Abstract Representation of a Black Hole with Glow

Mysteries of the Cosmic Void Unveiled

Artist
Boris Krum...
DDG Model
DaVinci2
Access
Public
Created
2mos ago
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  Mysteries of the Cosmic Void Unveiled
  
  Model: DaVinci2
  
  Size: 1152 X 864 (1.00 MP)
  
  Used settings:
  
  Prompt: Depict in 3D an arbitrary vector field $V_a(\bfx)$ can then be expanded as \begin{equation} V_a(\bfx) = \int \frac{d^3k}{(2\pi)^3} \left[ \tilde V^L(\bfk) \Psi^{L,\bfk}_a(\bfx) + \tilde V^1(\bfk) \Psi^{1,\bfk}_a(\bfx) + \tilde V^2(\bfk) \Psi^{2,\bfk}_a(\bfx) \right], \label{eqn:vectorexpansion} \end{equation} in terms of Fourier expansion coefficients, \begin{eqnarray} \tilde V^L(\bfk) = \int \, d^3x\, V^a(\bfx) \left[\Psi^{L,\bfk}_a(\bfx)\right]^* = -\int\, d^3x\,\left[\Psi^{\bfk}(\bfx) \right]^* \frac{1}{k} \nabla^a V_a(\bfx), \nn \\ \tilde V^1(\bfk) = \int \, d^3x\, V^a(\bfx) \left[\Psi^{1,\bfk}_a(\bfx)\right]^* = \int\, d^3x\, \left[\Psi^{\bfk}(\bfx) \right]^* \frac{1}{| \bfk \times \hatz |} \epsilon_{abc} \hat z^a \nabla^b V^c(\bfx), \nn \\ \tilde V^2(\bfk) = \int \, d^3x\, V^a(\bfx) \left[\Psi^{2,\bfk}_a(\bfx)\right]^* = \int\, d^3x\, \left[\Psi^{\bfk}(\bfx)\right]^* \frac{-i}{k| \bfk \times \hatz |} \hat{z}^a (\nabla_a \nabla_b - g_{ab} \nabla^2) V^b(\bfx). \end{eqnarray}
  
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  Aspect Ratio: landscape
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Prompt

Depict in 3D an arbitrary vector field $V_a(\bfx)$ can then be expanded as \begin{equation} V_a(\bfx) = \int \frac{d^3k}{(2\pi)^3} \left[ \tilde V^L(\bfk) \Psi^{L,\bfk}_a(\bfx) + \tilde V^1(\bfk) \Psi^{1,\bfk}_a(\bfx) + \tilde V^2(\bfk) \Psi^{2,\bfk}_a(\bfx) \right], \label{eqn:vectorexpansion} \end{equation} in terms of Fourier expansion coefficients, \begin{eqnarray} \tilde V^L(\bfk) = \int \, d^3x\, V^a(\bfx) \left[\Psi^{L,\bfk}_a(\bfx)\right]^* = -\int\, d^3x\,\left[\Psi^{\bfk}(\bfx) \right]^* \frac{1}{k} \nabla^a V_a(\bfx), \nn \\ \tilde V^1(\bfk) = \int \, d^3x\, V^a(\bfx) \left[\Psi^{1,\bfk}_a(\bfx)\right]^* = \int\, d^3x\, \left[\Psi^{\bfk}(\bfx) \right]^* \frac{1}{| \bfk \times \hatz |} \epsilon_{abc} \hat z^a \nabla^b V^c(\bfx), \nn \\ \tilde V^2(\bfk) = \int \, d^3x\, V^a(\bfx) \left[\Psi^{2,\bfk}_a(\bfx)\right]^* = \int\, d^3x\, \left[\Psi^{\bfk}(\bfx)\right]^* \frac{-i}{k| \bfk \times \hatz |} \hat{z}^a (\nabla_a \nabla_b - g_{ab} \nabla^2) V^b(\bfx). \end{eqnarray}

More about Mysteries of the Cosmic Void Unveiled

The image depicts a deep, dark void surrounded by a mesh-like grid, suggesting a three-dimensional representation of a black hole or a similar cosmic phenomenon. The blue tones create a sense of depth and mystery.