From Wikimedia Commons, the free media repository
Jump to navigation Jump to search
Kerr-Newman-Orbit-1.gif(758 × 500 pixels, file size: 4.09 MB, MIME type: image/gif, looped, 309 frames, 20 s)
Note: Due to technical limitations, thumbnails of high resolution GIF images such as this one will not be animated.


English: Kerr-Newman Orbit. Spin: Jc/G/M²=0.9, Charge: Q/M·√(K/G)=0.4. Red: neutral testparticle, dashed magenta: ZAMO
Source Own work (Code)
Author Yukterez (Simon Tyran, Vienna)
Other versions
A test particle approaching the ergosphere in the retrograde direction is forced to change its direction of motion


01) Coordinate time              08) Black hole angular momentum  15) Axial angular momentum  22) Framedragging delayed angular velocity
02) Proper time                  09) Black hole charge            16) Polar angular momentum  23) Framedragging local velocity
03) Total time dilation          10) Axial radius of gyration     17) Radial momentum         24) Framedragging observed velocity
04) Gravitational time dilation  11) kinetic energy               18) Cartesian radius        25) Observed particle velocity
05) Boyer Lindquist radius       12) Potential energy             19) Cartesian x-axis        26) Local escape velocity
06) BL Longitude in radians      13) Total particle energy        20) Cartesian y-axis        27) Delayed particle velocity
07) BL Latitude in radians       14) Carter Constant              21) Cartesian z-axis        28) Local particle velocity


Line-element in Boyer-Lindquist-coordinates:

Shorthand terms:

with the dimensionless spin parameter a=Jc/G/M² and the dimensionless electric charge parameter ℧=Qₑ/M·√(K/G). Here G=M=c=K=1 so that a=J und ℧=Qₑ, with lengths in GM/c² and times in GM/c³.

Co- and contravariant metric:

Contravariant Maxwell tensor:

The coordinate acceleration of a test-particle with the specific charge q is given by

with the Christoffel-symbols

So the second proper time derivatives are

for the time component,

for the radial component,

the poloidial component and

for the axial component of the 4-acceleration. The relation of the local 3-velocity and the first proper time derivatives is

so we get

for the radial,

for the poloidial,

for the axial and

for the total velocity, which also give the initial conditions. The total time dilation is

where the differentiation goes by the proper time τ for charged (q≠0) and neutral (q=0) particles (μ=-1, v<1), and for massless particles (μ=0, v=1) by the spatial affine parameter ŝ. The 3 conserved quantities in relation to the local 3-velocity v=√(vr²+vθ²+vφ²)=)(vx²+vy²+vz²) are

1) the Carter constant:

2) the total energy:

3) the axial angular momentum:

ω is the Frame-Dragging angular velocity

The ergospheres and horizons have the Boyer-Lindquist-radius

In this article the total mass equivalent M, which also contains the rotational and the electrical field energy, is set to 1; the relation of M with the irreducible mass is



German version (deutsche Version), Link:

Usage in Wikipedia-articles[edit]


I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons

attribution share alike

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
  • share alike – If you alter, transform, or build upon this work, you may distribute the resulting work only under the same or similar license to this one.

File history

Click on a date/time to view the file as it appeared at that time.

current10:22, 22 August 2017Thumbnail for version as of 10:22, 22 August 2017758 × 500 (4.09 MB)Yukterez (talk | contribs)User created page with UploadWizard
  • You cannot overwrite this file.

There are no pages that link to this file.