Ricci flat rotating black branes with a conformally invariant Maxwell source

TL;DR

This paper introduces rotating black brane solutions in Einstein gravity coupled with a conformally invariant Maxwell field, analyzing their thermodynamics, conserved quantities, and phase behavior across multiple dimensions.

Contribution

It presents new rotating black brane solutions in higher dimensions with conformally invariant Maxwell fields and explores their thermodynamic properties and phase structure.

Findings

Black brane solutions exist only in dimensions multiple of four.

Electric field expressions are dimension-independent.

No Hawking-Page phase transition occurs for these solutions.

Abstract

We consider Einstein gravity coupled to an $U(1)$ gauge field for which the density is given by a power of the Maxwell Lagrangian. In $d$-dimensions the action of Maxwell field is shown to enjoy the conformal invariance if the power is chosen as $d/4$. We present a class of charge rotating solutions in Einstein-conformally invariant Maxwell gravity in the presence of a cosmological constant. These solutions may be interpreted as black brane solutions with inner and outer event horizons or an extreme black brane depending on the value of the mass parameter. Since we are considering power of the Maxwell density, the black brane solutions exist only for dimensions which are multiples of four. We compute conserved and thermodynamics quantities of the black brane solutions and show that the expression of the electric field does not depend on the dimension. Also, we obtain a Smarr-type formula and show that these conserved and thermodynamic quantities of black branes satisfy the first law of thermodynamics. Finally, we study the phase behavior of the rotating black branes and show that there is no Hawking--Page phase transition in spite of conformally invariant Maxwell field.