Hawking Radiation of Apparent Horizon in a FRW Universe (0809.1554v2)

Abstract: Hawking radiation is an important quantum phenomenon of black hole, which is closely related to the existence of event horizon of black hole. The cosmological event horizon of de Sitter space is also of the Hawking radiation with thermal spectrum. By use of the tunneling approach, we show that there is indeed a Hawking radiation with temperature, $T=1/2\pi \tilde r_A$, for locally defined apparent horizon of a Friedmann-Robertson-Walker universe with any spatial curvature, where $\tilde r_A$ is the apparent horizon radius. Thus we fill in the gap existing in the literature investigating the relation between the first law of thermodynamics and Friedmann equations, there the apparent horizon is assumed to have such a temperature without any proof. In addition, we stress the implication of the Hawking temperature associated with the apparent horizon.

• The paper rigorously demonstrates that the apparent horizon in FRW universes emits Hawking radiation with temperature proportional to the inverse of its radius.
• It adapts the tunneling method and Hamilton-Jacobi equation to establish the radiation, challenging the traditional dependence on static event horizons.
• By linking thermodynamics with Friedmann equations, the study reinforces a thermodynamic interpretation of gravity with implications for quantum cosmology.

Analyzing Hawking Radiation of Apparent Horizons in FRW Universes

The paper "Hawking Radiation of Apparent Horizon in a FRW Universe" by Rong-Gen Cai, Li-Ming Cao, and Ya-Peng Hu fundamentally addresses the appearance of Hawking radiation in Friedmann-Robertson-Walker (FRW) universes, settling a gap in the theoretical framework that links thermodynamics and cosmological dynamics. The researchers rigorously establish that the apparent horizon in such a universe indeed emits Hawking radiation with a temperature, T = 1/˜A, where ˜A represents the apparent horizon radius, through the application of the tunneling method and the Hamilton-Jacobi equation.

Core Contributions

1. Existence of Hawking Radiation and Its Temperature: The authors provide proof that the locally defined apparent horizon of an FRW universe emits Hawking radiation with temperature proportional to the inverse of the apparent horizon radius. This demonstration fills a key gap in the field, as prior work assumed this temperature without rigorous validation.
2. Application of Tunneling Method: By adapting the tunneling framework used for black hole event horizons to the context of a cosmological apparent horizon, the authors show that thermal Hawking-like radiation can occur even without a static event horizon.
3. Link to Quantum Gravity and Thermodynamics: The framework highlights the relationship between gravitational thermodynamics and the dynamics encapsulated by the Friedmann equations. The implication is that the first law of thermodynamics may govern cosmological dynamics via an underlying spacetime equation of state, reinforcing Jacobson's conjecture regarding the Einstein field equation as a thermodynamic identity.
4. Role of the Kodama Vector: The paper underscores the Kodama vector's crucial role in defining conserved quantities and demonstrating the temperature experienced by observers within the apparent horizon. This provides a local analogue to the global killing vector in static spacetimes.

Implications and Theoretical Impacts

• Redefining Event Horizon Dependency: The work challenges the orthodox understanding that Hawking radiation is strictly reliant on the presence of a global event horizon, suggesting that local horizons are sufficient for radiation under certain conditions. This has substantial implications for the conceptualization of quantum gravity.
• Thermodynamic Interpretation of Gravity: By engaging the Clausius relation with entropy and temperature assigned to apparent horizons, the paper further establishes a thermodynamic pathway to derive Friedmann equations, hinting at a more profound thermodynamic structure of gravitation applicable across various gravitation theories, including Gauss-Bonnet and Lovelock gravities.
• Future Directions: This research opens avenues for exploring the impact of horizon dynamics, thermodynamic laws in evolving spacetimes, and potential deviations from perfect thermality when back-reaction effects are considered. Extending these concepts to other gravitational frameworks and higher-dimensional universes could yield further insights into the nature of gravity and quantum processes.

In conclusion, the paper advances our understanding of Hawking radiation beyond black hole physics into cosmological settings, furthering the intersection between thermodynamics and gravitational theories. This exploration not only enhances the current theoretical landscape but also provides a basis for future empirical assessments of cosmological horizons and their quantum properties.