Class KerrMetric

java.lang.Object
org.episteme.natural.physics.relativity.KerrMetric
All Implemented Interfaces:
Set<Vector4D>, MetricSpace<Vector4D>, TopologicalSpace<Vector4D>, SpacetimeMetric
public class KerrMetric extends Object implements SpacetimeMetric
The Kerr metric describing spacetime around a rotating uncharged axially-symmetric black hole.

Uses Boyer-Lindquist coordinates: $(ct, r, \theta, \phi)$. Metric signature: $(-, +, +, +)$. Main parameters:

  • $r_s$: Schwarzschild radius ($2GM/c^2$)
  • $a$: Spin parameter ($J/Mc$)

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

  • Constructor Details

    • KerrMetric

      public KerrMetric(Real schwarzschildRadius, Real spinParameter)
      Parameters:
      schwarzschildRadius - ($r_s = 2GM/c^2$)
      spinParameter - ($a = J/Mc$)

  • 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

    • containsPoint

      public boolean containsPoint(Vector4D p)
      Description copied from interface: TopologicalSpace
      Checks if this space contains the given point.

      Named containsPoint to avoid erasure conflict with Set.contains.

      Specified by:
      containsPoint in interface SpacetimeMetric
      Specified by:
      containsPoint in interface TopologicalSpace<Vector4D>
      Parameters:
      p - the point to check
      Returns:
      true if the point is in this space

    • 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:

    • isOpen

      public boolean isOpen()
      Description copied from interface: TopologicalSpace
      Checks if this set is open in the topology.
      Specified by:
      isOpen in interface SpacetimeMetric
      Specified by:
      isOpen in interface TopologicalSpace<Vector4D>
      Returns:
      true if this is an open set

    • isClosed

      public boolean isClosed()
      Description copied from interface: TopologicalSpace
      Checks if this set is closed in the topology.
      Specified by:
      isClosed in interface SpacetimeMetric
      Specified by:
      isClosed in interface TopologicalSpace<Vector4D>
      Returns:
      true if this is a closed set

    • description

      public String description()
      Description copied from interface: Set
      Returns a human-readable description of this set.

      Examples:

      • "ℝ (Real Numbers)"
      • "ℤ/12ℤ (Integers modulo 12)"
      • "{1, 2, 3, 4, 5}"

      Specified by:
      description in interface Set<Vector4D>
      Specified by:
      description in interface SpacetimeMetric
      Returns:
      a description of this set