Hawking radiation: black hole vs de Sitter

G.E. Volovik

arxiv: 2510.24502 · v6 · submitted 2025-10-28 · 🌀 gr-qc

Hawking radiation: black hole vs de Sitter

G.E. Volovik This is my paper

Pith reviewed 2026-05-18 03:02 UTC · model grok-4.3

classification 🌀 gr-qc

keywords Hawking radiationde Sitter spacetimeGibbons-Hawking entropycosmological horizonlocal thermodynamicsHubble volumehigher dimensions

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The pith

In higher-dimensional de Sitter spacetime the entropy inside the cosmological horizon becomes (d-1)A/8G instead of the usual Gibbons-Hawking value.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper compares how Hawking radiation shapes thermodynamics in black holes versus the de Sitter expansion of the universe. Black holes are compact objects, while de Sitter space is infinite and uniform, so the cosmological horizon creates two separate thermodynamic descriptions: one local and one tied to the horizon. The authors use a local temperature T_dS equal to H over pi, which governs activation processes deep inside the horizon and stays the same regardless of dimension. Integrating the resulting local entropy density over the Hubble volume yields a total entropy S_H of (d-1)A over 8G. This shows that the standard Gibbons-Hawking entropy A over 4G is recovered only when the spacetime has three spatial dimensions.

Core claim

The paper claims that the local de Sitter temperature T_dS = H/π, which is twice the Gibbons-Hawking temperature and independent of dimension d, defines a local entropy density whose integral over the Hubble volume equals S_H = (d-1)A/8G. This modifies the Gibbons-Hawking entropy S_GH = A/4G associated with the cosmological horizon, so the original form remains valid only for d=3.

What carries the argument

The local de Sitter temperature T_dS = H/π, which sets the local entropy density integrated over the Hubble volume to obtain the total entropy.

If this is right

The standard Gibbons-Hawking entropy formula holds only in three spatial dimensions plus time.
De Sitter thermodynamics splits into local processes inside the horizon and horizon-linked contributions.
Local activation events such as atom ionization occur at temperature H/π throughout the Hubble volume.
Hawking radiation produces different thermodynamic effects in an infinite homogeneous state than in a compact black hole.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Higher-dimensional cosmological models may need adjusted entropy accounting for the observable universe region.
The result raises questions about how information is stored when the horizon entropy changes with dimension.
Consistency checks could involve comparing the local temperature prediction against quantum field calculations in curved space of varying dimensions.

Load-bearing premise

The local temperature of de Sitter space equals H over pi, stays the same in every dimension, and can be used to define entropy density inside the horizon.

What would settle it

An explicit calculation of the integrated local entropy in five-dimensional de Sitter space that either matches or fails to match 4A/8G would confirm or refute the proposed modification.

read the original abstract

We discuss the difference between the thermodynamics of black holes and thermodynamics of the de Sitter expansion. Both systems experience the Hawking radiation, but its impact on thermodynamics is different. As distinct from the thermodynamics of black holes, which are finite compact objects, the de Sitter state is the infinite and homogeneous state. The presence of the cosmological horizon provides two sides of the de Sitter thermodynamics: the local thermodynamics and the thermodynamics related to the cosmological horizon. We discuss the connection between these two sides considering the entropy of the Hubble volume in de Sitter spacetime -- the region inside the horizon. On one hand there is the Gibbons-Hawking entropy $S_{\rm GH}=A/4G$ associated with the cosmological horizon. On the other hand this entropy can be obtained by integrating the local entropy density over the Hubble volume. In (3+1) spacetime, these two entropies coincide. This provides physical meaning and a natural explanation to the Gibbons-Hawking entropy -- it is the entropy in the volume $V_H$ bounded by the cosmological horizon. Here we consider whether the Gibbons-Hawking conjecture remains valid for the de Sitter state in general $d+1$ spacetime. To do this, we use the local de Sitter thermodynamics, characterized by a local temperature $T_{\rm dS}=H/\pi$. This temperature is not related to the horizon: it is the temperature of local activation processes, such as the ionization of an atom in the de Sitter environment, which occur deep within the cosmological horizon. This local temperature is universal and does not depend on dimension $d$, it is twice the Gibbons-Hawking temperature $T_{\rm GH}=H/2\pi$. We found that the entropy of the Hubble volume is $S_H=(d-1)A/8G$, which modifies the Gibbons-Hawking entropy of horizon. The original form of the Gibbons-Hawking entropy is valid only for $d=3$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript contrasts Hawking radiation effects in black-hole versus de Sitter thermodynamics. It argues that the entropy of the Hubble volume in (d+1)-dimensional de Sitter spacetime, obtained by integrating a local entropy density defined from the d-independent local temperature T_dS = H/π (twice the Gibbons-Hawking temperature), equals S_H = (d-1)A/8G. This modifies the standard Gibbons-Hawking horizon entropy S_GH = A/4G, which the authors state is valid only for d=3; the volume integral supplies a physical interpretation of the horizon entropy for general d.

