Temperature of black holes
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Black Hole Temperature: Hawking Temperature and Mass Dependence
The temperature of a black hole is most famously described by the Hawking temperature, which is inversely proportional to the mass of the black hole. This means that smaller black holes are hotter, while larger ones are cooler. Some research suggests that the internal temperature of a black hole increases during its formation due to heat generated by collapsing matter, and that the black hole maintains structural stability when its thermal energy density matches its mass-energy density. This approach leads to a version of the Hawking temperature formula where the black hole mass is replaced by the geometric mean of the black hole mass and the Planck mass, supporting the idea that black holes are hot, not cold . Other studies also discuss the equilibrium temperature of black holes, considering factors like blue-shifted cosmic background microwaves and high temperature limits at the Planck energy level .
Local and Observer-Dependent Black Hole Temperatures
The temperature experienced near a black hole can depend on the observer's position and motion. For example, the local temperature for observers in free fall outside a static black hole remains finite at the event horizon and matches the Hawking temperature at spatial infinity. In contrast, freely falling observers outside certain black holes, such as those in Anti-de Sitter (AdS) space, do not detect high-temperature thermal radiation even if the Hawking temperature is very high . For dynamical black holes, a local Hawking temperature can be defined using the surface gravity at the horizon, and this temperature is what would be measured by observers just outside the horizon. However, this local temperature diverges at the horizon itself, while the temperature measured at infinity is redshifted and generally lower .
Black Holes with Multiple Horizons and Multi-Black-Hole Systems
In black holes with multiple horizons, such as rotating and charged black holes, each horizon contributes to the overall Hawking temperature. For a four-dimensional rotating and charged black hole, the effective Hawking temperature depends only on its mass, similar to a Schwarzschild black hole. However, for other types, like the rotating BTZ black hole, the temperature also depends on angular momentum . In systems with multiple black holes, an average temperature can be defined using the surface gravities and horizon areas of all the black holes in the system, ensuring consistency with thermodynamic laws .
Quantum Effects, Negative Temperatures, and Stability
Quantum effects introduce new perspectives on black hole temperature. The concept of negative temperature, unique to quantum systems, has been proposed for black holes, suggesting that event horizons might create conditions for negative-temperature systems inside black holes, potentially leading to quantum-based outward pressure . Additionally, non-extensive statistical mechanics applied to black holes shows that there is a minimum temperature at a certain mass, and large black holes can be thermodynamically stable, which contrasts with the traditional view that all black holes are unstable .
Effective and Modified Black Hole Temperatures
The radiation spectrum of black holes is not strictly thermal, and this leads to the introduction of an effective temperature that accounts for quantum corrections. This effective temperature modifies the understanding of black hole entropy, area quantization, and the number of microstates, making them functions of quantum numbers . For regular black holes, the temperature of the event horizon can be determined using thermodynamic laws and quantum gravity approaches, further refining our understanding of black hole thermodynamics .
Conclusion
The temperature of black holes is a complex topic influenced by mass, observer position, quantum effects, and the presence of multiple horizons or black holes. While the Hawking temperature remains a central concept, ongoing research continues to refine and expand our understanding, revealing that black holes can be hot, observer-dependent, and even exhibit quantum behaviors such as negative temperatures and stability at large masses Seshavatharam2014Brynjolfsson2008Ram'irez-Valdez2021+7 MORE.
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