Abstract
It is well known that the black hole can have temperature and radiate the particles with black body spectrum, i.e. Hawking radiation. Therefore, if the black hole is surrounded by an isolated box, there is a thermal equilibrium between the black hole and radiation gas. A simple case considering the thermal equilibrium between the Schwarzschild black hole and radiation gas in an isolated box has been well investigated previously in detail, i.e. taking the conservation of energy and principle of maximal entropy for the isolated system into account. In this paper, following the above spirit, the effects of massive graviton on the thermal equilibrium will be investigated. For the gravity with massive graviton, we will use the de Rham–Gabadadze–Tolley (dRGT) massive gravity which has been proven to be ghost free. Because the graviton mass depends on two parameters in the dRGT massive gravity, here we just investigate two simple cases related to the two parameters, respectively. Our results show that in the first case the massive graviton can suppress or increase the condensation of black hole in the radiation gas although the T–E diagram is similar as the Schwarzschild black hole case. For the second case, a new T–E diagram has been obtained. Moreover, an interesting and important prediction is that the condensation of black hole just increases from the zero radius of horizon in this case, which is very different from the Schwarzschild black hole case.
Highlights
Among the studies on the black hole physics, a significant progress is the discovery that the black hole can have temperature and radiate the particles with black body spectrum, i.e. Hawking radiation [1]
After considering the conservation of energy and principle of maximal entropy for the isolated system, we have investigated the effects of massive graviton on the equilibrium
We mainly investigate the effects from massive graviton on the equilibrium between the black hole and radiation gas in an isolated box
Summary
Among the studies on the black hole physics, a significant progress is the discovery that the black hole can have temperature and radiate the particles with black body spectrum, i.e. Hawking radiation [1]. We will use the dRGT massive gravity to investigate the effect of massive graviton on the equilibrium between the black hole and thermal radiation gas in an isolated box. The black hole will become bigger, and the isolated system will reach the stable configuration state, i.e., the temperature of condensed black hole is equal to the temperature of radiation gas Note that, during this non-equilibrium process, this isolated system with fixed volume V will keep the same total energy. Since the graviton is massive, the condensed black hole among the radiation gas is usually not the Schwarzschild black hole, which should be considered under the massive gravity theory. Using the conservation of energy and principle of maximal entropy for an isolated system, we will investigate the equilibrium between the Schwarzschild-like black hole and radiation gas in an isolated box. The T –E diagram is similar as the Schwarzschild case in the first case, while it is different in the second case
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