Quasilocal Conservation Laws: Why We Need Them

TL;DR

This paper introduces a quasilocal conservation law based on the Brown-York tensor that effectively accounts for gravitational effects, explaining phenomena like kinetic energy increase via gravitational energy flux.

Contribution

It develops a general quasilocal conservation law incorporating gravity, addressing limitations of matter-only laws, and demonstrates its explanatory power with a relativistic energy flux example.

Findings

Quasilocal conservation law accounts for gravitational energy flux.

Energy transfer explained via frame dragging and gravitational flux.

Traditional matter-only laws fail to explain gravitational phenomena.

Abstract

We argue that conservation laws based on the local matter-only stress-energy-momentum tensor (characterized by energy and momentum per unit volume) cannot adequately explain a wide variety of even very simple physical phenomena because they fail to properly account for gravitational effects. We construct a general quasi}local conservation law based on the Brown and York total (matter plus gravity) stress-energy-momentum tensor (characterized by energy and momentum per unit area), and argue that it does properly account for gravitational effects. As a simple example of the explanatory power of this quasilocal approach, consider that, when we accelerate toward a freely-floating massive object, the kinetic energy of that object increases (relative to our frame). But how, exactly, does the object acquire this increasing kinetic energy? Using the energy form of our quasilocal conservation law, we can see precisely the actual mechanism by which the kinetic energy increases: It is due to a bona fide gravitational energy flux that is exactly analogous to the electromagnetic Poynting flux, and involves the general relativistic effect of frame dragging caused by the object's motion relative to us.