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# 3D Plotting of Time Dilation near Black holes

Posted 19 days ago
 Hi there, I have some basic code for plotting the gravitional time dilation as one moves closer to the event horizon of a black hole of a given mass. See code: ClearAll["Global*"]'; tp = 1; G = 6.67408*10^(-11); M = (6.5*10^9)*(1.989*10^30); c = 2.99*10^8; rs = (2*G* M)/(c^2); Print[]; Print[" Black hole mass:", M, "kg", " \ Schhwarzchild radius:", rs, "m"]; Print[]; Plot[ tp*Sqrt[1 - (rs/r)], {r, 0, 2*10^14}, AxesLabel -> {" ", "Time (s)"}, AxesLabel -> {Style[" (m)", Bold, 26], Style["Time (s)", Bold, 16]}, LabelStyle -> Directive[Black, 16], AxesOrigin -> {0, 0}, GridLines -> {{rs}, {}}, GridLinesStyle -> {Directive[{Dashed, Thick}, Red], Directive[Thick, Red]}, ColorFunction -> "NeonColors"]  I want to create a 3D plot for different masses of black holes ranging from the one given in the code to one a thousand times more massive, with a 3D sheet. I am not great at this, and while my basic code works fine, when I go to do a 3D plot, nothing seems to work.  Attachments:
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Posted 18 days ago
 Here are just some thoughts: You can do the plot with logarithmic scaling like so: Plot3D[tp*Sqrt[1 - ((2*G*M)/r)], {r, 0, 2*10^14}, {M, 1, (6.5*10^9)*(1.989*10^90)}, AxesLabel -> {" ", "Time (s)"}, AxesLabel -> {Style[" (m)", Bold, 26], Style["Time (s)", Bold, 16]}, LabelStyle -> Directive[Black, 16], AxesOrigin -> {0, 0}, Filling -> {1 -> Top}, PlotRange -> All, ScalingFunctions -> {"Log", "Log"}] Or instead of going to very high values with the arguments you simply go straight to infinity - MMA can actually do those plots! Plot3D[tp*Sqrt[1 - ((2*G*M)/r)], {r, 0, Infinity}, {M, 1, Infinity}, AxesLabel -> {" ", "Time (s)"}, AxesLabel -> {Style[" (m)", Bold, 26], Style["Time (s)", Bold, 16]}, LabelStyle -> Directive[Black, 16], AxesOrigin -> {0, 0}, Filling -> {1 -> Top}, PlotRange -> All] Maybe that might be on option when dealing with those very big numbers anyway.
Posted 17 days ago
 Thanks, you got similar results to my attempt but something is wrong with the plots.
Posted 18 days ago
 Try expressing your input in Sun masses, or something like that.
Posted 18 days ago
 I think I tried geometrized units but I will give it another go.Thanks.
Posted 19 days ago
 Very curious. Plots such as this Plot3D[1 + (m/r), {r, 0, 10^11}, {m, 0, 10}] give an empty box. The problem may be related to the large number 10^11. Try rescaling your problem so as to use smaller numbers.
Posted 18 days ago
 Indeed, hence the post. I also get an empty box. ClearAll["Global*"]'; tp = 1; G = 6.67408*10^(-11); M = (6.5*10^9)*(1.989*10^30); c = 2.99*10^8; Print[]; Print[" Black hole mass:", M, "kg", " \ Schhwarzchild radius:", rs, "m"]; Print[]; Plot3D[ tp*Sqrt[1 - ((2*G*M)/r)], {r, 0, 2*10^14}, {M, 1, (6.5*10^9)*(1.989*10^90)}, AxesLabel -> {" ", "Time (s)"}, AxesLabel -> {Style[" (m)", Bold, 26], Style["Time (s)", Bold, 16]}, LabelStyle -> Directive[Black, 16], AxesOrigin -> {0, 0}, Filling -> {1 -> Top}, PlotRange -> 2] The numbers have to stay the same as otherwise the plot means nothing. I even tried Log plot with no luck.