Soluția Reissner-Nordström

În fizică și astronomie, soluția Reissner-Nordström este o soluție a ecuațiilor de câmp ale lui Einstein din 1915. Soluția Reissner-Nordström descrie o gaură neagră cu sarcină electrică.

Metrică

Soluția Reissner-Nordström a fost descoperită de Hans Reissner și Gunnar Nordström și se scrie astfel: $c^{2}{d\tau }^{2}=\left(1-{\color {OliveGreen}{\frac {r_{s}}{r}}}+{\color {Red}{\frac {r_{Q}^{2}}{r^{2}}}}\right)c^{2}dt^{2}-{\frac {dr^{2}}{1-{\color {OliveGreen}{\frac {r_{s}}{r}}}+{\color {Red}{\frac {r_{Q}^{2}}{r^{2}}}}}}-r^{2}d\Omega ^{2}$

unde

τ este timpul propriu în secunde, măsurat cu un ceas care se mișcă odată cu particula
c este viteza luminii în metri pe secunde,
t este coordonata timp în secunde, măsurat cu un ceas care staționar se află la infinit
r este raza (circumferința unui cerc centrat pe stele împărțită la 2π), în metri,
Ω este unghiul solid,

\,d\Omega ^{2}=d\theta ^{2}+\sin ^{2}\theta \,d\phi ^{2}

- r_s este the raza Schwarzschild (în metri) al unui corp masiv, care are masa M

r_{s}={\frac {2GM}{c^{2}}}

unde

- G este constanta gravitațională, și
- r_Q este o lungime de scară care corespunde sarcinii electrice Q al masei

r_{Q}^{2}={\frac {Q^{2}G}{4\pi \varepsilon _{0}c^{4}}}

unde

- ${1 \over 4\pi \varepsilon _{0}}$ este constanta din legea lui Coulomb.^[1]

Soluția Reisner- Nordstrom și astrofizica găurilor negre

Soluția Reisner- Nordstrom reprezintă o gaura neagra cu sarcina electrica. S- a constatat , ca ea are doua orizonturi de evenimente: unul extern si altul intern, numit și orizont Cauchy, in cinstea matematicianului francez Augustin Louis Cauchy. Începând din anii 70 a prezentat interes, daca gaurile negre cu sarcina electrica foarte mare, pot să existe în Univers? S- a constatat, că găurile negre cu sarcina electrica foarte mare, sunt dispuse să se descarce printr-un proces electrodinamic de tip Schwinger, in rezultatul generării de cupluri particula- antiparticula in câmpul foarte intens electric din apropierea orizontului extern al gaurii negre^[2] ^[3]. In timp ce găurile negre microscopice, cu mase de ordinul 10^15 g,sau mai mici au tendința să se descarce electric printr-un proces Hawking de evaporare a găurilor negre^[4], păstrând statistic o sarcina electrica de ordinul unei sarcini elementare

Note. Referințe

^ Landau 1975.
^ W.T.Zaumen, Nature, vol.247, p.530, 1974
^ I.M.Ternov, A.B.Gaina, G.A. Chizhov, Sov.J. Nucl. Phys., vol.44 ( 2), August 1986
^ D. Page, Phys.Rev., D16, 2402, 1977

Reissner, H (1916). „Über die Eigengravitation des elektrischen Feldes nach der Einsteinschen Theorie”. Annalen der Physik. 50: 106–120. doi:10.1002/andp.19163550905.
Nordström, G (1918). „On the Energy of the Gravitational Field in Einstein's Theory”. Verhandl. Koninkl. Ned. Akad. Wetenschap., Afdel. Natuurk., Amsterdam. 26: 1201–1208.
Adler, R (1965). Introduction to General Relativity. New York: McGraw-Hill Book Company. pp. 395–401. ISBN 978-0-07-000420-7.
Wald, RM (1984). General Relativity. Chicago: The University of Chicago Press. pp. 158, 312–324. ISBN 978-0-226-87032-8.

Legături externe

spacetime diagrams Arhivat în 7 iulie 2007, la Wayback Machine. including Finkelstein diagram and Penrose diagram, by Andrew J. S. Hamilton
"Particle Moving Around Two Extreme Black Holes" by Enrique Zeleny, The Wolfram Demonstrations Project.

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