Event Horizon of the Monopole-Quadrupole solution: geometric and thermodynamic properties

TL;DR

This paper explores the geometric deformation and thermodynamic implications of the event horizon in a static, axisymmetric spacetime with mass and quadrupole moment, extending Schwarzschild black hole properties.

Contribution

It provides a detailed analysis of how quadrupole moments deform the event horizon and discusses associated thermodynamic consequences.

Findings

Quadrupole moment causes deformation of the Schwarzschild horizon.

Range of quadrupole values preserving horizon regularity is identified.

Thermodynamic implications of horizon deformation are discussed.

Abstract

We investigate the general geometric properties of the surface of infinite red-shift corresponding to the event horizon of the static and axisymmetric solution of the Einstein vacuum equations that only possesses mass $M$ and quadrupole moment $Q$. The deformation of the Schwarzschild surface $r=2M$ produced by the quadrupole moment is shown, and the range of values of this multipole moment is specified, which preserves a regular, closed, continuous and differentiable surface. Some thermodynamic consequences and speculations ensuing from our results are discussed.