSSN ML_BSSN_Helper" +ADMBase::evolution_method = "ML_BSSN" +ADMBase::lapse_evolution_method = "ML_BSSN" +ADMBase::shift_evolution_method = "ML_BSSN" +ADMBase::dtlapse_evolution_method= "ML_BSSN" +ADMBase::dtshift_evolution_method= "ML_BSSN" + +TmunuBase::support_old_CalcTmunu_mechanism = "no" + +ML_BSSN::timelevels = 3 + +ML_BSSN::harmonicN = 1 # 1+log +ML_BSSN::harmonicF = 1.0 # 1+log +ML_BSSN::LapseACoeff = 1.0 +ML_BSSN::ShiftBCoeff = 1.0 +ML_BSSN::ShiftGammaCoeff = 0.0 +ML_BSSN::AlphaDriver = 0.0 +ML_BSSN::BetaDriver = 0.0 +ML_BSSN::LapseAdvectionCoeff = 0.0 +ML_BSSN::ShiftAdvectionCoeff = 0.0 + +ML_BSSN::MinimumLapse = 1.0e-8 + +ML_BSSN::my_initial_boundary_condition = "extrapolate-gammas" +ML_BSSN::my_rhs_boundary_condition = "NewRad" + +ML_BSSN::ML_log_confac_bound = "none" +ML_BSSN::ML_metric_bound = "none" +ML_BSSN::ML_Gamma_bound = "none" +ML_BSSN::ML_trace_curv_bound = "none" +ML_BSSN::ML_curv_bound = "none" +ML_BSSN::ML_lapse_bound = "none" +ML_BSSN::ML_dtlapse_bound = "none" +ML_BSSN::ML_shift_bound = "none" +ML_BSSN::ML_dtshift_bound = "none" + + + +# init parameters +InitBase::initial_data_setup_method = "init_some_levels" + +ActiveThorns = "TOVSolver" + +ADMBase::initial_data = "tov" +ADMBase::initial_lapse = "tov" +ADMBase::initial_shift = "tov" +ADMBase::initial_dtlapse = "zero" +ADMBase::initial_dtshift = "zero" + +TOVSolver::TOV_Rho_Central[0] = 1.28e-3 +TOVSolver::TOV_Gamma[0] = 2.0 +TOVSolver::TOV_K[0] = 100.0 + + +IOBasic::outInfo_every = 1 +IOBasic::outInfo_vars = "HydroBase::rho ADMBase::lapse" + +IO::out_dir = $parfile + +IOScalar::outScalar_every = 32 +IOScalar::one_file_per_group = yes +IOScalar::outScalar_vars = " + HydroBase::rho + HydroBase::press + HydroBase::eps + HydroBase::vel + ADMBase::lapse + ADMBase::metric + ADMBase::curv + ADMConstraints::ham + ADMConstraints::momentum + +" + +IOASCII::out1D_every = 256 +IOASCII::one_file_per_group = yes +IOASCII::output_symmetry_points = no +IOASCII::out3D_ghosts = no +IOASCII::out3D_outer_ghosts = no +IOASCII::out1D_vars = " + HydroBase::rho + HydroBase::press + HydroBase::eps + HydroBase::vel + ADMBase::lapse + ADMBase::metric + ADMBase::curv + ADMConstraints::ham + ADMConstraints::momentum + +"

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[svn:einsteintoolkit] Workshop_Spring_2012/ (Rev. 54)
by knarf＠cct.lsu.edu 04 Apr '12

04 Apr '12

User: knarf Date: 2012/04/04 12:59 PM Added: /example_tov/ 2_rho.maximum.asc.xz, 4_rho.maximum.asc.xz Log: some precomputed tov data Directory Changes: Directory: /svn:mime-type/ ========================== + application/octet-stream File Changes: Directory: /example_tov/ ======================== File [added]: 2_rho.maximum.asc.xz Delta lines: +0 -0 =================================================================== (Binary files differ) Property changes on: example_tov/2_rho.maximum.asc.xz ___________________________________________________________________ File [added]: 4_rho.maximum.asc.xz Delta lines: +0 -0 =================================================================== (Binary files differ) Property changes on: example_tov/4_rho.maximum.asc.xz ___________________________________________________________________

