Black Hole Space

Black Hole Space




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G

μ
ν


+
Λ

g

μ
ν


=



8
π
G


c

4





T

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ν




{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={8\pi G \over c^{4}}T_{\mu \nu }}


Far away from the black hole, a particle can move in any direction, as illustrated by the set of arrows. It is restricted only by the speed of light.
Closer to the black hole, spacetime starts to deform. There are more paths going towards the black hole than paths moving away. [Note 3]
Inside of the event horizon, all paths bring the particle closer to the center of the black hole. It is no longer possible for the particle to escape.
Messier 87 galaxy – home of the first imaged black hole
The formula for the Bekenstein–Hawking entropy ( S ) of a black hole, which depends on the area of the black hole ( A ). The constants are the speed of light ( c ), the Boltzmann constant ( k ), Newton's constant ( G ), and the reduced Planck constant ( ħ ). In Planck units, this reduces to S = A / 4 .

^ The value of cJ/GM 2 can exceed 1 for objects other than black holes. The largest value known for a neutron star is ≤ 0.4, and commonly used equations of state would limit that value to < 0.7. [82]

^ The (outer) event horizon radius scales as:



M
+



M

2





(
J

/

M
)


2




Q

2




.


{\displaystyle M+{\sqrt {M^{2}-{(J/M)}^{2}-Q^{2}}}.}



^ The set of possible paths, or more accurately the future light cone containing all possible world lines (in this diagram the light cone is represented by the V-shaped region bounded by arrows representing light ray world lines), is tilted in this way in Eddington–Finkelstein coordinates (the diagram is a "cartoon" version of an Eddington–Finkelstein coordinate diagram), but in other coordinates the light cones are not tilted in this way, for example in Schwarzschild coordinates they simply narrow without tilting as one approaches the event horizon, and in Kruskal–Szekeres coordinates the light cones do not change shape or orientation at all. [85]

^ This is true only for four-dimensional spacetimes. In higher dimensions more complicated horizon topologies like a black ring are possible. [97] [98]

^ In particular, he assumed that all matter satisfies the weak energy condition .



^ Wald 1984 , pp. 299–300

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^ Webster, B. Louise; Murdin, Paul (1972), "Cygnus X-1—a Spectroscopic Binary with a Heavy Companion?", Nature , 235 (5332): 37–38, Bibcode : 1972Natur.235...37W , doi : 10.1038/235037a0 , S2CID 4195462

^ Bolton, C. T. (1972), "Identification of Cygnus X-1 with HDE 226868", Nature , 235 (5336): 271–273, Bibcode : 1972Natur.235..271B , doi : 10.1038/235271b0 , S2CID 4222070

^ Clery D (2020). "Black holes caught in the act of swallowing stars". Science . 367 (6477): 495. Bibcode : 2020Sci...367..495C . doi : 10.1126/science.367.6477.495 . PMID 32001633 .

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^ Siegel, Ethan. "Five Surprising Truths About Black Holes From LIGO" . Forbes . Retrieved 12 April 2019 .

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^ Bouman, Katherine L. ; Johnson, Michael D.; Zoran, Daniel; Fish, Vincent L.; Doeleman, Sheperd S.; Freeman, William T. (2016). "Computational Imaging for VLBI Image Reconstruction". 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) . pp. 913–922. arXiv : 1512.01413 . doi : 10.1109/CVPR.2016.105 . hdl : 1721.1/103077 . ISBN 978-1-4673-8851-1 . S2CID 9085016 .

^ Gardiner, Aidan (12 April 2018). "When a Black Hole Finally Reveals Itself, It Helps to Have Our Very Own Cosmic Reporter – Astronomers announced Wednesday that they had captured the first image of a black hole. The Times's Dennis Overbye answers readers' questions" . The New York Times . Retrieved 15 April 2019 .

