How is the deficit angle due to a relativistic cosmic string derived?

In summary, the presence of a cosmic string does not cause gravitational attraction but does deform the geometry of planes orthogonal to it, resulting in a cone shape. The deficit angle of the cosmic string can be derived from general relativity by solving the linearized field equations and transforming the resulting metric into a flat one with an angular deficit.
  • #1
Dilatino
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The presence of a cosmic string does not lead to gravitational attraction of a particle placed some distance away from it. But it affects the geometry of planes orthogonal to the cosmic string, such that the circumference of a circle traced out when moving around it at a distance r is given by

$$
C = r(2\pi -\Delta)
$$

which means that the flat plane is deformed to a cone.

How can the deficit angle due to a relativistic string

$$
\Delta = \frac{8\pi G T_0}{c^4} = \frac{8\pi G \mu_0}{c^2}
$$

be derived from general relativity?
 
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  • #2
This page has a derivation. He starts with an infinite line source having mass density μ and tension T. Solves the linearized field equations (or claims to), and shows that the resulting metric can be transformed into a metric which is flat, but with an angular deficit.
 
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1. What is a relativistic cosmic string?

A relativistic cosmic string is a hypothetical object in space that is thought to be formed in the early universe. It is a long, thin, and extremely dense object that has a tremendous amount of mass and energy. It is believed to have a strong gravitational pull that can even bend light.

2. How is the deficit angle of a cosmic string related to its mass and length?

The deficit angle of a cosmic string is directly related to its mass and length. As the mass and length of the string increase, the deficit angle also increases. This is because the mass and length determine the strength of the gravitational pull, which in turn affects the curvature of space-time around the string.

3. What is the significance of the deficit angle in understanding cosmic strings?

The deficit angle is an important concept in understanding cosmic strings because it gives us a way to measure and characterize these objects. It also helps us understand the gravitational effects of cosmic strings on the surrounding space-time and how they may influence the formation of structures in the universe.

4. How is the deficit angle of a cosmic string calculated?

The deficit angle of a cosmic string can be calculated using the formula θ = 8πGμ, where G is the gravitational constant and μ is the linear mass density of the string. This formula is derived from Einstein's theory of general relativity and is based on the assumption that the string is infinitely thin and straight.

5. Can the deficit angle of a cosmic string be observed or measured?

Currently, the deficit angle of a cosmic string cannot be directly observed or measured. However, scientists are using various methods, such as gravitational lensing and cosmic microwave background radiation, to indirectly detect the presence and effects of cosmic strings. These observations can help us estimate the deficit angle and provide evidence for the existence of cosmic strings.

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