2,595 research outputs found
Thermodynamic Interpretation of Field Equations at Horizon of BTZ Black Hole
A spacetime horizon comprising with a black hole singularity acts like a
boundary of a thermal system associated with the notions of temperature and
entropy. In case of static metric of BTZ black hole, the field equations near
horizon boundary can be expressed as a thermal identity ,
where is the mass of BTZ black hole, is the change in the area of
the black hole horizon when the horizon is displaced infinitesimally small,
is the radial pressure provided by the source of Einstein equations,
is the entropy and is the Hawking temperature
associated with the horizon. This approach is studied further to generalize it
for non-static BTZ black hole and show that it is also possible to interpret
the field equation near horizon as a thermodynamic identity , where is the angular velocity and is the
angular momentum of BTZ black hole. These results indicate that the field
equations for BTZ black hole possess intrinsic thermodynamic properties near
horizon.Comment: 8 page
Random versus holographic fluctuations of the background metric. II. Note on the dark energies arising due to microstructure of space-time
Over the last few years a certain class of dark-energy models decaying
inversely proportional to the square of the horizon distance emerged on the
basis either of Heisenberg uncertainty relations or of the uncertainty relation
between the four-volume and the cosmological constant. The very nature of these
dark energies is understood to be the same, namely it is the energy of
background space/metric fluctuations. Putting together these uncertainty
relations one finds that the model of random fluctuations of the background
metric is favored over the holographic one.Comment: 3 page
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
Quantum cosmology of a classically constrained nonsingular Universe
The quantum cosmological version of a nonsingular Universe presented by
Mukhanov and Brandenberger in the early nineties has been developed and the
Hamilton Jacobi equation has been found under semiclassical (WKB)
approximation. It has been pointed out that, parameterization of classical
trajectories with semiclassical time parameter, for such a classically
constrained system, is a nontrivial task and requires Lagrangian formulation
rather than the Hamiltonian formalism.Comment: 15 page
Dark Energy and Gravity
I review the problem of dark energy focusing on the cosmological constant as
the candidate and discuss its implications for the nature of gravity. Part 1
briefly overviews the currently popular `concordance cosmology' and summarises
the evidence for dark energy. It also provides the observational and
theoretical arguments in favour of the cosmological constant as the candidate
and emphasises why no other approach really solves the conceptual problems
usually attributed to the cosmological constant. Part 2 describes some of the
approaches to understand the nature of the cosmological constant and attempts
to extract the key ingredients which must be present in any viable solution. I
argue that (i)the cosmological constant problem cannot be satisfactorily solved
until gravitational action is made invariant under the shift of the matter
lagrangian by a constant and (ii) this cannot happen if the metric is the
dynamical variable. Hence the cosmological constant problem essentially has to
do with our (mis)understanding of the nature of gravity. Part 3 discusses an
alternative perspective on gravity in which the action is explicitly invariant
under the above transformation. Extremizing this action leads to an equation
determining the background geometry which gives Einstein's theory at the lowest
order with Lanczos-Lovelock type corrections. (Condensed abstract).Comment: Invited Review for a special Gen.Rel.Grav. issue on Dark Energy,
edited by G.F.R.Ellis, R.Maartens and H.Nicolai; revtex; 22 pages; 2 figure
Unification of Dark Matter and Dark Energy in a Modified Entropic Force Model
In Verlinde's entropic force scenario of gravity, Newton's laws and Einstein
equations can be obtained from the first pinciples and general assumptions.
However, the equipartition law of energy is invalid at very low temperatures.
We show clearly that the threshold of the equipartition law of energy is
related with horizon of the universe. Thus, a one-dimension Debye (ODD) model
in the direction of radius of the modified entropic force (MEF) maybe suitable
in description of the accelerated expanding universe. We present a Friedmann
cosmic dynamical model in the ODD-MEF framework. We examine carefully
constraints on the ODD-MEF model from the Union2 compilation of the Supernova
Cosmology Project (SCP) collaboration, the data from the observation of the
large-scale structure (LSS) and the cosmic microwave background (CMB), i.e. SNe
Ia+LSS+CMB. The combined numerical analysis gives the best-fit value of the
model parameters and , with
. The corresponding age of the universe agrees with the
result of D. Spergel {\it et al.}\cite{Spergel2003} at 95% confidence level.
