Dnes som pozeral túto inšpiráciu: https://www.youtube.com/watch?v=-ft0dCCcnos

No a zaujalo ma, že ak oni tvrdia, že dva blesky udrú na nástupište a pozorovateľ z vlaku ich vidí v rôznom čase, čo však pozorovateľ, ktorý je na podobnom mieste vo vesmíre a letí loďou ku čiernej diere. Ak je to takto s dvoma bleskami, napadlo ma, či je to takto aj s Hawkingom a jeho gradientom času. Čuduj sa svete, konštanty musia sedieť:

Á tok času sa mení ako? No podľa Einsteina :) Takto:

Moje simulácie by boli takéto: A jedná sa o rovnaké simulácie, len jednu som nechal vodorovne a napadlo ma pozrieť si ju prepracovanú kruhovo:

https://hrubos.tech/repository/blesky_simulacia.mp4

Á teraz si pozrite tú 1/4 ^^^ resp 3/4, ktoré sa zachovajú u Hawkinga podľa Einsteina: https://hrubos.tech/repository/blesky-kruhova_simulacia_s_hodnotami.mp4

Tu je tá štvrtina vypichnutá pre 2 blesky letiace k sebe na nástupišti vodorovne a okolo prechádza konštantnou rýchlosťou vlak: https://hrubos.tech/blogy/content/images/20260409211102-gradient-casu-simulacia.png

using Pkg
Pkg.add("Plots")
Pkg.add("FFMPEG")

using Plots

# parametre
c = 1.0
R = 5.0

v = 0.8c
γ = 1 / sqrt(1 - (v/c)^2)

ω_light = c / R
ω_train = 2.0 * ω_light   # vizuálne "nadsvetelné"

tmax = 12
dt = 0.05

# uhly
θL(t) = π + ω_light * t
θR(t) = 0 - ω_light * t
θ_train(t) = ω_train * t

pos(θ) = (R*cos(θ), R*sin(θ))

anim = @animate for t in 0:dt:tmax
    p = plot(xlim=(-7,7), ylim=(-7,7),
             aspect_ratio=1,
             legend=false)

    # kružnica
    θ = range(0, 2π, length=200)
    plot!(R*cos.(θ), R*sin.(θ), linestyle=:dash)

    # pozície
    xL, yL = pos(θL(t))
    xR, yR = pos(θR(t))
    xt, yt = pos(θ_train(t))

    # body
    scatter!([xL], [yL], markersize=10, label="")
    scatter!([xR], [yR], markersize=10, label="")
    scatter!([0], [0], color=:red, markersize=10)
    scatter!([xt], [yt], color=:green, markersize=10)

    # uhly (oblúky)
    plot!(0.7R*cos.(range(0, θL(t), length=50)),
          0.7R*sin.(range(0, θL(t), length=50)), linewidth=2)

    plot!(0.5R*cos.(range(0, θR(t), length=50)),
          0.5R*sin.(range(0, θR(t), length=50)), linewidth=2)

    plot!(0.9R*cos.(range(0, θ_train(t), length=50)),
          0.9R*sin.(range(0, θ_train(t), length=50)), linestyle=:dot)

    # radiálne čiary
    plot!([0, xL], [0, yL], linestyle=:dot)
    plot!([0, xR], [0, yR], linestyle=:dot)
    plot!([0, xt], [0, yt], linestyle=:dot)

    # TEXTOVÉ INFO 🔥
    annotate!(9, 6, text("t = $(round(t, digits=2))", 10))
    annotate!(9, 5, text("v/c = $(round(v/c, digits=2))", 10))
    annotate!(9, 4, text("γ = $(round(γ, digits=3))", 10))

    # aktuálne uhly
    annotate!(9, 3, text("θL = $(round(θL(t), digits=2))", 10))
    annotate!(9, 2, text("θR = $(round(θR(t), digits=2))", 10))
    annotate!(9, 1, text("θ_train = $(round(θ_train(t), digits=2))", 10))

    # rozdiel uhlov (kľúčová vec!)
    Δθ = abs(θL(t) - θR(t))
    annotate!(9, 0, text("Δθ = $(round(Δθ, digits=2))", 10))
end

mp4(anim, "kruhova_simulacia_s_hodnotami.mp4", fps=30)

println("Hotovo: kruhova_simulacia_s_hodnotami.mp4")
println("Stlač Enter pre ukončenie...")
readline()

Okay a pome ďalej. Ak Hawking Einstein tvrdia, že ich rovnice sú univerzálne, tak musia sedieť pre veľké aj malé čierne diery, poďme to ukázať u Hruboša: https://hrubos.tech/repository/blesky-cierne_diery_kruh_v_kruhu.mp4

