feat: added Kerr with dark matter metric

src/metrics/kerr-dark-matter.jl

@@ -0,0 +1,74 @@
+module __KerrDarkMatter
+using ..StaticArrays
+using ..MuladdMacro
+using ..Gradus: _smooth_interpolate
+
+@muladd @fastmath begin
+    Σ(r, a, θ) = r^2 + a^2 * cos(θ)^2
+    Δ(r, R, a) = r^2 + a^2 - R * r
+
+    function G(r, Δr, rₛ)
+        dr = (r - rₛ) / Δr
+        (3 - 2 * dr) * dr^2
+    end
+
+    function dark_matter_mass(r, Δr, rₛ, M)
+        if r < rₛ
+            zero(r)
+        elseif r < rₛ + Δr
+            M * G(r, Δr, rₛ)
+        else
+            M
+        end
+    end
+
+    # the way this function must be defined is a little complex
+    # but helps with type-stability
+    function metric_components(M_bh, a, M_dm, Δr, rₛ, rθ)
+        (r, θ) = rθ
+
+        M = M_bh + dark_matter_mass(r, Δr, rₛ, M_dm)
+
+        R = 2M
+        sinθ2 = sin(θ)^2
+        cosθ2 = (1 - sinθ2)
+        # slightly faster, especially when considering AD evals
+        Σ₀ = r^2 + a^2 * cosθ2
+
+        tt = -(1 - (R * r) / Σ₀)
+        rr = Σ₀ / Δ(r, R, a)
+        θθ = Σ₀
+        ϕϕ = sinθ2 * (r^2 + a^2 + (sinθ2 * R * r * a^2) / Σ₀)
+
+        tϕ = (-R * r * a * sinθ2) / Σ₀
+        @SVector [tt, rr, θθ, ϕϕ, tϕ]
+    end
+end
+
+end # module
+
+"""
+    struct KerrDarkMatter
+
+$(FIELDS)
+
+https://arxiv.org/pdf/2003.06829.pdf
+"""
+@with_kw struct KerrDarkMatter{T} <: AbstractStaticAxisSymmetric{T}
+    @deftype T
+    "Black hole mass."
+    M = 1.0
+    "Black hole spin."
+    a = 0.0
+    "Dark matter mass."
+    M_dark_matter = 2.0
+    Δr = 20.0
+    rₛ = 10.0
+end
+
+# implementation
+metric_components(m::KerrDarkMatter{T}, rθ) where {T} =
+    __KerrDarkMatter.metric_components(m.M, m.a, m.M_dark_matter, m.Δr, m.rₛ, rθ)
+inner_radius(m::KerrDarkMatter{T}) where {T} = m.M + √(m.M^2 - m.a^2)
+
+export KerrDarkMatter