Generalized Thermodynamic Properties of Lifshitz black holes

The generalized effective potential for motion in Lifshitz geometry (with arbitrary value of both the dynamical exponent $z$ and $f(r)$) is presented. Based on this effective potential energy, we shall show that bounded orbits are forbidden for positive values of $z$ and allowed for negative values of $z$. The stability of these bounded orbits are analysed in full detail. Besides, by comparison, we quote a theorem which should be very helpful in searching thermodynamical properties of these gravitational black holes. Based on this theorem, generalized thermodynamic properties of Lifshitz black holes are computed. Examples are given where the entropy still satisfies the area law. The calculated mass, temperature and entropy satisfy both the first thermodynamic principle of black holes and a Smarr formula.