Fix typos

README.md

@@ -2,7 +2,7 @@
 
 This Julia language package that accurately and efficiently solves for null geodesics in the Kerr spacetime.
 
-The package is intended mainly for scientic usage for astrophysical observations, and thus, have constrained the observer to lie at asmyptptic infinity.
+The package is intended mainly for scientic usage for astrophysical observations, and thus, have constrained the observer to lie at asymptotic infinity.
 These algorithms mainly follow the formalism of [Gralla & Lupsasca](https://journals.aps.org/prd/abstract/10.1103/PhysRevD.101.044032), with the exception for a new sub image indexing scheme and a regularized time integral definition.
 The ray tracing scheme has been optimized for GPU compatibility and automatic differentiability with [Enzyme.jl](https://enzyme.mit.edu/julia/stable/). 
 These considerations allow our algorithms to be easily used in Machine Learning applications with the existing julia infrastructure.

docs/src/time_regularization.md

@@ -30,7 +30,7 @@ where,
 \end{align}
 ```
 
-One idiosyncracy of this coordinate is that it introduces ambiguities when evaluating the elapsed time of any geodesic terminating at the asmyptptic observer.
+One idiosyncracy of this coordinate is that it introduces ambiguities when evaluating the elapsed time of any geodesic terminating at the asymptotic observer.
 The ambiguity is due to logarithmic and linear divergences in the integral $I_t$ at $r_o=\infty$ which take the form,[^CAZ]
 ```math
 \begin{align}

examples/mino-time-example.jl

@@ -10,7 +10,7 @@ import GLMakie as GLMk
 GLMk.Makie.inline!(true)
 
 #
-# We will use a 0.99 spin Kerr black hole viewed by an asmyptptic observer at an inclination angle of θo=π/4. 
+# We will use a 0.99 spin Kerr black hole viewed by an asymptotic observer at an inclination angle of θo=π/4. 
 # A region spanned by radii between the horizon and 20M at varying inclinations will be raytraced onto the 20Mx20M 
 # screen of the observer.
 metric = Krang.Kerr(0.99); # Kerr spacetime with 0.99 spin

examples/polarization-example.jl

@@ -20,7 +20,7 @@ curr_theme = Theme(
 set_theme!(merge!(curr_theme, theme_latexfonts()))
 
 #
-# We will use a $0.94$ spin Kerr black hole viewed by an asmyptptic observer at an inclination angle of $θo=17^\circ$. 
+# We will use a $0.94$ spin Kerr black hole viewed by an asymptotic observer at an inclination angle of $θo=17^\circ$. 
 # The emission to be raytraced is 
 metric = Krang.Kerr(0.94);
 θo = 17 * π / 180;

examples/raytracing-mesh-example.jl

@@ -7,7 +7,7 @@ using FileIO
 metric = Krang.Kerr(0.99) # Kerr metric with a spin of 0.99
 θo = 90/180*π # Inclination angle of the observer
 ρmax = 12.0 # Horizontal and Vertical extent of the screen
-sze = 50 # Resolution of the screen is sze x sze
+sze = 100 # Resolution of the screen is sze x sze
 
 camera = Krang.SlowLightIntensityCamera(metric, θo, -ρmax, ρmax, -ρmax, ρmax, sze)
 
@@ -57,10 +57,10 @@ end
 
 GLMk.hidedecorations!(ax)
 sphere = GLMk.Sphere(GLMk.Point(0.0,0.0,0.0), horizon(metric)) # Sphere to represent black hole
-lines_to_plot = Krang.generate_ray.(camera.screen.pixels, 90) # 100 is the number of steps to take along the ray
+lines_to_plot = Krang.generate_ray.(camera.screen.pixels, 100) # 100 is the number of steps to take along the ray
 
