Non singular black hole solutions

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Discussion Overview

The discussion centers around a paper proposing a non-singular solution for the interior of spherically symmetric and static structures in the context of general relativity. Participants are exploring the implications of this solution, particularly its relationship to black hole theories and singularities.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants inquire about the interior solution described in the paper, noting that it presents a non-singular solution with infinite central density.
  • Others express skepticism about the paper's claims, suggesting that the solution does not describe a black hole, as it lacks an event horizon and features unbounded pressure and density as radius approaches zero.
  • One participant argues that resolving singularities implies a black hole solution, questioning how a non-singular solution could exist without violating the Penrose-Hawking singularity theorems.
  • Another participant clarifies that black hole spacetimes are non-stationary inside the event horizon, contrasting this with the static nature of the solution discussed in the paper.
  • Some participants reference the Schwarzschild metric, discussing its implications for black holes and the nature of singularities, while others challenge the interpretation of the Schwarzschild interior solution as static.
  • There is mention of the difficulty in accessing the full paper, which limits the ability to fully evaluate the claims made by the authors.

Areas of Agreement / Disagreement

Participants express disagreement regarding whether the discussed solution can be classified as a black hole solution. Some maintain that it cannot be, while others argue that resolving singularities is inherently linked to black hole characteristics. The discussion remains unresolved.

Contextual Notes

Participants note that the paper's claims depend on the definitions of singularities and the assumptions underlying the Penrose-Hawking theorems. The discussion highlights the complexity of matching interior and exterior solutions in general relativity.

  • #31
TrickyDicky said:
The WP page geodesic entry after explaining the different null, timelike and spacelike types says: "Note that a geodesic cannot be spacelike at one point and timelike at another". Is there a difference in this respect between vectors and geodesics?

Yes, even though vectors and curves are related, there is, in principle, a difference in this respect. In particular, the integral curves associated with the Killing vector field [itex]\partial_t[/itex] (curves of contant r, theta,a and phi) are not geodesics, so your result could possible fail for them. It, however, does not fail, i.e., an individual integral curve for [itex]\partial_t[/itex] does not change its causal character, but different integral curves for [itex]\partial_t[/itex] can different characters. Outside the event horizon (where spactime is static), the integral curves of [itex]\partial_t[/itex] are all timelike; inside the event horizon (where spacetime is not even stationary), the integral curves of [itex]\partial_t[/itex] are all spacelike.

The integral curves for [itex]\partial_t[/itex] are the curved dashed lines on

http://www.google.com/imgres?imgurl...MkRTtjWJfTLsQKpl6i-Cg&ved=0CDcQ9QEwBQ&dur=235

These means that the vectors that make up the vector field [itex]\partial_t[/itex] are tangent vectors for these curves. Note the different causal character outside and inside the event horizon.
 
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  • #32
Thanks.
 

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