^ Overbye, Dennis (24 March 2021). "The Most Intimate Portrait Yet of a Black Hole - Two years of analyzing the polarized light from a galaxy's giant black hole has given scientists a glimpse at how quasars might arise" . The New York Times . Retrieved 25 March 2021 .

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^ "Ripped Apart by a Black Hole" . ESO Press Release . Archived from the original on 21 July 2013 . Retrieved 19 July 2013 .

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^ Michell, J. (1784). "On the Means of Discovering the Distance, Magnitude, &c. of the Fixed Stars, in Consequence of the Diminution of the Velocity of Their Light, in Case Such a Diminution Should be Found to Take Place in any of Them, and Such Other Data Should be Procured from Observations, as Would be Farther Necessary for That Purpose. By the Rev. John Michell, B. D. F. R. S. In a Letter to Henry Cavendish, Esq. F. R. S. and A. S" . Philosophical Transactions of the Royal Society . 74 : 35–57. Bibcode : 1784RSPT...74...35M . doi : 10.1098/rstl.1784.0008 . JSTOR 106576 .

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^ Slayter, Elizabeth M.; Slayter, Henry S. (1992). Light and Electron Microscopy . Cambridge University Press. ISBN 978-0-521-33948-3 . Archived from the original on 30 November 2017.

^ Crass, Institute of Astronomy – Design by D.R. Wilkins and S.J. "Light escaping from black holes" . www.ast.cam.ac.uk . Retrieved 10 March 2018 .

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Translation: Antoci, S.; Loinger, A. (1999). "On the gravitational field of a mass point according to Einstein's theory". arXiv : physics/9905030 . and Schwarzschild, K. (1916). "Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie" . Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften . 18 : 424–434. Bibcode : 1916skpa.conf..424S .
Translation: Antoci, S. (1999). "On the gravitational field of a sphere of incompressible fluid according to Einstein's theory". arXiv : physics/9912033 .

^ Droste, J. (1917). "On the field of a single centre in Einstein's theory of gravitation, and the motion of a particle in that field" (PDF) . Proceedings Royal Academy Amsterdam . 19 (1): 197–215. Archived from the original (PDF) on 18 May 2013 . Retrieved 16 September 2012 .

^ Kox, A. J. (1992). "General Relativity in the Netherlands: 1915–1920" . In Eisenstaedt, Jean; Kox, A. J. (eds.). Studies in the history of general relativity . Birkhäuser. p. 41. ISBN 978-0-8176-3479-7 .

^ 't Hooft, G. (2009). "Introduction to the Theory of Black Holes" (PDF) . Institute for Theoretical Physics / Spinoza Institute. pp. 47–48. Archived from the original (PDF) on 21 May 2009 . Retrieved 24 June 2010 .

^ Eddington, Arthur (1926). The Internal Constitution of the Stars . Science . 52 . Cambridge University Press. pp. 233–40. doi : 10.1126/science.52.1341.233 . ISBN 978-0-521-33708-3 . PMID 17747682 . Archived from the original on 11 August 2016.

^ Thorne, Kip S.; Hawking, Stephen (1994). Black Holes and Time Warps: Einstein's Outrageous Legacy . W. W. Norton & Company. pp. 134 –135. ISBN 978-0-393-31276-8 . Retrieved 12 April 2019 . The first conclusion was the Newtonian version of light not escaping; the second was a semi-accurate, relativistic description; and the third was typical Eddingtonian hyperbole ... when a star is as small as the critical circumference, the curvature is strong but not infinite, and space is definitely not wrapped around the star. Eddington may have known this, but his description made a good story, and it captured in a whimsical way the spirit of Schwarzschild's spacetime curvature."

^ Venkataraman, G. (1992). Chandrasekhar and his limit . Universities Press. p. 89. ISBN 978-81-7371-035-3 . Archived from the original on 11 August 2016.

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^ Bombaci, I. (1996). "The Maximum Mass of a Neutron Star". Astronomy and Astrophysics . 305 : 871–877. Bibcode : 1996A&A...305..871B .