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[svn:einsteintoolkit] Workshop_Spring_2012/numerical_relativity/ (Rev. 53)
by bcmsma＠astro.rit.edu 04 Apr '12

04 Apr '12

User: bmundim Date: 2012/04/04 12:51 PM Modified: /numerical_relativity/ numerical_relativity.tex Log: Outline. File Changes: Directory: /numerical_relativity/ ================================= File [modified]: numerical_relativity.tex Delta lines: +9 -0 =================================================================== --- numerical_relativity/numerical_relativity.tex 2012-04-04 17:35:10 UTC (rev 52) +++ numerical_relativity/numerical_relativity.tex 2012-04-04 17:51:11 UTC (rev 53) @@ -23,6 +23,15 @@ \item Finite differencing. \item The method of lines. \item McLachlan. + \item GRMHD - Valencia Formulation. + \item Conservation Laws. + \item Finite Volume Methods. + \item Riemann Problem. + \item Example: Burgers Equation. + \item Approximate Riemann Solvers. + \item Slope Limiters + \item Algorithm Overview. + \item Shocktube Test. \end{itemize} }

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[svn:einsteintoolkit] Workshop_Spring_2012/example_wavetoy/ (Rev. 52)
by roland.haas＠physics.gatech.edu 04 Apr '12

04 Apr '12

User: rhaas Date: 2012/04/04 12:35 PM Modified: /example_wavetoy/ example_wavetoy.tex Log: add energy exercise to wavetoy File Changes: Directory: /example_wavetoy/ ============================ File [modified]: example_wavetoy.tex Delta lines: +7 -0 =================================================================== --- example_wavetoy/example_wavetoy.tex 2012-04-04 17:34:23 UTC (rev 51) +++ example_wavetoy/example_wavetoy.tex 2012-04-04 17:35:10 UTC (rev 52) @@ -659,6 +659,13 @@ \end{itemize} } +\frame{\frametitle{Exercise: compute wave energy} +\begin{itemize} +\item compute energy density $\rho_E = \phi^2 \, \mathrm{d}x \, \mathrm{d}y \, \mathrm{d}z$ +\item compute integral as '\texttt{sum}' reduction of \texttt{IOScalar::out\_reductions} during output +\end{itemize} +} + %\frame[containsverbatim]{ \frametitle{WaveToy Thorn} % \begin{enumerate} % \item Define a new variable in \verb|interface.ccl|, and allocate storage

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[svn:einsteintoolkit] Workshop_Spring_2012/ (Rev. 51)
by roland.haas＠physics.gatech.edu 04 Apr '12

04 Apr '12

User: rhaas Date: 2012/04/04 12:34 PM Added: /example_wavetoy/ example_wavetoy.pdf Log: add example_wavetoy slides Directory Changes: Directory: /svn:mime-type/ ========================== + application/octet-stream File Changes: Directory: /example_wavetoy/ ============================ File [added]: example_wavetoy.pdf Delta lines: +0 -0 =================================================================== (Binary files differ) Property changes on: example_wavetoy/example_wavetoy.pdf ___________________________________________________________________

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New changesets in Carpet Mercurial
by Carpet mercurial repositories 04 Apr '12

04 Apr '12

changeset: 3506:cd3d378c628a tag: tip user: Erik Schnetter <schnetter(a)gmail.com> date: Wed Apr 04 13:10:45 2012 -0400 summary: CarpetIOASCII: Declare function prototype

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[svn:einsteintoolkit] Workshop_Spring_2012/ (Rev. 50)
by jfaber＠einsteintoolkit.org 04 Apr '12

