Class SchwarzschildMetric

java.lang.Object
org.episteme.natural.physics.relativity.SchwarzschildMetric
All Implemented Interfaces:
Set<Vector4D>, MetricSpace<Vector4D>, TopologicalSpace<Vector4D>, SpacetimeMetric
public class SchwarzschildMetric extends Object implements SpacetimeMetric
The Schwarzschild metric describing spacetime around a static, spherically summetric mass.

Coordinates must be spherical: $(ct, r, \theta, \phi)$. Metric signature: $(-, +, +, +)$ used here for consistency with typical particle physics conventions, or $(+, -, -, -)$ widely used in GR texts. To be specific: $ds^2 = -(1 - r_s/r)(c dt)^2 + (1 - r_s/r)^{-1} dr^2 + r^2 d\Omega^2$ using $(-+++)$ signature.

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Reference:
Schwarzschild, K. (1916). Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie. Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften.

Since:
1.0
Author:
Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

  • Constructor Details

    • SchwarzschildMetric

      public SchwarzschildMetric(Real schwarzschildRadius)
      Parameters:
      schwarzschildRadius - ($r_s = 2GM/c^2$)

  • Method Details

    • getMetricTensor

      public Tensor<Real> getMetricTensor(Vector4D point)
      Description copied from interface: SpacetimeMetric
      Calculates the covariant metric tensor $g_{\mu\nu}$ at the given event coordinates.

      Returns a rank-2 tensor of shape [4, 4].

      Specified by:
      getMetricTensor in interface SpacetimeMetric
      Parameters:
      point - the spacetime coordinates
      Returns:
      the metric tensor instance

    • isEmpty

      public boolean isEmpty()
      Description copied from interface: Set
      Returns true if this set contains no elements.

      The empty set (∅) is a fundamental concept in set theory. It is the unique set containing no elements.

      Specified by:
      isEmpty in interface Set<Vector4D>
      Returns:
      true if this set is empty

    • contains

      public boolean contains(Vector4D item)
      Description copied from interface: Set
      Tests whether this set contains the specified element.

      This is the fundamental operation of a set - membership testing.

      Specified by:
      contains in interface Set<Vector4D>
      Parameters:
      item - the element to test for membership
      Returns:
      true if this set contains the element, false otherwise
      See Also: