[Paper Review] Black hole : Equipartition of matter and potential energy

Naresh Dadhich|ArXiv.org|May 14, 1997

Black Holes and Theoretical Physics3 citations

TL;DR

This paper proposes a novel characterization of the static black hole horizon using the Brown-York quasilocal energy, showing that the horizon is the surface where energy equipartitions between matter and gravitational potential energy. The key result is that this equipartition condition uniquely identifies the horizon, offering a thermodynamically motivated definition rooted in energy balance.

ABSTRACT

Black hole horizon is usually defined as the limit for existence of timelike worldline or when a spatially bound surface turns oneway (it is crossable only in one direction). It would be insightful and physically appealing to find its characterization involving an energy consideration. By employing the Brown-York [1] quasilocal energy we propose a new and novel characterization of the horizon of static black hole. It is the surface at which the Brown-York energy equipartitions itself between the matter and potential energy. It is also equivalent to equipartitioning of the binding energy and the gravitational charge enclosed by the horizon.

Motivation & Objective

• To provide a physically intuitive, energy-based characterization of the black hole horizon beyond the standard causal definition.
• To explore whether the horizon can be defined through a balance of matter and potential energy using quasilocal energy formalism.
• To establish a connection between gravitational binding energy and the gravitational charge enclosed by the horizon.
• To offer a thermodynamically motivated definition of the horizon that aligns with physical intuition.

Proposed method

• Utilizes the Brown-York quasilocal energy formalism to define energy content within a finite boundary enclosing the black hole.
• Analyzes the energy distribution on a spacelike 2-surface to identify where matter energy and potential energy are equally partitioned.
• Applies the condition of energy equipartition to derive the location of the horizon in static spacetimes.
• Demonstrates equivalence between equipartition of matter and potential energy and equipartition of binding energy and gravitational charge.
• Uses the Einstein field equations and static spherically symmetric solutions to validate the condition.
• Relies on the quasilocal energy expression derived from the boundary term in the Einstein-Hilbert action.

Experimental results

Research questions

• RQ1 Can the black hole horizon be characterized by an energy balance condition rather than purely causal or geometric criteria?
• RQ2 Does the Brown-York quasilocal energy allow for a physical definition of the horizon based on equipartition of energy components?
• RQ3 Is there a direct link between the binding energy of matter and the gravitational charge enclosed by the horizon?
• RQ4 How does the equipartition of matter and potential energy relate to the standard definition of the event horizon?
• RQ5 Can the horizon be uniquely identified as the surface where energy is equally shared between matter and gravitational potential energy?

Key findings

• The horizon of a static black hole is identified as the surface where the Brown-York quasilocal energy equally partitions between matter and gravitational potential energy.
• This equipartition condition is equivalent to the equality between the binding energy and the gravitational charge enclosed by the horizon.
• The result provides a new, physically motivated definition of the horizon based on energy balance, independent of causal structure.
• The characterization holds for static black holes and is derived from the quasilocal energy formalism without requiring global spacetime properties.
• The paper establishes a thermodynamic-like interpretation of the horizon, linking energy distribution to its geometric location.
• The condition is invariant under the choice of boundary surface and uniquely determines the horizon in spherically symmetric static spacetimes.