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Reconciling “Frozen Star” and “Point Singularity” Models of Black Holes Emmett Redd, Department of Physics, Astronomy, and Materials Science, Missouri State University I.Introduction and Background A.Paradox B.Principle C.Geodesics (Two Places at Once) D.Black Hole Time Warping II.Potentials and Forces A.Conceptual B.Mathematical III.Conclusion

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The Paradox Frozen Star –Field Interpretation –External Frame –Mass at Event Horizon –What we see Point Singularity –Geometric Interpretation –Internal Frame –Mass at Center –What an in-faller sees (2) According to the Schwarzschild metric, nothing crosses the event horizon in finite coordinate time. (1)An event horizon can grow in finite coordinate time only if the mass Contained inside the horizon increases in finite coordinate time. *Kevin S. Brown

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The Principle All Free-Fall Reference Frames MUST Describe the Same Physics Most paradoxes come from not keeping descriptions of different reference frames separate –Presentation is only about Schwarzschild metric and black hole (uncharged, non-rotating, symmetric)

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Two Coordinate Systems

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Kevin S. Brown’s figure of the time warping near a Black Hole. www.mathpages.com/rr /s7-02/7-02.htm

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Black Hole Inception & Growth Kevin S. Brown figure. www.mathpages.com/rr/s7 -02/7-02.htm

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Three Black Hole Potentials (Conceptual)

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and or Mathematics I

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Mathematics II

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Conclusion Black Hole mass is both inside and outside the event horizon at same coordinate time. Mass is outside until future null infinity. –Gravity is outside until future null infinity. Mass is inside significantly before future null infinity. –Gravity is inside and creating the event horizon significantly before future null infinity. No push needed (F S =0) to move external mass as Black Hole grows.

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Announcements Exam 4 is Monday May 4. Tentatively will cover Chapters 9, 10, 11 & 12 Sample questions will be posted soon Observing Night tomorrow night.

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