04 Apr '12

User: jfaber Date: 2012/04/04 12:05 PM Added: /genrel/ subtle.png Modified: /genrel/ genrel.aux, genrel.log, genrel.nav, genrel.pdf, genrel.tex Log: Typo fixes Directory Changes: Directory: /svn:mime-type/ ========================== + application/octet-stream File Changes: Directory: /genrel/ =================== File [modified]: genrel.aux Delta lines: +7 -5 =================================================================== --- genrel/genrel.aux 2012-04-04 16:54:47 UTC (rev 49) +++ genrel/genrel.aux 2012-04-04 17:05:53 UTC (rev 50) @@ -59,8 +59,10 @@ \@writefile{nav}{\headcommand {\beamer@framepages {22}{22}}} \@writefile{nav}{\headcommand {\slideentry {0}{0}{23}{23/23}{}{0}}} \@writefile{nav}{\headcommand {\beamer@framepages {23}{23}}} -\@writefile{nav}{\headcommand {\beamer@partpages {1}{23}}} -\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{23}}} -\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{23}}} -\@writefile{nav}{\headcommand {\beamer@documentpages {23}}} -\@writefile{nav}{\headcommand {\def \inserttotalframenumber {23}}} +\@writefile{nav}{\headcommand {\slideentry {0}{0}{24}{24/24}{}{0}}} +\@writefile{nav}{\headcommand {\beamer@framepages {24}{24}}} +\@writefile{nav}{\headcommand {\beamer@partpages {1}{24}}} +\@writefile{nav}{\headcommand {\beamer@subsectionpages {1}{24}}} +\@writefile{nav}{\headcommand {\beamer@sectionpages {1}{24}}} +\@writefile{nav}{\headcommand {\beamer@documentpages {24}}} +\@writefile{nav}{\headcommand {\def \inserttotalframenumber {24}}} File [modified]: genrel.log Delta lines: +50 -52 =================================================================== --- genrel/genrel.log 2012-04-04 16:54:47 UTC (rev 49) +++ genrel/genrel.log 2012-04-04 17:05:53 UTC (rev 50) @@ -1,4 +1,4 @@ -This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009) (format=pdflatex 2009.11.7) 4 APR 2012 08:50 +This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009) (format=pdflatex 2009.11.7) 4 APR 2012 13:05 entering extended mode \write18 enabled. %&-line parsing enabled. @@ -1144,108 +1144,106 @@ {/usr/local/texlive/2009/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] [2 -] -LaTeX Font Info: Try loading font information for U+msa on input line 40. +] <subtle.png, id=77, 702.625pt x 1055.945pt> +File: subtle.png Graphic file (type png) + <use subtle.png> [3 + + <./subtle.png>] +LaTeX Font Info: Try loading font information for U+msa on input line 47. 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(/usr/local/texlive/2009/texmf-dist/tex/latex/amsfonts/umsb.fd File: umsb.fd 2009/06/22 v3.00 AMS symbols B -) [3 +) [4 -] [4 +] [5 ] -<edmb.png, id=136, 1028.84375pt x 908.39375pt> +<edmb.png, id=165, 1028.84375pt x 908.39375pt> File: edmb.png Graphic file (type png) <use edmb.png> -Overfull \vbox (0.88663pt too high) detected at line 58 +Overfull \vbox (0.88663pt too high) detected at line 65 [] -[5 +[6 - <./edmb.png (PNG copy)>] <timedilate.png, id=163, 905.3825pt x 478.78876pt> + <./edmb.png (PNG copy)>] <timedilate.png, id=192, 905.3825pt x 478.78876pt> File: timedilate.png Graphic file (type png) -<use timedilate.png> [6 +<use timedilate.png> [7 - <./timedilate.png>] [7 + <./timedilate.png>] [8 -] [8 +] [9 ] -<lortrans.png, id=247, 501.875pt x 488.82625pt> +<lortrans.png, id=275, 501.875pt x 488.82625pt> File: lortrans.png Graphic file (type png) <use lortrans.png> -Overfull \vbox (61.71777pt