The Mukhanov-Bekenstein theory

by Erik Aurell (KTH)

Thursday 7 Sept 2023, 13:00 → 15:00 Europe/Stockholm

AlbaNova C4:3059 - Café Planck (AlbaNova Main Building)

Viacheslav Mukhanov and Jacob Bekenstein quite long ago advanced arguments that if a black hole is a quantized object, then the area of the horizon should be quantized [1,2]. State n of a Schwarzschild black hole (of area proportional to n) then has energy (mass) proportional to the square root of n, and is exponentially degenerate (number of states with the same energy is proportional to  2ⁿ) . The argument was more recently reviewed and extended by Mukhanov [3].  

In contrast to many other arguments in this field of physics, the Mukhanov-Bekenstein theory can be presented in an almost elementary manner, which I will try to do.

The theory also raises a problem in analysis of operators: is there a natural Hamiltonian operator which has a density of states growing as quickly with energy as Mukhanov and Bekenstein have to assume?

 

[1] V. Mukhanov, Pis. Eksp. Teor. Fiz. 44, 50 (1986)

[2] Jacob D. Bekenstein, V. F. Mukhanov, "Spectroscopy of the quantum black hole", Phys.Lett. B360 (1995) 7-12 [arXiv:gr-qc/9505012]

[3] Viatcheslav  Mukhanov, "Quantum Black Holes", in: Jacob Bekenstein, page 99-108 (World Scientific 2018) [arXiv:1810.03525]