We are aware that there are various types of metrics that can be used in the study of compact stars. Therefore, I am curious to know if it is feasible to utilize the Weyl metric formalism.
The study of compact stars, such as neutron stars, often involves solving Einstein's field equations in general relativity to obtain interior solutions that describe the structure and properties of these dense, massive objects. The choice of metric or metric formalism can depend on the specific characteristics of the problem and the assumptions made about the star's interior.
The Weyl metric, also known as the Lewis-Papapetrou metric, is an axially symmetric solution to Einstein's field equations in vacuum, meaning it describes the gravitational field outside of a compact star (i.e., in the exterior region). It is typically used to describe the spacetime around an object with axial symmetry, like a rotating black hole.
While the Weyl metric itself is not typically used to describe the interior of compact stars (where matter is present), it can still play a role in understanding the spacetime around compact stars, especially if the star is rotating. In this context, it's often used to describe the exterior Kerr spacetime around a rotating star.
To describe the interior of compact stars, researchers typically use metrics that are appropriate for the properties and equations of state of matter inside the star. Some commonly used metrics for this purpose include:
1. Schwarzschild Metric: For spherically symmetric, non-rotating stars, the Schwarzschild metric is often used. It describes the spacetime around a non-rotating, spherically symmetric massive object.
2. Tolman-Oppenheimer-Volkoff (TOV) Metric: This metric is derived from the Schwarzschild metric and is used to describe the interior of spherically symmetric, static compact stars. It takes into account the pressure and density of matter inside the star.
3. Numerical Methods: In cases where analytical solutions are not feasible, numerical methods and computer simulations are often employed to model the interior of compact stars. These methods can take into account a wide range of physical conditions and equations of state.
While the Weyl metric is not typically used to describe the interior of compact stars, it can be relevant for understanding the spacetime around rotating compact stars. The choice of metric depends on the specific characteristics and properties of the compact star being studied, and researchers often use metrics and methods that are appropriate for the problem at hand.
Rajasmita Sahoo, we can deduce the stellar structure of Compact stars using axial symmetric Weyl metric.
Ankit Khunt, Could you kindly recommend any research work that employs Weyl metric formalism to investigate the stellar structure of compact stars ?
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