# Thermodynamics of charged black points in vacuum nonlinear electrodynamics

## TL;DR

This paper investigates the thermodynamic behavior of charged black points in vacuum nonlinear electrodynamics, revealing their compliance with the third law and analyzing their phase transition properties.

## Contribution

It introduces the concept of black points as a special state of charged black holes and examines their thermodynamic properties, including horizon degeneracy and phase transitions.

## Key findings

- Black points satisfy the third law of thermodynamics.
- Formation of black points is not a first-order phase transition.
- Black points can have a doubly degenerate horizon similar to extremal black holes.

## Abstract

The paper analyzes the thermodynamic properties of a special state of charged black holes, in which the event horizon becomes point-like and coincides with the singularity. It is shown that for such states, called black points, in contrast to Reissner-Nordstr\"{o}m black holes, the third law of thermodynamics in Planck's formulation is fulfilled. It is also shown that the formation of a black point is not a first-order phase transition. Considerable attention is paid to the special state of a black point with a doubly degenerate horizon, similar to the extreme state of a Reissner-Nordstr\"om black hole.