The Physics of De Sitter Black Hole Heat Capacity

In summary: However, since T+ is already greater than T++, the increase in T+ is not as large as the increase in T++. Therefore, the black hole's horizon radius, which is determined by T+, will shrink while the cosmological horizon's radius, which is determined by T++, will increase. This results in a net flux of energy from the black hole to the cosmological horizon.
  • #1
PeteSampras
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2
I am reading the paper https://arxiv.org/pdf/0801.4591.pdf ,

says "Fortunately, the fact that the heat capacity of the cosmological horizon be positive permits to foresee the evolution of the space in absence of any external source. Taking the correct signs for the temperatures one can notice that, for a given value of M, T+ > T++. Therefore, during their interaction due to its positive heat capacity the cosmological horizon would increase its temperature, and so its radius. Conversely, the black hole horizon would become even hotter because of its negative heat capacity and shrink. In this way, there should be a net flux of energy from the black hole horizon into cosmological horizon. "

where T+, and T++ are the temperature of the black hole and cosmological horizon, respectively.

Why the fact that T+>T++ and C++>0 implies that the cosmological horizon radii increase?, and
Why the fact that T+>T++ and C+<0 implies that the black hole horizon radii shrink?,

I think in a scheme as the figure.

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  • #2
PeteSampras said:
Why the fact that T+>T++ and C++>0 implies that the cosmological horizon radii increase?

The cosmological horizon radius increases if its temperature increases because C++> 0. That has nothing to do with the relative temperatures of the two horizons.

PeteSampras said:
Why the fact that T+>T++ and C+<0 implies that the black hole horizon radii shrink?

The black hole's horizon radius shrinks if its temperature increases because C+<0. That has nothing to do with the relative temperature of the two horizons.

The only role that T+>T++ plays in the logic is to make heat flow from the black hole to the cosmological horizon. It plays no role in determining how the radius of each horizon changes.
 
  • #3
PeterDonis said:
The cosmological horizon radius increases if its temperature increases because C++> 0.

PeterDonis said:
The black hole's horizon radius shrinks if its temperature increases because C+<0.

To expand on this a bit: we have a situation in which T+ > T++, which means heat flows from the black hole to the cosmological horizon. That means the heat flow into the cosmological horizon, which I'll call Q++, is positive. Then the fact that C++ is also positive means that T++ increases.

Also, the heat flow into the black hole, which I'll call Q+, is negative, because heat is flowing out of the black hole. Then the fact that C+ is also negative means that T+ increases.
 

1. What is a De Sitter black hole?

A De Sitter black hole is a theoretical type of black hole that is characterized by its mass and angular momentum. It is a solution to Einstein's field equations of general relativity and is described by a de Sitter space-time, which is a type of space-time with a positive cosmological constant. In simpler terms, it is a type of black hole that exists in a universe with a positive curvature.

2. What is the heat capacity of a De Sitter black hole?

The heat capacity of a De Sitter black hole is a measure of how much the black hole's temperature changes when its mass changes. It is an important quantity in understanding the thermodynamics of black holes and is related to the stability of the black hole. In general, the heat capacity of a De Sitter black hole is positive, meaning that it can gain or lose energy without undergoing a phase transition.

3. How is the heat capacity of a De Sitter black hole calculated?

The heat capacity of a De Sitter black hole can be calculated using the first law of black hole thermodynamics, which states that the change in the black hole's mass is equal to the change in its internal energy plus the work done on the black hole. The heat capacity is then defined as the ratio of the change in the black hole's internal energy to the change in its temperature.

4. What is the significance of the heat capacity in the study of black holes?

The heat capacity is an important quantity in the study of black holes because it provides insights into the thermodynamic properties and stability of the black hole. A positive heat capacity indicates that the black hole is thermodynamically stable, while a negative heat capacity indicates that it is unstable and can undergo a phase transition. The heat capacity also plays a role in the Hawking radiation process, which is the emission of particles from a black hole due to quantum effects.

5. Are there any real-world implications of the physics of De Sitter black hole heat capacity?

While De Sitter black holes are currently only theoretical objects, the study of their heat capacity has implications for our understanding of the thermodynamics of black holes in general. This can have applications in fields such as astrophysics and cosmology, where black holes play a significant role. Additionally, the study of black hole thermodynamics is also important in the search for a unified theory of physics, as it combines ideas from general relativity and quantum mechanics.

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