Is Papapetrou line element the same as cylindrical coordinates?

In summary, the Papapetrou line element describes axial symmetric stationary spacetimes with coordinates labeled ρ, z, and phi, which are similar to cylindrical coordinates. The transformation to spherical or cartesian coordinates is the same as in the literature, but they tend to the usual Euclidean cylindrical coordinates at large distances where the spacetime becomes flat.
  • #1
Saeide
12
0
Hi all,

Papapetrou line element describes an axial symmetric stationary spacetimes and the coordinates that appear in this metric are just similar to cylindrical coordinates; I mean they are labeled ρ, z and phi. I want to know if they are really the cylindrical coordinate or not; In other words, are their transformation to spherical or cartesian coordinates the same as what we have in the literature?

So thanks in advance,

Saeide
 
Physics news on Phys.org
  • #2
Saeide, The spacetime is curved, so I don't understand what you mean by "really" the cylindrical coordinates. At large distances where the spacetime becomes flat they tend to the usual Euclidean cylindrical coordinates.
 
  • #3
Yes you're right. I forgot about the flat space limit.
 

What is the Papapetrou line element and what is it used for?

The Papapetrou line element is a mathematical equation used in the field of general relativity to describe the geometry of spacetime around a rotating mass. It is also known as the Kerr metric and is used to calculate the gravitational field and motion of objects near a rotating black hole.

How is the Papapetrou line element different from the Schwarzschild line element?

The Papapetrou line element is used to describe the spacetime around a rotating black hole, while the Schwarzschild line element is used for a non-rotating black hole. The Papapetrou line element includes an additional term for the rotation of the black hole, while the Schwarzschild line element does not.

What are the variables and constants in the Papapetrou line element equation?

The variables in the Papapetrou line element equation include the coordinates of the spacetime (t, r, θ, φ), the mass of the black hole (M), the angular momentum of the black hole (J), and the speed of light (c). The constant G, which represents the gravitational constant, is also included in the equation.

How does the Papapetrou line element relate to the Kerr solution?

The Papapetrou line element is a specific form of the Kerr solution, which is a solution to Einstein's field equations in general relativity. The Kerr solution describes the geometry of spacetime around a rotating mass, and the Papapetrou line element is a specific representation of this solution.

What implications does the Papapetrou line element have for our understanding of black holes?

The Papapetrou line element, along with the Kerr solution, has helped us understand the physics of rotating black holes and their effects on the surrounding spacetime. It has also allowed for the development of theories and predictions about the behavior of matter and light near black holes, leading to a better understanding of these mysterious cosmic objects.

Similar threads

I Schwarzschild spacetime in Kruskal coordinates
    • Special and General Relativity
2
Replies
44
Views
1K
I Coord Transform in de Sitter Space: Phys Significance &Linearity?
    • Special and General Relativity
Replies
5
Views
1K
I Eddington-Finkelstein coordinates for Schwarzschild metric
    • Special and General Relativity
Replies
9
Views
1K
A Papapetrou transformation: Conditions to be satisfied to achieve transformation
    • Special and General Relativity
Replies
1
Views
795
A Find 2D Geometry of Line Element in Coordinates
    • Special and General Relativity
Replies
14
Views
2K
B Creating Metric Describing Large Disk
    • Special and General Relativity
Replies
3
Views
703
A Can We Construct a Coordinate Chart Where Bell Observers Are At Rest?
    • Special and General Relativity
Replies
11
Views
427
I Schwarzschild in Cartesian: Tricks for Transformation
    • Special and General Relativity
Replies
18
Views
2K
A Comparing Gullstrand-Painleve & Lemaitre Coordinates
    • Special and General Relativity
Replies
8
Views
2K
I Einstein Definition of Simultaneity for Langevin Observers
    • Special and General Relativity
Replies
12
Views
1K

Hot Threads

Recent Insights

Back
Top