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Generalized transformations and coordinates for static spherically symmetric general relativity.

James M Hill1, Joseph O'Leary1,2

  • 1School of Information Technology and Mathematical Sciences, University of South Australia, PO Box 2471, Adelaide, South Australia 5001, Australia.

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Summary
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Researchers found a new general relativity solution that avoids the Schwarzschild singularity. This novel approach offers a more suitable coordinate chart and allows for generalizations of key transformations in gravitational physics.

Keywords:
Einstein field equationscoordinate transformationexact solutions

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Area of Science:

  • Theoretical physics
  • General relativity
  • Gravitational physics

Background:

  • Standard derivations of the Schwarzschild solution rely on specific coordinate transformations and dynamical assumptions.
  • These assumptions limit the scope of possible solutions within general relativity.
  • The Schwarzschild solution, while fundamental, possesses a coordinate singularity.

Purpose of the Study:

  • To explore alternative solutions to the empty space field equations of general relativity.
  • To develop a formalism that circumvents the limitations of standard Schwarzschild solution derivations.
  • To investigate a solution that avoids the coordinate singularity inherent in the Schwarzschild metric.

Main Methods:

  • Examining a static, spherically symmetric solution using a non-orthogonal line element.
  • Relaxing convenient coordinate transformations and dynamical assumptions used in standard derivations.
  • Obtaining a more suitable coordinate chart to describe the spacetime geometry.

Main Results:

  • A new general relativity solution is derived, encompassing the Schwarzschild solution as a special case.
  • The new solution successfully avoids the coordinate singularity.
  • The solution contains two arbitrary constants, one linked to the Newtonian gravitational potential.

Conclusions:

  • The derived solution offers a more general framework for understanding static, spherically symmetric spacetimes.
  • It provides a pathway to generalize the Eddington-Finkelstein and Kruskal-Szekeres transformations.
  • This work opens new avenues for exploring gravitational physics beyond the standard Schwarzschild model.