3 research outputs found
Black Holes in de Sitter Space: Masses, Energies and Entropy Bounds
In this paper we consider spacetimes in vacuum general relativity --possibly
coupled to a scalar field-- with a positive cosmological constant . We
employ the Isolated Horizons (IH) formalism where the boundary conditions
imposed are that of two horizons, one of black hole type and the other, serving
as outer boundary, a cosmological horizon. As particular cases, we consider the
Schwarzschild-de Sitter spacetime, in both 2+1 and 3+1 dimensions. Within the
IH formalism, it is useful to define two different notions of energy for the
cosmological horizon, namely, the "mass" and the "energy". Empty de Sitter
space provides an striking example of such distinction: its horizon energy is
zero but the horizon mass takes a finite value given by .
For both horizons we study their thermodynamic properties, compare our results
with those of Euclidean Hamiltonian methods and construct some generalized
Bekenstein entropy bounds. We discuss these new entropy bounds and compare them
with some recently proposed entropy bounds in the cosmological setting.Comment: 28 pages, 8 figures, revtex4. References added. Version to appear in
PR
Boundary Conditions, Energies and Gravitational Heat in General Relativity (a Classical Analysis)
The variation of the energy for a gravitational system is directly defined
from the Hamiltonian field equations of General Relativity. When the variation
of the energy is written in a covariant form it splits into two (covariant)
contributions: one of them is the Komar energy, while the other is the
so-called covariant ADM correction term. When specific boundary conditions are
analyzed one sees that the Komar energy is related to the gravitational heat
while the ADM correction term plays the role of the Helmholtz free energy.
These properties allow to establish, inside a classical geometric framework, a
formal analogy between gravitation and the laws governing the evolution of a
thermodynamic system. The analogy applies to stationary spacetimes admitting
multiple causal horizons as well as to AdS Taub-bolt solutions.Comment: Latex file, 31 pages; one reference and two comments added, misprints
correcte
Concept of temperature in multi-horizon spacetimes: Analysis of Schwarzschild-De Sitter metric
In case of spacetimes with single horizon, there exist several
well-established procedures for relating the surface gravity of the horizon to
a thermodynamic temperature. Such procedures, however, cannot be extended in a
straightforward manner when a spacetime has multiple horizons. In particular,
it is not clear whether there exists a notion of global temperature
characterizing the multi-horizon spacetimes. We examine the conditions under
which a global temperature can exist for a spacetime with two horizons using
the example of Schwarzschild-De Sitter (SDS) spacetime. We systematically
extend different procedures (like the expectation value of stress tensor,
response of particle detectors, periodicity in the Euclidean time etc.) for
identifying a temperature in the case of spacetimes with single horizon to the
SDS spacetime. This analysis is facilitated by using a global coordinate chart
which covers the entire SDS manifold. We find that all the procedures lead to a
consistent picture characterized by the following features: (a) In general, SDS
spacetime behaves like a non-equilibrium system characterized by two
temperatures. (b) It is not possible to associate a global temperature with SDS
spacetime except when the ratio of the two surface gravities is rational (c)
Even when the ratio of the two surface gravities is rational, the thermal
nature depends on the coordinate chart used. There exists a global coordinate
chart in which there is global equilibrium temperature while there exist other
charts in which SDS behaves as though it has two different temperatures. The
coordinate dependence of the thermal nature is reminiscent of the flat
spacetime in Minkowski and Rindler coordinate charts. The implications are
discussed.Comment: 12 page