Energy conservation for dynamical black holes

Area of Science:

• Theoretical physics
• General relativity
• Black hole thermodynamics

Background:

• Black holes are fundamental objects in astrophysics and general relativity.
• Understanding black hole dynamics and energy conservation is crucial for theoretical physics.
• Existing models may not fully capture the interplay between mass-energy, matter, and gravitational radiation.

Purpose of the Study:

• To describe a novel energy conservation law for general black holes.
• To express black hole mass-energy increase using energy densities of infalling matter and gravitational radiation.
• To provide a framework for understanding black hole growth and stability.

Main Methods:

• Formulation of a first law of black-hole dynamics.
• Derivation of an effective gravitational-radiation energy tensor.
• Identification of an energy flux and its relation to horizon properties.
• Development of a Gibbs-like equation for energy supply.

Main Results:

• A comprehensive energy conservation law for black holes is presented.
• The law quantifies mass-energy increase based on infalling matter and gravitational radiation.
• An effective energy tensor measures gravitational radiation (ingoing/outgoing, transverse/longitudinal).
• A Gibbs-like equation relates energy supply to area increase and surface gravity.

Conclusions:

• The derived first law of black-hole dynamics is regular in the limit of no growth.
• The framework provides a detailed understanding of energy exchange at the black hole horizon.
• The new formulation unifies concepts of black hole growth, energy density, and thermodynamics.