Static and Infalling Quasilocal Energy of Charged and Naked Black Holes

TL;DR

This paper extends the quasilocal energy formalism to include electromagnetic and dilaton fields, analyzing energy distribution around charged and naked black holes from different observer perspectives, with implications for AdS/CFT and spacetime characterization.

Contribution

It introduces a generalized quasilocal energy formalism accommodating electromagnetic and dilaton fields, and explores energy distributions in charged and naked black holes from static and infalling observers.

Findings

Quasilocal energy transforms under boosts via Lorentz-like laws.

Energy distribution around black holes aligns with Newtonian intuition in certain limits.

Naked black holes can be characterized by their quasilocal energy profiles.

Abstract

We extend the quasilocal formalism of Brown and York to include electromagnetic and dilaton fields and also allow for spatial boundaries that are not orthogonal to the foliation of the spacetime. The extension allows us to study the quasilocal energy measured by observers who are moving around in a spacetime. We show that the quasilocal energy transforms with respect to boosts by Lorentz-type transformation laws. The resulting formalism can be used to study spacetimes containing electric or magnetic charge but not both, a restriction inherent in the formalism. The gauge dependence of the quasilocal energy is discussed. We use the thin shell formalism of Israel to reinterpret the quasilocal energy from an operational point of view and examine the implications for the recently proposed AdS/CFT inspired intrinsic reference terms. The distribution of energy around Reissner-Nordstr\"{o}m and naked black holes is investigated as measured by both static and infalling observers. We see that this proposed distribution matches a Newtonian intuition in the appropriate limit. Finally the study of naked black holes reveals an alternate characterization of this class of spacetimes in terms of the quasilocal energies.