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Maximal acceleration and black hole evaporation

Ricardo Gallego Torromé

Department of Mathematics, Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska, Koper, Slovenia

E-mail Address: rigato39@gmail.com

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https://doi.org/10.1142/S0219887822500645Cited by:0 (Source: Crossref)

Abstract

In this paper, we discuss how in certain theories of spacetime admitting a maximal proper acceleration Hawking radiation does not completely evaporate the black hole. The black hole remnant’s mass depends on the inverse of the maximal acceleration. Furthermore, as a consequence of a duality between the minimum mass that a Schwarzschild black hole can have in such spacetimes and the maximal acceleration, we show that in certain theories with a maximal acceleration, there must be an upper uniform bound on the value of the force that can be exerted on test particles.

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References

1. P. M. Alsing and P. W. Milonni , Simplified derivation of the Hawking-Unruh temperature for an accelerated observer in vacuum, Am. J. Phys. 72 (2004) 1524. Crossref, Web of Science, Google Scholar
2. D. Bao, S. S. Chern and Z. Shen , An Introduction to Riemann-Finsler Geometry, Graduate Texts in Mathematics, Vol. 200 (Springer-Verlag, 2000). Crossref, Google Scholar
3. J. D. Barrow and G. W. Gibbons , Maximum tension: With and without a cosmological constant, Mon. Not. R. Astron. Soc. 446 (2014) 3874. Crossref, Web of Science, Google Scholar
4. E. Benedetto and A. Feoli , Unruh temperature with maximal acceleration, Mod. Phys. Lett. A 30(13) (2015) 1550075. Link, Web of Science, Google Scholar
5. M. Born and L. Infeld , Foundations of a new field theory, Proc. R. Soc. Lond. A 144 (1934) 425. Crossref, Google Scholar
6. M. J. Bowick and S. B. Giddins , High-temperature strings, Nucl. Phys. B 325 (1989) 631. Crossref, Web of Science, Google Scholar
7. V. Bozza, G. Lambiase, G. Papini and G. Scarpetta , Quantum violations of the equivalence principle in a modified Schwarzschild geometry. Neutrino oscillations, Phys. Lett. A 279 (2001) 163–168. Crossref, Web of Science, Google Scholar
8. V. Bozza, A. Feoli, G. Papini and G. Scarpetta , Maximal acceleration effects in Reissner-Nordstr $ö m$ space, Phys. Lett. A 271 (2000) 35. Crossref, Web of Science, Google Scholar
9. V. Bozza, A. Feoli, G. Lambiase, G. Papini and G. Scarpetta , Maximal acceleration effects in Kerr space, Phys. Lett. A 283 (2001) 53. Crossref, Web of Science, Google Scholar
10. H. E. Brandt , Maximal proper acceleration relative to the vacuum, Lett. Nuovo. Cimento 38 (1983) 522. Crossref, Web of Science, Google Scholar
11. H. E. Brandt , Maximal proper acceleration and the structure of spacetime, Found. Phys. Lett. 2 (1989) 39. Crossref, Google Scholar
12. E. R. Caianiello , Is there a maximal acceleration, Lett. Nuovo Cimento 32 (1981) 65. Crossref, Web of Science, Google Scholar
13. E. Caianiello and G. Landi , Maximal acceleration and Sakharov’s limiting temperature, Lett. Nuovo Cimento 42 (1985) 70. Crossref, Web of Science, Google Scholar
14. E. Caianiello, A. Feoli, M. Gasperini and G. Scarpetta , Quantum corrections to the spacetime metric from geometric phase space quantization, Int. J. Theor. Phys. 29 (1990) 131. Crossref, Web of Science, Google Scholar
15. P. Caldirola , On the existence of a maximal acceleration in the relativistic theory of the electron, Lett. Nuovo Cimento 32(9) (1981) 264. Crossref, Web of Science, Google Scholar
16. A. Di Piazza, C. Mueller, K. Z. Hatsagortsyan and C. H. Keitel , Extremely high-intensity laser interactions with fundamental quantum systems, Rev. Mod. Phys. 84 (2012) 1177. Crossref, Web of Science, Google Scholar
17. A. Einstein , The Meaning of Relativity (Princeton University Press, 1923). Google Scholar