^ Cho, A. (16 February 2018). "A weight limit emerges for neutron stars". Science . 359 (6377): 724–725. Bibcode : 2018Sci...359..724C . doi : 10.1126/science.359.6377.724 . PMID 29449468 .

^ Margalit, B.; Metzger, B. D. (1 December 2017). "Constraining the Maximum Mass of Neutron Stars from Multi-messenger Observations of GW170817". The Astrophysical Journal . 850 (2): L19. arXiv : 1710.05938 . Bibcode : 2017ApJ...850L..19M . doi : 10.3847/2041-8213/aa991c . S2CID 119342447 .

^ Shibata, M.; Fujibayashi, S.; Hotokezaka, K.; Kiuchi, K.; Kyutoku, K.; Sekiguchi, Y.; Tanaka, M. (22 December 2017). "Modeling GW170817 based on numerical relativity and its implications". Physical Review D . 96 (12): 123012. arXiv : 1710.07579 . Bibcode : 2017PhRvD..96l3012S . doi : 10.1103/PhysRevD.96.123012 . S2CID 119206732 .

^ Ruiz, M.; Shapiro, S. L.; Tsokaros, A. (11 January 2018). "GW170817, general relativistic magnetohydrodynamic simulations, and the neutron star maximum mass" . Physical Review D . 97 (2): 021501. arXiv : 1711.00473 . Bibcode : 2018PhRvD..97b1501R . doi : 10.1103/PhysRevD.97.021501 . PMC 6036631 . PMID 30003183 .

^ Rezzolla, L.; Most, E. R.; Weih, L. R. (9 January 2018). "Using Gravitational-wave Observations and Quasi-universal Relations to Constrain the Maximum Mass of Neutron Stars". Astrophysical Journal . 852 (2): L25. arXiv : 1711.00314 . Bibcode : 2018ApJ...852L..25R . doi : 10.3847/2041-8213/aaa401 . S2CID 119359694 .

^ Ruffini, R. ; Wheeler, J. A. (1971). "Introducing the black hole" (PDF) . Physics Today . 24 (1): 30–41. Bibcode : 1971PhT....24a..30R . doi : 10.1063/1.3022513 . Archived from the original (PDF) on 25 July 2011 . Retrieved 5 December 2009 .

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^ Pilkington, J. D. H.; et al. (1968). "Observations of some further Pulsed Radio Sources". Nature . 218 (5137): 126–129. Bibcode : 1968Natur.218..126P . doi : 10.1038/218126a0 . S2CID 4253103 .

^ Hewish, A. (1970). "Pulsars". Annual Review of Astronomy and Astrophysics . 8 (1): 265–296. Bibcode : 1970ARA&A...8..265H . doi : 10.1146/annurev.aa.08.090170.001405 .

^ Newman, E. T. ; et al. (1965). "Metric of a Rotating, Charged Mass". Journal of Mathematical Physics . 6 (6): 918. Bibcode : 1965JMP.....6..918N . doi : 10.1063/1.1704351 .

^ Israel, W. (1967). "Event Horizons in Static Vacuum Space-Times". Physical Review . 164 (5): 1776. Bibcode : 1967PhRv..164.1776I . doi : 10.1103/PhysRev.164.1776 .

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^ Carter, B. (1977). "The vacuum black hole uniqueness theorem and its conceivable generalisations". Proceedings of the 1st Marcel Grossmann meeting on general relativity . pp. 243–254.

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^ Ford, L. H. (2003). "The Classical Singularity Theorems and Their Quantum Loopholes". International Journal of Theoretical Physics . 42 (6): 1219–1227. arXiv : gr-qc/0301045 . Bibcode : 2003gr.qc.....1045F . doi : 10.1023/A:1025754515197 . S2CID 14404560 .

^ "The Nobel Prize in Physics 2020" . NobelPrize.org . Retrieved 8 October 2020 .

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^ Jump up to: a b
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