[Paper Review] Astrophysical black holes may radiate, but they do not evaporate

George Ellis|arXiv (Cornell University)|Oct 17, 2013

Black Holes and Theoretical Physics41 references12 citations

TL;DR

This paper argues that astrophysical black holes do not fully evaporate via Hawking radiation due to the local nature of emission near a timelike marginally outer trapped surface (EMOTS), with most radiation falling into a spacelike singularity rather than escaping to infinity. As a result, a finite remnant mass and entropy persist, resolving the information paradox by confining information loss behind the event horizon.

ABSTRACT

This paper argues that the effect of Hawking radiation on an astrophysical black hole situated in a realistic cosmological context is not total evaporation of the black hole; rather there will always be a remnant mass. The key point is that the locus of emission of Hawking radiation is not the globally defined event horizon. Rather the emission domain lies just outside a timelike Marginal Outer Trapped Surface that is locally defined. The emission domain is mainly located inside the event horizon. A spacelike singularity forms behind the event horizon, and most of the Hawking radiation ends up at this singularity rather than at infinity. Whether any Hawking radiation reaches infinity depends on the relation between the emission domain and the event horizon. From the outside view, even if radiation is seen as always being emitted, the black hole never evaporates away, rather its mass and entropy asymptote to finite non-zero limits, and the event horizon always acts as a sink for matter and information. From an inside view, the matter and information disappear into the singularity, which is the boundary of spacetime. The argument is based on the nature of the processes at work plus a careful delineation of the relevant causal domains; in order to confirm this model and determine details of the outcome, detailed calculations of the expectation value of the stress-energy-momentum tensor are needed to determine back reaction effects.

Motivation & Objective

• To challenge the prevailing view that astrophysical black holes fully evaporate via Hawking radiation.
• To resolve the black hole information paradox by showing that information is lost at the spacelike singularity rather than at infinity.
• To establish that the event horizon is not the emission locus of Hawking radiation, but rather a causal boundary where radiation is absorbed.
• To propose a new thermodynamic third law for black holes, stating that entropy cannot be reduced to zero by radiation processes.
• To argue that the final state of a black hole is a stable remnant with non-zero mass and entropy, not complete evaporation.

Proposed method

• Analyzes the causal structure of spacetime in spherical symmetry, focusing on the location of the emission domain relative to the event horizon and trapped surfaces.
• Identifies the emission of Hawking radiation as originating from a locally defined, timelike EMOTS (marginally outer trapped surface) rather than the globally defined event horizon.
• Uses the Parikh-Wilczek particle emission model to describe radiation as a local process with energy loss from the EMOTS, not the event horizon.
• Considers backreaction effects on the EMOTS and OMOTS (outermost marginally outer trapped surface), which determine the final mass and event horizon location.
• Applies the stress-energy-momentum tensor expectation value to model radiation backreaction, though full calculation remains to be done.
• Compares two scenarios: 'Bright' (radiation escapes to infinity) and 'Dark' (radiation falls into singularity), with the latter being more plausible due to spacetime geometry.

Experimental results

Research questions

• RQ1 Does Hawking radiation originate from the event horizon or from a locally defined trapped surface?
• RQ2 Can Hawking radiation escape to infinity, or does it predominantly fall into the spacelike singularity?
• RQ3 What determines the final remnant mass of a black hole after radiation emission?
• RQ4 How does the presence of a spacelike singularity affect the information and energy balance in black hole evaporation?
• RQ5 Is the final state of a black hole a stable remnant, or does complete evaporation occur?

Key findings

• Hawking radiation is emitted from a locally defined, timelike EMOTS just outside the trapped surface, not from the globally defined event horizon.
• Most Hawking radiation is directed toward the future spacelike singularity rather than escaping to infinity, due to spacetime curvature and CMB focusing.
• The final remnant mass is given by $ m_{\text{final}} = m_0 - \Delta m_{\text{emit}} $, where $ \Delta m_{\text{emit}} \geq 0 $, and $ m_{\text{final}} > 0 $, implying non-zero mass remains.
• The final state is a spacelike singularity surrounded by an event horizon, with the black hole never fully evaporating.
• The information loss paradox is resolved because information is lost at the singularity, which is causally disconnected from the external universe.
• A new thermodynamic third law is implied: it is impossible to reduce a black hole’s entropy to zero via radiation, as a finite remnant always remains.