A Smarr formula for charged black holes in nonlinear electrodynamics

Abstract

It is well known that the Smarr formula does not hold for black holes in non-linear electrodynamics. The main reason for this is the fact that the trace of the energy momentum tensor for nonlinear electrodynamics does not vanish as it is for Maxwell's electrodynamics. Starting from the Komar integral, we derived a new Smarr-type formula for spherically symmetric static electrically charged black hole solutions in nonlinear electrodynamics. We show that this general formula is in agreement with some that are obtained for black hole solutions with nonlinear electrodynamics.

First law and Smarr formula of black hole mechanics in nonlinear gauge theories

“…In our prescription, it is crucial to consider extra parameters in the Lagrangian, which lead to additional terms in the first law and the Smarr relation. We showed that these terms in the Smarr relation can be written as an integral of the trace of the stress-energy tensor, in agreement with the result in [35] and [36].…”

Scale-dependent ( $$2+1$$ 2 + 1 )-dimensional electrically charged black holes in Einstein-power-Maxwell theory

“…The scale dependent effect is notoriously small for those quantities. Regarding the Smarr formula and the first law of black hole mechanics, we remark a couple of facts first: given that we work in the framework of non-linear electrodynamics, we expect to have a modified relation compared to Maxwell's linear theory, as it has been shown in [92]. Furthermore, the Smarr formula requires knowledge of the total mass M, which unfortunately in the present work is unknown.…”

Black Holes With Many Horizons in the Theories of Nonlinear Electrodynamics

“…Concretely, we shall derive the Smarr formula and the first law of thermodynamics. It is worth noting that many studies in NLE in this respect have been carried out, for example in [47][48][49][50][51][52]. Hawking showed that for the outermost, event horizon in an asymptotically flat spacetime, the temperature of black hole is…”