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James Clerk Maxwell (1831–1879) was one of the significant contributors to physics in the nineteenth century. He is probably best known for having combined existing knowledge of the laws of electricity and the laws of magnetism with his insights to form a complete overarching electromagnetic theory, represented by Maxwell's equations. The four basic laws of electricity and magnetism were discovered experimentally through the work of physicists such as Oersted, Coulomb, Gauss, and...
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Imagine a rigid body that is rotating at an angular velocity of ω within an inertial frame of reference. Along with this, picture a second rotating frame that is attached to the body itself. This frame moves along with the body and possesses an angular velocity of Ω. The total moment about the center of mass is calculated by adding the rate of change of angular momentum about the center of mass in relation to the rotating frame and the cross-product of the body's angular velocity...
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Axisymmetric solutions to Einstein field equations via integral transforms.

D Batic1, N B Debru2, M Nowakowski3,4

  • 1Department of Mathematics, Khalifa University of Science and Technology, Main Campus, Abu Dhabi, United Arab Emirates.

Heliyon
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Researchers found new solutions to Einstein

Keywords:
Axisymmetric Einstein equationsErnst equationHankel transformNaked singularity

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Area of Science:

  • General Relativity
  • Theoretical Physics

Background:

  • Einstein field equations are central to understanding gravity.
  • Axisymmetric solutions are crucial in general relativity.

Purpose of the Study:

  • To find new vacuum solutions to Einstein's field equations.
  • To explore solutions with naked singularities.

Main Methods:

  • Hankel integral transform method
  • Analysis of axisymmetric and reflection symmetric spacetimes

Main Results:

  • Three new vacuum solutions exhibiting naked singularities were discovered.
  • The new solutions reinforce the significance of axisymmetric spacetimes.
  • The role of integral transforms in general relativity was highlighted.

Conclusions:

  • The study reinforces the importance of axisymmetric solutions in general relativity.
  • Integral transform methods are effective for complex general relativity problems.
  • New metrics with naked singularities were characterized, including blueshift effects.