Ideal Gas in a strong Gravitational field: Area dependence of Entropy
arXiv:1012.5421 · doi:10.1103/PhysRevD.83.064034
Abstract
We study the thermodynamic parameters like entropy, energy etc. of a box of gas made up of indistinguishable particles when the box is kept in various static background spacetimes having a horizon. We compute the thermodynamic variables using both statistical mechanics as well as by solving the hydrodynamical equations for the system. When the box is far away from the horizon, the entropy of the gas depends on the volume of the box except for small corrections due to background geometry. As the box is moved closer to the horizon with one (leading) edge of the box at about Planck length (L_p) away from the horizon, the entropy shows an area dependence rather than a volume dependence. More precisely, it depends on a small volume A*L_p/2 of the box, upto an order O(L_p/K)^2 where A is the transverse area of the box and K is the (proper) longitudinal size of the box related to the distance between leading and trailing edge in the vertical direction (i.e in the direction of the gravitational field). Thus the contribution to the entropy comes from only a fraction O(L_p/K) of the matter degrees of freedom and the rest are suppressed when the box approaches the horizon. Near the horizon all the thermodynamical quantities behave as though the box of gas has a volume A*L_p/2 and is kept in a Minkowski spacetime. These effects are: (i) purely kinematic in their origin and are independent of the spacetime curvature (in the sense that Rindler approximation of the metric near the horizon can reproduce the results) and (ii) observer dependent. When the equilibrium temperature of the gas is taken to be equal to the the horizon temperature, we get the familiar A/L_p^2 dependence in the expression for entropy. All these results hold in a D+1 dimensional spherically symmetric spacetime.
arXiv comment19 pages, added some discussion, matches published version
References in corpus (14)
- Black Hole Entropy is Noether Charge
- Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
- Thermodynamical Aspects of Gravity: New insights
- Equipartition of energy in the horizon degrees of freedom and the emergence of gravity
- Duality and zero-point length of spacetime
- Lessons from Classical Gravity about the Quantum Structure of Spacetime
- Near-Thermal Radiation in Detectors, Mirrors and Black Holes: A Stochastic Approach
- Quantum structure of spacetime and blackhole entropy
- Event horizon - Magnifying glass for Planck length physics
- An Operational Approach To Black Hole Entropy
- Response of Unruh-DeWitt detector with time-dependent acceleration
- Area scaling entropies for gravitating systems
- Finite entanglement entropy from the zero-point-area of spacetime
- Classical relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated reference frame
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