 img = zeros(sze, sze)
-recording = GLMk.record(fig, "mesh.mp4", 1:sze*sze, framerate=100) do i
+recording = GLMk.record(fig, "mesh.mp4", 1:sze*sze, framerate=400) do i
     line = lines_to_plot[i] 
 
     img[i] = intersections[i]

src/materials/ElectronSynchrotronPowerLawPolarization.jl

@@ -1,5 +1,5 @@
 """
-Returns the screen polarization associated with a killing spinor κ as seen seen by an asmyptptic observer.
+Returns the screen polarization associated with a killing spinor κ as seen seen by an asymptotic observer.
 """
 function screen_polarization(metric::Kerr{T}, κ::Complex, θ, α, β) where {T}# Eq 31 10.1103/PhysRevD.104.044060
     a = metric.spin

src/metrics/Kerr/misc.jl

@@ -732,7 +732,7 @@ function It_inf_case2(metric::Kerr{T}, roots::NTuple{4}, λ) where {T}
     #equation B37
     I1_total = log(16 / (r31 + r42)^2) / 2 + r43 * (coef * regularized_Pi(n, asin(inv(√n)), k))# Removed the logarithmic divergence
     #equation B38
-    I2_total = r3 - E_o # asmyptptic Divergent piece is not included
+    I2_total = r3 - E_o # asymptotic Divergent piece is not included
 
     coef_p = 2 / √(r31 * r42) * r43 / (rp3 * rp4)
     coef_m = 2 / √(r31 * r42) * r43 / (rm3 * rm4)
@@ -901,7 +901,7 @@ function It_w_I0_terms_case2(metric::Kerr{T}, rs, τ, roots::NTuple{4}, λ, νr)
     I1_total = r3 * I0_total + r43 * (-1)^νr * Π1_s# Removed the logarithmic divergence
     #equation B38
     I2_s = √(evalpoly(rs, poly_coefs)) / (rs - r3) - E_s
-    I2_total = - (r1 * r4 + r2 * r3) / 2 * τ + (-1)^νr * I2_s# asmyptptic Divergent piece is not included
+    I2_total = - (r1 * r4 + r2 * r3) / 2 * τ + (-1)^νr * I2_s# asymptotic Divergent piece is not included
 
     coef_p = 2 / √(r31 * r42) * r43 / (rp3 * rp4)
     coef_m = 2 / √(r31 * r42) * r43 / (rm3 * rm4)
@@ -1046,7 +1046,7 @@ function radial_inf_integrals_case2(metric::Kerr{T}, roots::NTuple{4}) where {T}
     #equation B37
     I1o_m_I0_terms =  log(16 / (r31 + r42)^2) / 2 + r43 * (coef * regularized_Pi(n, asin(inv(√n)), k) )
     #equation B38
-    I2o_m_I0_terms = r3 - E_o# asmyptptic Divergent piece is not included
+    I2o_m_I0_terms = r3 - E_o# asymptotic Divergent piece is not included
 
     coef_p = 2 / √(r31 * r42) * r43 / (rp3 * rp4)
     coef_m = 2 / √(r31 * r42) * r43 / (rm3 * rm4)
@@ -1195,7 +1195,7 @@ function radial_w_I0_terms_integrals_case2(metric::Kerr{T}, rs, roots::NTuple{4}
     I1_total = - r3 * I0_total - r43 * (-1)^νr * Π1_s# Removed the logarithmic divergence
     #equation B38
     I2_s = √abs(evalpoly(rs, poly_coefs)) / (rs - r3) - E_s
-    I2_total = (r1 * r4 + r2 * r3) / 2 * τ - (-1)^νr * I2_s# asmyptptic Divergent piece is not included
+    I2_total = (r1 * r4 + r2 * r3) / 2 * τ - (-1)^νr * I2_s# asymptotic Divergent piece is not included
 
     coef_p = 2 / √(r31 * r42) * r43 / (rp3 * rp4)
     coef_m = 2 / √(r31 * r42) * r43 / (rm3 * rm4)