Manifestly covariant Juumlttner distribution and equipartition theorem

作者：Chacon Acosta Guillermo^*; Dagdug Leonardo; Morales Tecolt Hugo A

来源：Physical Review E, 2010, 81(2): 021126.

DOI：10.1103/PhysRevE.81.021126

The relativistic equilibrium velocity distribution plays a key role in describing several high-energy and astrophysical effects. Recently, computer simulations favored Juumlttner's as the relativistic generalization of Maxwell's distribution for d=1,2,3 spatial dimensions and pointed to an invariant temperature. In this work, we argue an invariant temperature naturally follows from manifest covariance. We present a derivation of the manifestly covariant Juumlttner's distribution and equipartition theorem. The standard procedure to get the equilibrium distribution as a solution of the relativistic Boltzmann's equation, which holds for dilute gases, is here adopted. However, contrary to previous analysis, we use Cartesian coordinates in d+1 momentum space, with d spatial components. The use of the multiplication theorem of Bessel functions turns crucial to regain the known invariant form of Juumlttner's distribution. Since equilibrium kinetic-theory results should agree with thermodynamics in the comoving frame to the gas the covariant pseudonorm of a vector entering the distribution can be identified with the reciprocal of temperature in such comoving frame. Then by combining the covariant statistical moments of Juumlttner's distribution a form of the equipartition theorem is advanced which also accommodates the invariant comoving temperature and it contains, as a particular case, a previous not manifestly covariant form.

• 出版日期2010-2