Non-Vacuum Solutions for Black Hole Evaporation and Quantum Gravity

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SUMMARY

The discussion focuses on the exploration of non-vacuum solutions to Einstein's equations in the context of black hole evaporation and quantum gravity. Participants highlight the relevance of the Schwarzschild solution with small perturbations, particularly in relation to Hawking radiation. The Vaidya metric is mentioned as a significant reference for understanding radiating matter from a central mass. Additionally, the complexities of Eddington-Finkelstein coordinates and their implications for variable mass functions are addressed.

PREREQUISITES
  • Understanding of Einstein's equations and general relativity
  • Familiarity with the Schwarzschild solution and its perturbations
  • Knowledge of Hawking radiation and its implications
  • Basic grasp of Eddington-Finkelstein coordinates
NEXT STEPS
  • Research the Vaidya metric and its applications in black hole physics
  • Study the derivation and implications of Eddington-Finkelstein coordinates
  • Explore non-vacuum solutions to Einstein's equations in detail
  • Investigate the relationship between black hole evaporation and quantum gravity theories
USEFUL FOR

Physicists, astrophysicists, and researchers interested in black hole thermodynamics, quantum gravity, and the mathematical frameworks of general relativity.

Tomas Vencl
Although the complete quantum gravity is unknown as the exact details of black hole evaporating, is there known some symmetric non vacuum solution of E. equations which includes radiating of matter from central mass ? One can say, that Schwarzschild solution with small perturbation is good enough (as the Hawking radiation is weak), but if BH evaporates, exact solution can not be vacuum and static (which can be connected with extremely different behavior at strong field regions) .
Thanks for some links to learn more about such a solutions .
 
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Thanks.
I think undertsand the deriving Eddington-Finkelstein coordinates (eq. 1-5), then at the equation 6 they put M=constant to M(u).
But I do not understand how can be still correct derivative of equation 2 (and next steps) when now M is function u ?
Sorry for this stupid question.
 

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