195 research outputs found
A Quantal Tolman Temperature
The conventional Tolman temperature based on the assumption of the traceless
condition of energy-momentum tensor for matter fields is infinite at the
horizon if Hawking radiation is involved. However, we note that the temperature
associated with Hawking radiation is of relevance to the trace anomaly, which
means that the traceless condition should be released. So, a trace
anomaly-induced Stefan-Boltzmann law is newly derived by employing the first
law of thermodynamics and the property of the temperature independence of the
trace anomaly. Then, the Tolman temperature is quantum-mechanically generalized
according to the anomaly-induced Stefan-Boltzmann law. In an exactly soluble
model, we show that the Tolman factor does not appear in the generalized Tolman
temperature which is eventually finite everywhere, in particular, vanishing at
the horizon. It turns out that the equivalence principle survives at the
horizon with the help of the quantum principle, and some puzzles related to the
Tolman temperature are also resolved.Comment: 5 pages, 1 figure, version to appear in EPJ
Entropy and temperatures of Nariai black hole
The statistical entropy of the Nariai black hole in a thermal equilibrium is
calculated by using the brick-wall method. Even if the temperature depends on
the choice of the time-like Killing vector, the entropy can be written by the
ordinary area law which agrees with the Wald entropy. We discuss some physical
consequences of this result and the properties of the temperatures.Comment: 12 pages, no figur
The role of the cosmological constant as a pressure in the (2+1)-dimensional black string
It has been claimed that the cosmological constant in AdS black holes such as
the BTZ black hole plays the role of the thermodynamic variable of a pressure
in the thermodynamic first law and the Smarr relation from the scaling law of
the Christodoulou-Ruffini formula. However, the dual solution of the BTZ black
hole is the black string which is asymptotically flat despite the presence of
the cosmological constant, and so the explicit form of the pressure with the
role of the cosmological constant is unclear in the black string since the
pressure is subject to the choice of the energy-momentum tensor. Thus, we show
that if the pressure of the black string is still assumed to be proportional to
the cosmological constant similar to the case of the BTZ black hole, then the
thermodynamic first law is consistent with the Smarr relation from the
Christodoulou-Ruffini formula, and the thermodynamic quantities for the
pressure are well-behaved under the dual transformation.Comment: 15 pages, version to appear in PL
Proper temperature of Schwarzschild AdS black hole revisited
The Unruh temperature calculated from the global embedding of the
Schwarzschild AdS spacetime into Minkowski spacetime was identified with the
local temperature measured by a free-fall observer; however, it would be
imaginary in a certain region outside the event horizon. So, the temperature
was assumed to be zero of no thermal radiation for that region. In this paper,
we revisit this issue in the exactly soluble two-dimensional Schwarzschild AdS
black hole and present an alternative resolution to this problem by using the
Tolman's procedure. However, the process is not straightforward in the sense
that one should extend the original procedure to rest upon the traceless
energy-momentum tensor in such a way that it could encompass the case of the
non-vanishing trace of energy-momentum tensor in the presence of the trace
anomaly. Consequently, we show that the free-fall temperature turns out to be
real everywhere outside the event horizon without any imaginary value, in
particular, it vanishes both at the horizon and at the asymptotic infinity.Comment: 12 pages, 1 figure, version published in PL
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