too high) detected at line 106 +Overfull \vbox (61.71777pt too high) detected at line 113 [] -[9 +[10 - <./lortrans.png>] [10 + <./lortrans.png>] [11 -] <elevator.png, id=301, 347.2975pt x 236.885pt> +] <elevator.png, id=329, 347.2975pt x 236.885pt> File: elevator.png Graphic file (type png) -<use elevator.png> <orbits.png, id=302, 701.62125pt x 440.64626pt> +<use elevator.png> <orbits.png, id=330, 701.62125pt x 440.64626pt> File: orbits.png Graphic file (type png) <use orbits.png> -Overfull \hbox (19.05467pt too wide) in paragraph at lines 121--121 +Overfull \hbox (19.05467pt too wide) in paragraph at lines 128--128 [][] [] -[11 +[12 - <./elevator.png (PNG copy)> <./orbits.png (PNG copy)>] [12 + <./elevator.png (PNG copy)> <./orbits.png (PNG copy)>] [13 -] [13 - ] [14 +] [15 + ] Package amsmath Warning: Foreign command \over; (amsmath) \frac or \genfrac should be used instead -(amsmath) on input line 193. +(amsmath) on input line 200. -[15 +[16 -] <covderiv.png, id=435, 180.675pt x 130.4875pt> +] <covderiv.png, id=463, 180.675pt x 130.4875pt> File: covderiv.png Graphic file (type png) <use covderiv.png> -<curvtens.png, id=436, 226.8475pt x 155.58125pt> +<curvtens.png, id=464, 226.8475pt x 155.58125pt> File: curvtens.png Graphic file (type png) - <use curvtens.png> [16 + <use curvtens.png> [17 - <./covderiv.png (PNG copy)> <./curvtens.png (PNG copy)>] [17 + <./covderiv.png (PNG copy)> <./curvtens.png (PNG copy)>] [18 -] [18 - ] [19 +] [20 + ] -<lapseshift.png, id=542, 245.91875pt x 140.525pt> +<lapseshift.png, id=570, 245.91875pt x 140.525pt> File: lapseshift.png Graphic file (type png) - <use lapseshift.png> [20 + <use lapseshift.png> [21 - <./lapseshift.png (PNG copy)>] [21 + <./lapseshift.png (PNG copy)>] [22 -] +] [23 -LaTeX Warning: Command \d invalid in math mode on input line 282. - - -LaTeX Warning: Command \d invalid in math mode on input line 282. - -[22 - -] <gwpol.png, id=620, 803.0pt x 401.5pt> +] <gwpol.png, id=648, 803.0pt x 401.5pt> File: gwpol.png Graphic file (type png) - <use gwpol.png> [23 +<use gwpol.png> [24 + <./gwpol.png (PNG copy)>] \tf@nav=\write6 \openout6 = `genrel.nav'. @@ -1263,10 +1261,10 @@ ) Here is how much of TeX's memory you used: - 15014 strings out of 493848 - 276863 string characters out of 3149207 + 15023 strings out of 493848 + 276967 string characters out of 3149207 358008 words of memory out of 3000000 - 17808 multiletter control sequences out of 15000+200000 + 17814 multiletter control sequences out of 15000+200000 11753 words of font info for 43 fonts, out of 3000000 for 9000 718 hyphenation exceptions out of 8191 47i,16n,57p,830b,534s stack positions out of 5000i,500n,10000p,200000b,50000s @@ -1284,9 +1282,9 @@ al/texlive/2009/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy6.pfb></usr/local /texlive/2009/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy8.pfb></usr/local/t exlive/2009/texmf-dist/fonts/type1/public/amsfonts/symbols/msam10.pfb> -Output written on genrel.pdf (23 pages, 2422055 bytes). +Output written on genrel.pdf (24 pages, 3113109 bytes). PDF statistics: - 703 PDF objects out of 1000 (max. 8388607) - 47 named destinations out of 1000 (max. 500000) - 102 words of extra memory for PDF output out of 10000 (max. 10000000) + 732 PDF objects out of 1000 (max. 8388607) + 49 named destinations out of 1000 (max. 500000) + 107 words of extra memory for PDF output out of 