TY - JOUR

T1 - Braneworld puzzle about entropy bounds and a maximal temperature

AU - Brustein, Ram

AU - Eichler, David

AU - Foffa, Stefano

PY - 2005/6/15

Y1 - 2005/6/15

N2 - Entropy bounds applied to a system of N species of light quantum fields in thermal equilibrium at temperature T are saturated in four dimensions at a maximal temperature Tmax =MPlanck/N. We show that the correct setup for understanding the reason for the saturation is a cosmological one, and that a possible explanation is the copious production of black holes at this maximal temperature which prevents any further rise in temperature. The proposed explanation implies, if correct, that N light fields cannot be in thermal equilibrium in an ideal gas phase at temperatures T above Tmax. However, we have been unable to identify a concrete mechanism that is efficient and quick enough to prevent the universe from exceeding this limiting temperature. The same issues can be studied in the framework of AdS/CFT by using a brane moving in a five dimensional AdS-Schwarzschild space to model a radiation dominated universe. In this case we show that Tmax is the temperature at which the brane just reaches the horizon of the black hole, and that entropy bounds and the generalized second law of thermodynamics seem to be violated when the brane continues to fall into the black hole. We find, again, that the known physical mechanisms, including black hole production, are not efficient enough to prevent the brane from falling into the black hole. We propose several possible explanations for the apparent violation of entropy bounds, but none is a conclusive one.

AB - Entropy bounds applied to a system of N species of light quantum fields in thermal equilibrium at temperature T are saturated in four dimensions at a maximal temperature Tmax =MPlanck/N. We show that the correct setup for understanding the reason for the saturation is a cosmological one, and that a possible explanation is the copious production of black holes at this maximal temperature which prevents any further rise in temperature. The proposed explanation implies, if correct, that N light fields cannot be in thermal equilibrium in an ideal gas phase at temperatures T above Tmax. However, we have been unable to identify a concrete mechanism that is efficient and quick enough to prevent the universe from exceeding this limiting temperature. The same issues can be studied in the framework of AdS/CFT by using a brane moving in a five dimensional AdS-Schwarzschild space to model a radiation dominated universe. In this case we show that Tmax is the temperature at which the brane just reaches the horizon of the black hole, and that entropy bounds and the generalized second law of thermodynamics seem to be violated when the brane continues to fall into the black hole. We find, again, that the known physical mechanisms, including black hole production, are not efficient enough to prevent the brane from falling into the black hole. We propose several possible explanations for the apparent violation of entropy bounds, but none is a conclusive one.

UR - http://www.scopus.com/inward/record.url?scp=33644530117&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.71.124015

DO - 10.1103/PhysRevD.71.124015

M3 - Article

AN - SCOPUS:33644530117

VL - 71

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 12

M1 - 124015

ER -