Pomery trojuholníkov sedia, je to teda len ká násobok rovníc :)

using Pkg
Pkg.add("Plots")
Pkg.add("FFMPEG")

using Plots

# parametre
c = 1.0

# dva horizonty (malý = ostrý, veľký = mäkký)
R_small = 3.0
R_large = 6.0

# povrchová gravitácia (z polomeru)
κ_small = c^2 / (2R_small)
κ_large = c^2 / (2R_large)

# uhlové rýchlosti
ω_light_small = c / R_small
ω_light_large = c / R_large

ω_train_small = 2.0 * ω_light_small
ω_train_large = 2.0 * ω_light_large

tmax = 12
dt = 0.05

# uhly
θL_s(t) = π + ω_light_small * t
θR_s(t) = 0 - ω_light_small * t
θT_s(t) = ω_train_small * t

θL_l(t) = π + ω_light_large * t
θR_l(t) = 0 - ω_light_large * t
θT_l(t) = ω_train_large * t

pos(R, θ) = (R*cos(θ), R*sin(θ))

anim = @animate for t in 0:dt:tmax
    p = plot(xlim=(-7,7), ylim=(-7,7),
             aspect_ratio=1,
             legend=false,
             title="Ostrá vs mäkká čierna diera (kruh v kruhu)")

    # veľký kruh (mäkký horizont)
    θ = range(0, 2π, length=200)
    plot!(R_large*cos.(θ), R_large*sin.(θ), linestyle=:dash)

    # malý kruh (ostrý horizont)
    plot!(R_small*cos.(θ), R_small*sin.(θ), linewidth=2)

    # --- MALÁ ČIERNA DIERA ---
    xLs, yLs = pos(R_small, θL_s(t))
    xRs, yRs = pos(R_small, θR_s(t))
    xTs, yTs = pos(R_small, θT_s(t))

    scatter!([xLs, xRs], [yLs, yRs], markersize=8)
    scatter!([xTs], [yTs], color=:green, markersize=8)

    # --- VEĽKÁ ČIERNA DIERA ---
    xLl, yLl = pos(R_large, θL_l(t))
    xRl, yRl = pos(R_large, θR_l(t))
    xTl, yTl = pos(R_large, θT_l(t))

    scatter!([xLl, xRl], [yLl, yRl], markersize=6)
    scatter!([xTl], [yTl], color=:orange, markersize=6)

    # stred
    scatter!([0], [0], color=:red, markersize=10)

    # oblúky (uhly)
    plot!(0.8R_small*cos.(range(0, θT_s(t), length=50)),
          0.8R_small*sin.(range(0, θT_s(t), length=50)), linestyle=:dot)

    plot!(0.8R_large*cos.(range(0, θT_l(t), length=50)),
          0.8R_large*sin.(range(0, θT_l(t), length=50)), linestyle=:dot)

    # text 🔥
    annotate!(9, 6, text("t = $(round(t,digits=2))", 10))

    annotate!(9, 5, text("SMALL BH:", 10))
    annotate!(9, 4.5, text("R = $R_small", 9))
    annotate!(9, 4, text("κ = $(round(κ_small,digits=3))", 9))

    annotate!(9, 3, text("LARGE BH:", 10))
    annotate!(9, 2.5, text("R = $R_large", 9))
    annotate!(9, 2, text("κ = $(round(κ_large,digits=3))", 9))
end

mp4(anim, "blesky-cierne_diery_kruh_v_kruhu.mp4", fps=30)

println("Hotovo: cierne_diery_kruh_v_kruhu.mp4")
println("Stlač Enter pre ukončenie...")
readline()

A ak už ani teraz neveríte, že Hawking/Einstein/Hruboš má rovnaké pomery ká násobku, ukážem vám 50 mäkkých a tvrdých čiernych dier:https://hrubos.tech/repository/blesky-gradient_cierne_diery.mp4

using Pkg
Pkg.add("Plots")
Pkg.add("FFMPEG")

using Plots

# parametre
c = 1.0
N = 50                 # počet kruhov
R_min = 2.0
R_max = 8.0

radii = range(R_min, R_max, length=N)

tmax = 15
dt = 0.05

# farby (gradient)
colors = cgrad(:plasma, N)

pos(R, θ) = (R*cos(θ), R*sin(θ))

anim = @animate for t in 0:dt:tmax
    p = plot(xlim=(-9,9), ylim=(-9,9),
             aspect_ratio=1,
             legend=false,
             title="Gradient čiernych dier: rotácie a κ")

    for (i, R) in enumerate(radii)

        # uhlová rýchlosť (svetlo)
        ω = c / R

        # blesky (opačné smery)
        θL = π + ω * t
        θR = 0 - ω * t

        # "vlak"
        θT = 2.0 * ω * t

        xL, yL = pos(R, θL)
        xR, yR = pos(R, θR)
        xT, yT = pos(R, θT)

        col = colors[i]

        # kružnica
        θ = range(0, 2π, length=100)
        plot!(R*cos.(θ), R*sin.(θ), color=col, alpha=0.3)

        # blesky
        scatter!([xL, xR], [yL, yR], markersize=3, color=col)

        # vlak
        scatter!([xT], [yT], markersize=3, color=col)
    end

    # stred
    scatter!([0], [0], color=:white, markersize=6)

    # info text
    annotate!(9, 8, text("t = $(round(t,digits=2))", 10))
    annotate!(9, 7, text("vnútri: rýchla rotácia", 9))
    annotate!(9, 6, text("vonku: pomalá rotácia", 9))
end

mp4(anim, "blesky-gradient_cierne_diery.mp4", fps=30)

println("Hotovo: gradient_cierne_diery.mp4")
println("Stlač Enter pre ukončenie...")
readline()

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