Electrodynamics Modified by Some Dimension-five Lorentz Violating Interactions: Radiative Corrections

We study radiative corrections to massless quantum electrodynamics modified by two dimension-five LV interactions $\bar{\Psi} \gamma^{\mu} b'^{\nu} F_{\mu\nu}\Psi$ and $\bar{\Psi}\gamma^{\mu}b^{\nu} \tilde{F}_{\mu\nu} \Psi$ in the framework of effective field theories. All divergent one-particle-irreducible Feynman diagrams are calculated at one-loop order and several related issues are discussed. It is found that massless quantum electrodynamics modified by the interaction $\bar{\Psi} \gamma^{\mu} b'^{\nu} F_{\mu\nu}\Psi$ alone is one-loop renormalizable and the result can be understood on the grounds of symmetry. In this context the one-loop Lorentz-violating beta function is derived and the corresponding running coefficients are obtained.Comment: 13 pages, 1 figure. Version to appear in EPJ

Phase Transition of RN-AdS Black Hole with Fixed Electric Charge and Topological Charge

Phase transition of RN-AdS black hole is investigated from a new perspective. Not only the cosmological constant is treated as pressure, but also the spatial curvature of black hole is treated as topological charge. We obtain the extended thermodynamic first law from which the mass is naturally viewed as enthalpy instead of energy. In canonical ensemble with fixed topological charge and electric charge, interesting van der Waals system's oscillatory behavior in $T-S$, $P-V$ graphes and swallow tail behavior in $G-T$, $G-P$ graphes are observed. By applying the Maxwell equal area law and by analysing the gibbs free energy, we obtain analytical phase transition coexistence curves ($T-P$) which are consistent with each other.Comment: 18 pages, 5 figure

A note on Maxwell's equal area law for black hole phase transition

The state equation of the charged AdS black hole is reviewed in the $T-r$ plane. Thinking of the phase transition, the $T-S$, $P-V$, $P-\nu$ graphs are plotted and then the equal area law is used in the three cases to get the phase transition point (P,T). The analytical phase transition point relations for P-T of charged AdS black hole has been obtained successfully. By comparing the three results, we find that the equal area law possibly cannot be used directly for $P-\nu$ plane. According to the $T-S$, $P-V$ results, we plot the $P-T-Q$ graph and find that for a highly charged black hole a very low temperature condition is required for the phase transition

A New Phase Transition Related to the Black Hole's Topological Charge

The topological charge $\epsilon$ of AdS black hole is introduced in Ref.[1,2], where a complete thermodynamic first law is obtained. In this paper, we investigate a new phase transition related to the topological charge in Einstein-Maxwell theory. Firstly, we derive the explicit solutions corresponding to the divergence of specific heat $C_{\epsilon}$ and determine the phase transition critical point. Secondly, the $T-r$ curve and $T-S$ curve are investigated and they exhibit an interesting van der Waals system's behavior. Critical physical quantities are also obtained which are consistent with those derived from the specific heat analysis. Thirdly, a van der Waals system's swallow tail behavior is observed when $\epsilon>\epsilon_{c}$ in the $F-T$ graph. What's more, the analytic phase transition coexistence lines are obtained by using the Maxwell equal area law and free energy analysis, the results of which are consistent with each other.Comment: 11 pages, 5 figure