Significance. If the central derivation holds, the result supplies a volume-based origin for cosmological-horizon entropy that is consistent with local activation processes inside the horizon and extends the Gibbons-Hawking picture to higher dimensions. It also sharpens the distinction between the thermodynamics of compact black holes and the infinite homogeneous de Sitter state. The approach of defining entropy density from a local temperature rather than surface gravity is a potentially useful alternative route.

major comments (2)

Abstract and the paragraph introducing local de Sitter thermodynamics: the claim that T_dS = H/π is universal and independent of d is load-bearing for obtaining the exact prefactor (d-1) in S_H. Standard surface-gravity calculations give T = H/2π in any dimension; without an explicit derivation or reference showing why the local activation temperature (ionization, etc.) carries no additional d-dependent factors, the volume integral cannot be guaranteed to produce precisely (d-1)A/8G rather than a different d-dependent coefficient.
The integration step that yields S_H = (d-1)A/8G: the abstract states the final formula but does not display the intermediate steps relating the local entropy density s = (energy density)/T_dS to the Hubble volume element in d spatial dimensions. Because the result is sensitive to the precise d-dependence (or lack thereof) of T_dS, the missing algebra prevents verification that the (d-1) factor arises solely from the volume integration.

minor comments (1)

Notation: the manuscript uses both S_GH and S_H; a brief clarifying sentence distinguishing the horizon entropy from the integrated Hubble-volume entropy would help readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report on our manuscript. The comments highlight the need for greater clarity on the local temperature and explicit integration details, which we address below. We have revised the manuscript to incorporate these improvements.

read point-by-point responses

Referee: Abstract and the paragraph introducing local de Sitter thermodynamics: the claim that T_dS = H/π is universal and independent of d is load-bearing for obtaining the exact prefactor (d-1) in S_H. Standard surface-gravity calculations give T = H/2π in any dimension; without an explicit derivation or reference showing why the local activation temperature (ionization, etc.) carries no additional d-dependent factors, the volume integral cannot be guaranteed to produce precisely (d-1)A/8G rather than a different d-dependent coefficient.

Authors: We agree that the d-independence of the local activation temperature T_dS = H/π requires explicit support. This temperature characterizes local processes (e.g., ionization) occurring deep inside the horizon in the approximately flat local geometry, where the de Sitter expansion sets an effective scale leading to a temperature twice the Gibbons-Hawking value. Because the effect is local, no global dimensional factors from the total spacetime dimension d enter at leading order. We will add a short derivation or key references justifying this in the revised manuscript. revision: yes
Referee: The integration step that yields S_H = (d-1)A/8G: the abstract states the final formula but does not display the intermediate steps relating the local entropy density s = (energy density)/T_dS to the Hubble volume element in d spatial dimensions. Because the result is sensitive to the precise d-dependence (or lack thereof) of T_dS, the missing algebra prevents verification that the (d-1) factor arises solely from the volume integration.

Authors: We acknowledge that the intermediate integration steps were insufficiently detailed. With local entropy density s = ρ / T_dS (T_dS d-independent) and the Hubble volume element in d spatial dimensions, the integral over the region bounded by the horizon produces the prefactor (d-1) from the standard relation between d-dimensional volume and (d-1)-dimensional surface area. We will insert the explicit algebra, including the relevant volume integral, into the revised manuscript. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper introduces the local temperature T_dS = H/π as an independent input characterizing local activation processes deep inside the horizon (distinct from horizon thermodynamics), then defines a local entropy density from the thermodynamic relation involving this T_dS and integrates it over the Hubble volume. The resulting S_H = (d-1)A/8G follows from the d-dimensional geometric relation V ~ A/(d H) combined with the d-dependence in the de Sitter energy density; this is a direct calculation, not a reduction of the output to the input by definition or fitting. No self-citation is shown to be load-bearing for the central step, and the volume integration is self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the universality of the local temperature T_dS = H/π across dimensions and on the procedure of integrating local entropy density over the Hubble volume to obtain a total entropy that can be compared with the horizon expression.

free parameters (1)

local temperature prefactor
The coefficient 1/π in T_dS = H/π is introduced to characterize local activation processes independent of the horizon.

axioms (1)

domain assumption Local temperature in de Sitter spacetime is T_dS = H/π and is independent of spacetime dimension d
Invoked when defining the local entropy density that is integrated over the Hubble volume.

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discussion (0)

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We found that the entropy of the Hubble volume is S_H=(d-1)A/8G, which modifies the Gibbons-Hawking entropy of horizon. The original form of the Gibbons-Hawking entropy is valid only for d=3.

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