An AdS black hole on-shell action is a mathematical formula that describes the dynamics of a black hole in Anti-de Sitter (AdS) space. It is a key concept in the study of black holes and is used to understand the thermodynamics and behavior of these objects.
The AdS black hole on-shell action is closely related to the holographic principle, which states that the information contained in a region of space can be described by the information on the boundary of that region. The on-shell action is used to calculate the entropy of a black hole, which is related to the amount of information it contains.
The AdS black hole on-shell action is calculated using a mathematical technique called the holographic renormalization. This involves mapping the AdS black hole solution onto a simpler, asymptotically AdS space, and then calculating the action using this simplified space.
In string theory, the AdS black hole on-shell action is used to study the AdS/CFT correspondence, which relates a theory of gravity in AdS space to a theory of quantum field theory on its boundary. This allows for a better understanding of the nature of black holes and their behavior.
Yes, the concept of the AdS black hole on-shell action has been extended to other types of black holes, such as charged black holes and rotating black holes. It has also been used to study the thermodynamics and behavior of these black holes in various dimensions and theories of gravity.