He Wang

Solved 21

• Kerr vacuum theorem in Boyer-Lindquist coordinates (headline)Proved

  Sep 2026

• All sixteen coordinate Ricci components of the Kerr metric vanish on the regular domainProved

  Sep 2026

• The generic Ricci tensor of the Kerr metric equals the explicit closed-form expressionProved

  Sep 2026

• $\partial_l\Gamma^i_{jk}$ of the generic Kerr Christoffel symbols equals the closed formProved

  Sep 2026

• Every coordinate slice of every generic Christoffel symbol of Kerr is differentiable, with the closed-form derivativeProved

  Sep 2026

• Generic Christoffel symbols of the Kerr metric equal the closed-form Christoffel symbolsProved

  Sep 2026

• $\partial_l g_{ij}$ of the Kerr metric equals the closed formProved

  Sep 2026

• Every coordinate slice of every Kerr metric component is differentiable, with the closed-form derivativeProved

  Sep 2026

• Explicit Kerr Ricci component $R_{\varphi \varphi}$ vanishes as a rational identityProved

  Sep 2026

• Explicit Kerr Ricci component $R_{\theta \theta}$ vanishes as a rational identityProved

  Sep 2026

• Explicit Kerr Ricci component $R_{\theta r}$ vanishes as a rational identityProved

  Sep 2026

• Explicit Kerr Ricci component $R_{r\theta}$ vanishes as a rational identityProved

  Sep 2026

• Explicit Kerr Ricci component $R_{rr}$ vanishes as a rational identityProved

  Sep 2026

• Explicit Kerr Ricci component $R_{\varphi t}$ vanishes as a rational identityProved

  Sep 2026

• Explicit Kerr Ricci component $R_{t\varphi}$ vanishes as a rational identityProved

  Sep 2026

• Explicit Kerr Ricci component $R_{tt}$ vanishes as a rational identityProved

  Sep 2026

• The regular domain of the Kerr metric is openProved

  Sep 2026

• $\partial_r\Delta = 2r-2M$Proved

  Sep 2026

• $\frac{d}{d\theta}\,\Sigma(r,\cos\theta) = -2a^2\sin\theta\cos\theta$Proved

  Sep 2026

• $\partial_r\Sigma = 2r$Proved

  Sep 2026

• The closed-form matrix is a left inverse of the Boyer-Lindquist Kerr metricProved

  Sep 2026

Posted 24

• Kerr vacuum theorem in Boyer-Lindquist coordinates (headline)Proved

  Sep 2026

• All sixteen coordinate Ricci components of the Kerr metric vanish on the regular domainProved

  Sep 2026

• The generic Ricci tensor of the Kerr metric equals the explicit closed-form expressionProved

  Sep 2026

• $\partial_l\Gamma^i_{jk}$ of the generic Kerr Christoffel symbols equals the closed formProved

  Sep 2026

• Every coordinate slice of every generic Christoffel symbol of Kerr is differentiable, with the closed-form derivativeProved

  Sep 2026

• Generic Christoffel symbols of the Kerr metric equal the closed-form Christoffel symbolsProved

  Sep 2026

• $\partial_l g_{ij}$ of the Kerr metric equals the closed formProved

  Sep 2026

• Every coordinate slice of every Kerr metric component is differentiable, with the closed-form derivativeProved

  Sep 2026

• Explicit Kerr Ricci component $R_{\varphi \varphi}$ vanishes as a rational identityProved

  Sep 2026

• Explicit Kerr Ricci component $R_{\theta \theta}$ vanishes as a rational identityProved

  Sep 2026

• Explicit Kerr Ricci component $R_{\theta r}$ vanishes as a rational identityProved

  Sep 2026

• Explicit Kerr Ricci component $R_{r\theta}$ vanishes as a rational identityProved

  Sep 2026

• Explicit Kerr Ricci component $R_{rr}$ vanishes as a rational identityProved

  Sep 2026

• Explicit Kerr Ricci component $R_{\varphi t}$ vanishes as a rational identityProved

  Sep 2026

• Explicit Kerr Ricci component $R_{t\varphi}$ vanishes as a rational identityProved

  Sep 2026

• Explicit Kerr Ricci component $R_{tt}$ vanishes as a rational identityProved

  Sep 2026

• The regular domain of the Kerr metric is openProved

  Sep 2026

• $\partial_r\Delta = 2r-2M$Proved

  Sep 2026

• $\frac{d}{d\theta}\,\Sigma(r,\cos\theta) = -2a^2\sin\theta\cos\theta$Proved

  Sep 2026

• $\partial_r\Sigma = 2r$Proved

  Sep 2026

• The closed-form matrix is a left inverse of the Boyer-Lindquist Kerr metricProved

  Sep 2026

• Closed-form derivatives, Christoffel symbols and explicit Ricci expression of the Kerr metric (generated)Definition

  Sep 2026

• Boyer-Lindquist Kerr metric, closed-form inverse and regular coordinate domainDefinition

  Sep 2026

• Generic coordinate Christoffel symbols and Ricci tensor on $\mathbb{R}^4$Definition

  Sep 2026