Boyer–Lindquist coordinates
E77120
Boyer–Lindquist coordinates are a spheroidal coordinate system commonly used in general relativity to express the Kerr solution describing the spacetime around a rotating black hole.
Aliases (2)
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
coordinate system
→
curvilinear coordinate system → spheroidal coordinate system → |
| coordinateSingularityAt |
event horizon of Kerr black hole
→
Δ = 0 → |
| definesFunction |
Δ = r^2 - 2Mr + a^2 + Q^2
→
Σ = r^2 + a^2 cos^2θ → |
| domainOfDefinition |
0 ≤ θ ≤ π
→
0 ≤ φ < 2π → r > 0 → |
| generalizes |
Schwarzschild coordinates
→
|
| hasCoordinate |
r
→
t → θ → φ → |
| hasParameter |
charge Q
→
mass M → spin parameter a → |
| hasProperty |
adapted to axial symmetry
→
asymptotically spherical at large r → reduce to Schwarzschild coordinates when a=0 → time coordinate t is asymptotically Minkowskian → θ is polar angle from rotation axis → φ is azimuthal angle around rotation axis → |
| hasSignature |
(-,+,+,+)
→
|
| hasSymmetry |
axisymmetry
→
stationarity → |
| introducedBy |
Richard W. Lindquist
→
Robert H. Boyer NERFINISHED → |
| introducedInContext |
Kerr solution
→
|
| metricComponent |
g_rr = Σ/Δ
→
g_tt = -(1 - 2Mr/Σ) → g_tφ = -2Mar sin^2θ / Σ → g_θθ = Σ → g_φφ = (r^2 + a^2 + 2Ma^2 r sin^2θ / Σ) sin^2θ → |
| relatedTo |
Boyer–Lindquist r coordinate
→
Boyer–Lindquist time coordinate → Eddington–Finkelstein coordinates → Kerr–Schild coordinates → |
| usedFor |
Kerr metric
→
Kerr–Newman metric → accretion disk modeling around rotating black holes → frame dragging analysis → geodesic calculations in Kerr spacetime → gravitational lensing in Kerr spacetime → quasinormal mode calculations of rotating black holes → rotating black hole spacetime → stationary axisymmetric spacetimes → |
| usedIn |
general relativity
→
|
| yearIntroduced |
1967
→
|
Referenced by (5)
| Subject (surface form when different) | Predicate |
|---|---|
|
Boyer–Lindquist coordinates
("Boyer–Lindquist r coordinate")
→
Boyer–Lindquist coordinates ("Boyer–Lindquist time coordinate") → Kerr–Schild coordinates → |
relatedTo |
|
Kerr metric
→
Kerr–Newman black hole → |
hasCoordinateSystem |