Sakharov’s Temperature Limit in a Schwarzchild Metric Modified by the Cosmological Constant Λ

In this paper we are going to examine the effect, if any exists, that a modification of the Schwarzchild metric by a lamda term could have on the so called Sakharov’s upper temperature limit. It’s known that Zakharov’s limit is the maximum possible black body temperature that can occur in our universe. Introduction: In 1966 Sakharov first came up with an upper temperature bound for the black body radiation by using the thermodynamic properties of the hot matter in an isotropic universe. This upper bound can be written as follows:[1] K G c k c T B 32 5 0 max 10 419 . 1 T × ≅ = ≤ h (1) where T is the temperature of the black body radiation, kB = is Boltman’s constant, h is Planck’s constant, c is the speed of light, and G is the gravitational constant, and c0 is a constant of the order of unit. This temperature is the maximum temperature of any substance in equilibrium with the radiation field. Following Massa’s work [2] we now include a cosmological constant Λ in the suggested metric equation (2) and work out possible differences, if any, in the original definition of Sakharov’s limit. To start our analysis we first write out the appropriate metric modified by the cosmological constant Λ: