Effective Values of Komar Conserved Quantities and Their Applications

TL;DR

This paper derives effective Komar conserved quantities for Kerr-Newman black holes at any radius and establishes a local identity linking these quantities with thermodynamic properties, leading to a generalized Smarr formula.

Contribution

It introduces a method to calculate effective Komar quantities at any radius and connects them to black hole thermodynamics through a new local identity.

Findings

Effective Komar angular momentum valid outside the horizon.

Derived a local identity relating conserved charge to thermodynamics.

Established a generalized Smarr formula for Kerr-Newman black holes.

Abstract

We calculate the effective Komar angular momentum for the Kerr-Newman (KN) black hole. This result is valid at any radial distance on and outside the black hole event horizon. The effcetive values of mass and angular momentum are then used to derive an identity ($K_{\chi^{\mu}}=2ST$) which relates the Komar conserved charge ($K_{\chi^{\mu}}$) corresponding to the null Killing vector ($\chi^{\mu}$) with the thermodynamic quantities of this black hole. As an application of this identity the generalised Smarr formula for this black hole is derived. This establishes the fact that the above identity is a local form of the inherently non-local generalised Smarr formula.