Hawking radiation: black hole vs de Sitter
Volovik G.E.

Received: February 17, 2026

DOI: 10.31857/S0044451026110022

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We discuss the difference between the thermodynamics of black holes and the 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_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_dS=H/π . 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_GH=H/2π . We found that the entropy of the Hubble volume is S_H=(d-1)A/8G, which modifies the Gibbons-Hawking entropy of the horizon. The original form of the Gibbons-Hawking entropy is valid only for d=3. Keywords: de Sitter thermodynamics, cosmological horizon, Hawking radiation, Gibbons-Hawking entropy, local temperature, holography Contribution for the JETP special issue dedicated to black hole physics (Hawking black hole evaporation)