A black hole that possesses an electric charge, affecting its thermodynamic properties.A charged black hole is a black hole that carries an electric charge, in addition to its mass and angular momentum. In classical general relativity, such objects are described by the Reissner-Nordström solution (for non-rotating) or the Kerr-Newman solution (for rotating). The charge fundamentally alters the black hole's thermodynamic properties: it changes the temperature, entropy, and the way the black hole radiates. For instance, a charged black hole can cool to zero temperature at a finite mass, a state known as an extremal black hole, where the Hawking radiation ceases.
The Reissner-Nordström solution was derived independently by Hans Reissner (1916) and Gunnar Nordström (1918), shortly after Einstein's general relativity. The thermodynamic interpretation of black holes, including charged ones, was developed by Jacob Bekenstein and Stephen Hawking in the 1970s.
The electric charge creates an electrostatic field that extends outside the event horizon. This field stores energy, which modifies the black hole's mass-energy balance. In thermodynamics, the charge acts as a thermodynamic variable analogous to volume in a gas: changing the charge changes the black hole's temperature and entropy. The presence of charge also introduces a second horizon (the inner Cauchy horizon) and can lead to instabilities or the possibility of extracting energy via processes like superradiance.
Charged black holes are primarily theoretical tools used to test quantum gravity and black hole thermodynamics, such as in the study of Hawking radiation and the information paradox. They also appear in gauge/gravity duality (AdS/CFT) as models for strongly coupled quantum systems.
A charged black hole can act as a refrigerator: by carefully adjusting its charge, it can extract heat from its surroundings and cool down, a process studied in the context of black hole thermodynamics.