18. A. Feoli, G. Lambiase, G. Papini and G. Scarpetta , Classical electrodynamics of a particle with maximal acceleration corrections, Nuovo Cim. B 112 (1997) 913–922. Google Scholar
19. A. Feoli, G. Lambiase, G. Papini and G. Scarpetta , Schwasrzschild field with maximal acceleration corrections, Phys. Lett. A 263 (1999) 147. Crossref, Web of Science, Google Scholar
20. V. P. Frolov and N. Sanchez , Instability of accelerated strings and the problem of limiting acceleration, Nucl. Phys. B 349 (1991) 815. Crossref, Web of Science, Google Scholar
21. R. G. Torromé , On a covariant version of Caianiello’s model, Gen. Relativ. Gravit. 39 (2007) 1833–1845. Crossref, Web of Science, Google Scholar
22. R. G. Torromé , An effective theory of metrics with maximal proper acceleration, Class. Quantum Grav. 32 (2015) 2450007. Crossref, Web of Science, Google Scholar
23. R. G. Torromé , On singular generalized Berwald spacetimes and the equivalence principle, Int. J. Geom. Methods Mod. Phys. 14(06) (2017) 1750091. Link, Web of Science, Google Scholar
24. R. G. Torromé , A second order differential equation for a point Charged particle, Int. J. Geom. Methods Mod. Phys. 14(04) (2017) 1750049. Link, Web of Science, Google Scholar
25. R. G. Torromé and P. Nicolini , Theories with maximal acceleration, Int. J. Mod. Phys. A 33 (2018) 1830019. Link, Web of Science, Google Scholar
26. R. G. Torromé , Some consequences of theories with maximal acceleration in laser-plasma acceleration, Mod. Phys. Lett. A 34 (2019) 1950118. Link, Web of Science, Google Scholar
27. S. B. Giddings , Black holes and massive remnants, Phys. Rev. D. 46(4) (1992) 1347–1352. Crossref, Web of Science, Google Scholar
28. S. B. Giddings , The black hole information paradox, Particles, Strings and Cosmology. Johns Hopkins Workshop on Current Problems in Particle Theory 19 and the PASCOS Interdisciplinary Symp., 22–25 March 1995, Baltimore, USA, pp. 415–428. Google Scholar
29. G. W. Gibbons , The maximum tension principle in general relativity, Found. Phys. 32 (2002) 1891. Crossref, Web of Science, Google Scholar
30. S. W. Hawking , Black hole explosions? Nature 248 (1974) 30–31. Crossref, Web of Science, Google Scholar
31. G. Lambiase, G. Papini and G. Scarpetta , Maximal acceleration corrections to the lamb shift of hydrogen, deuterium and He+, Phys. Lett. A 244 (1998) 349–354. Crossref, Web of Science, Google Scholar
32. H. Nikolic , Gravitational crystal inside the black hole, Mod. Phys. Lett. A 30(37) (2015) 1550201. Link, Web of Science, Google Scholar
33. R. Parentani and R. Potting , Accelerating observer and the Hagedorn temperature, Phys. Rev. Lett. 63 (1989) 945. Crossref, Web of Science, Google Scholar
34. G. Papini, G. Scarpetta, V. Bozza, A. Feoli and G. Lambiase , Radiation bursts from particles in the field of compact, impenetrable, astrophysical objects, Phys. Lett. A 300 (2002) 603–61. Crossref, Web of Science, Google Scholar
35. G. Papini , Shadows of a maximal acceleration, Phys. Lett. A 305 (2002) 359–364. Crossref, Web of Science, Google Scholar
36. G. Papini , Revisiting Caianiello’s maximal acceleration, Nuovo Cim. B 117 (2003) 1325–1331. Google Scholar
37. C. Rovelli and F. Vidotto , Maximal acceleration in covariant loop gravity and singularity resolution, Phys. Rev. Lett. 111 (2013) 091303. Crossref, Web of Science, Google Scholar
38. C. Schiller , General relativity and cosmology derived from principle of maximum power or force, Int. J. Theor. Phys. 44 (2005) 1629. Crossref, Web of Science, Google Scholar
39. F. P. Schuller , Born-infeld kinematics, Ann. Phys. 209 (2002) 1–34. Google Scholar
40. J. Schwinger , On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951) 664. Crossref, Web of Science, Google Scholar
41. W. G. Unruh , Notes on black hole evaporation, Phys. Rev. D 14 (1976) 870. Crossref, Web of Science, Google Scholar
42. R. M. Wald , Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics, Chicago Lectures in Physics (University of Chicago Press, 1994). Google Scholar