10000 (max. 10000000) File [modified]: genrel.nav Delta lines: +7 -5 =================================================================== --- genrel/genrel.nav 2012-04-04 16:54:47 UTC (rev 49) +++ genrel/genrel.nav 2012-04-04 17:05:53 UTC (rev 50) @@ -45,8 +45,10 @@ \headcommand {\beamer@framepages {22}{22}} \headcommand {\slideentry {0}{0}{23}{23/23}{}{0}} \headcommand {\beamer@framepages {23}{23}} -\headcommand {\beamer@partpages {1}{23}} -\headcommand {\beamer@subsectionpages {1}{23}} -\headcommand {\beamer@sectionpages {1}{23}} -\headcommand {\beamer@documentpages {23}} -\headcommand {\def \inserttotalframenumber {23}} +\headcommand {\slideentry {0}{0}{24}{24/24}{}{0}} +\headcommand {\beamer@framepages {24}{24}} +\headcommand {\beamer@partpages {1}{24}} +\headcommand {\beamer@subsectionpages {1}{24}} +\headcommand {\beamer@sectionpages {1}{24}} +\headcommand {\beamer@documentpages {24}} +\headcommand {\def \inserttotalframenumber {24}} File [modified]: genrel.pdf Delta lines: +0 -0 =================================================================== (Binary files differ) File [modified]: genrel.tex Delta lines: +11 -4 =================================================================== --- genrel/genrel.tex 2012-04-04 16:54:47 UTC (rev 49) +++ genrel/genrel.tex 2012-04-04 17:05:53 UTC (rev 50) @@ -23,9 +23,16 @@ \item Linearized gravity and gravitational radiation \end{itemize} -For a very nice treatment of GR available freely online, I suggest Sean Carroll's notes: gr-qc/9712019. } +\frame{\frametitle{Other sources} +For a very nice treatment of GR available freely online, I suggest Sean Carroll's notes: gr-qc/9712019. + +For the best scientific biography of Einstein, including a discussion of the divergenceless of various tensors with full equations, I suggest {\em Subtle is the Lord}, by Abraham Pais. + +\includegraphics[width=1in]{subtle} +} + \frame{\frametitle{Space and time in Newtonian physics} \begin{itemize} \item In Newtonian physics, there is space, and there is time, and they are different.\\ @@ -81,7 +88,7 @@ 0&0&0&1\end{array}\right) ; ~~(x')^{\mu'} = \left[\sum_{\nu=0}^3\right] \Lambda^{\mu'}{}_\nu x^\nu \end{equation} -where $\phi = \tanh\beta$. +where $\phi = \tanh^{-1}\beta$. } \frame{\frametitle{Special relativity: Invariants} @@ -270,8 +277,8 @@ The most familiar black hole solution, for an uncharged BH without any angular momentum, is the Schwarzschild solution: \begin{equation} - ds^2 = -\left(1-{{2GM}\over r}\right)\d t^2 + - \left(1-{{2GM}\over r}\right)^{-1}\d r^2 + ds^2 = -\left(1-{{2GM}\over r}\right)d t^2 + + \left(1-{{2GM}\over r}\right)^{-1}dr^2 + r^2 d\Omega^2 \end{equation} where $d\Omega^2 = d\theta^2+\sin^2\theta d\phi^2$. This is a stationary solution to Einstein's equations. At $r=2M$, we have a singularity, since there is no change in distance in time, and the radial term goes to infinity. This is the BH horizon. While indeed light cannot escape from the horizon, the singularity is an artifact of the coordinates we chose. If we let $R = \frac{1}{2}(r-M+\sqrt{r(r-2M)})$, we find the metric takes the isotropic form: File [added]: subtle.png Delta lines: +0 -0 =================================================================== (Binary files differ) Property changes on: genrel/subtle.png ___________________________________________________________________

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