The numerical result also yields an accelerated expanding universe without
invoking any kind of dark energy. Taking as a
running parameter associated with the structure scale , we obtain a possible
unified scenario of the asymptotic flatness of the radial velocity dispersion
of spiral galaxies, the accelerated expanding universe and the Pioneer 10/11
anomaly in the entropic force framework of Verlinde.Comment: 23 pages, 6 figure
Phase transition and scaling behavior of topological charged black holes in Horava-Lifshitz gravity
Gravity can be thought as an emergent phenomenon and it has a nice
"thermodynamic" structure. In this context, it is then possible to study the
thermodynamics without knowing the details of the underlying microscopic
degrees of freedom. Here, based on the ordinary thermodynamics, we investigate
the phase transition of the static, spherically symmetric charged black hole
solution with arbitrary scalar curvature in Ho\v{r}ava-Lifshitz gravity at
the Lifshitz point . The analysis is done using the canonical ensemble
frame work; i.e. the charge is kept fixed. We find (a) for both and
, there is no phase transition, (b) while case exhibits the second
order phase transition within the {\it physical region} of the black hole. The
critical point of second order phase transition is obtained by the divergence
of the heat capacity at constant charge. Near the critical point, we find the
various critical exponents. It is also observed that they satisfy the usual
thermodynamic scaling laws.Comment: Minor corrections, refs. added, to appear in Class. Quant. Grav.
arXiv admin note: text overlap with arXiv:1111.0973 by other author
Cosmology with mirror dark matter I: linear evolution of perturbations
This is the first paper of a series devoted to the study of the cosmological
implications of the parallel mirror world with the same microphysics as the
ordinary one, but having smaller temperature, with a limit set by the BBN
constraints. The difference in temperature of the ordinary and mirror sectors
generates shifts in the key epochs for structure formation, which proceeds in
the mirror sector under different conditions. We consider adiabatic scalar
primordial perturbations as an input and analyze the trends of all the relevant
scales for structure formation (Jeans length and mass, Silk scale, horizon
scale) for both ordinary and mirror sectors, comparing them with the CDM case.
These scales are functions of the fundamental parameters of the theory (the
temperature of the mirror plasma and the amount of mirror baryonic matter), and
in particular they are influenced by the difference between the cosmological
key epochs in the two sectors. Then we used a numerical code to compute the
evolution in linear regime of density perturbations for all the components of a
Mirror Universe: ordinary baryons and photons, mirror baryons and photons, and
possibly cold dark matter. We analyzed the evolution of the perturbations for
different values of mirror temperature and baryonic density, and obtained that
for x=T'/T less than a typical value x_eq, for which the mirror baryon-photon
decoupling happens before the matter-radiation equality, mirror baryons are
equivalent to the CDM for the linear structure formation process. Indeed, the
smaller the value of x, the closer mirror dark matter resembles standard cold
dark matter during the linear regime.Comment: 33 pages, 24 figures; minor corrections in introduction, conclusions
and references; accepted for publication in IJMP
Thermodynamic structure of Lanczos-Lovelock field equations from near-horizon symmetries
It is well known that, for a wide class of spacetimes with horizons, Einstein
equations near the horizon can be written as a thermodynamic identity. It is
also known that the Einstein tensor acquires a highly symmetric form near
static, as well as stationary, horizons. We show that, for generic static
spacetimes, this highly symmetric form of the Einstein tensor leads quite
naturally and generically to the interpretation of the near-horizon field
equations as a thermodynamic identity. We further extend this result to generic
static spacetimes in Lanczos-Lovelock gravity, and show that the near-horizon
field equations again represent a thermodynamic identity in all these models.
These results confirm the conjecture that this thermodynamic perspective of
gravity extends far beyond Einstein's theory.Comment: RevTeX 4; 10 pages; no figure
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