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Abstract: We study the system formed by a gaz of black holes and strings within amicrocanonical formulation. We derive the microcanonical content of the system:entropy, equation of state, number of components N, temperature T and specificheat. The pressure and the specific heat are negative reflecting thegravitational unstability and a non-homogeneous configuration. The asymptoticbehaviour of the temperature for large masses emerges as the Hawkingtemperature of the system classical or semiclassical phase in which theclassical black hole behaviour dominates, while for small masses quantum blackhole or string behavior the temperature becomes the string temperature whichemerges as the critical temperature of the system. At low masses, a phasetransition takes place showing the passage from the classical black hole toquantum string behaviour. Within a microcanonical field theory formulation,the propagator describing the string-particle-black hole system is derived andfrom it the interacting four point scattering amplitude of the system isobtained. For high masses it behaves asymptotically as the degeneracy of statesof the system ie duality or crossing symmetry. The microcanonical propagatorand partition function are derived from a Nambu-Goto formulation of theN-extended objects and the mass spectrum of the black-hole-string system isobtained: for small masses quantum behaviour these yield the usual purestring scattering amplitude and string-particle spectrum M n\approx \sqrt{n};for growing mass it pass for all the intermediate states up to the pure blackhole behaviour. The different black hole behaviours according to the differentmass ranges: classical, semiclassical and quantum or string behaviours arepresent in the model.



Autor: D. J. Cirilo-Lombardo Bogoliubov Laboratory JINR, Dubna, N.G. Sanchez Observatoire de Paris LERMA

Fuente: https://arxiv.org/







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