14 research outputs found
Structure of Lanczos-Lovelock Lagrangians in Critical Dimensions
The Lanczos-Lovelock models of gravity constitute the most general theories
of gravity in D dimensions which satisfy (a) the principle of of equivalence,
(b) the principle of general co-variance, and (c) have field equations
involving derivatives of the metric tensor only up to second order. The mth
order Lanczos-Lovelock Lagrangian is a polynomial of degree m in the curvature
tensor. The field equations resulting from it become trivial in the critical
dimension and the action itself can be written as the integral of an
exterior derivative of an expression involving the vierbeins, in the
differential form language. While these results are well known, there is some
controversy in the literature as to whether the Lanczos-Lovelock Lagrangian
itself can be expressed as a total divergence of quantities built only from the
metric and its derivatives (without using the vierbeins) in . We settle
this issue by showing that this is indeed possible and provide an algorithm for
its construction. In particular, we demonstrate that, in two dimensions, for a doublet of functions which
depends only on the metric and its first derivatives. We explicitly construct
families of such R^j -s in two dimensions. We also address related questions
regarding the Gauss-Bonnet Lagrangian in . Finally, we demonstrate the
relation between the Chern-Simons form and the mth order Lanczos-Lovelock
Lagrangian.Comment: 15 pages, no figure
Entropy increase during physical processes for black holes in Lanczos-Lovelock gravity
We study quasi-stationary physical process for black holes within the context
of Lanczos-Lovelock gravity. We show that the Wald entropy of stationary black
holes in Lanczos-Lovelock gravity monotonically increases for quasi-stationary
physical processes in which the horizon is perturbed by the accretion of
positive energy matter and the black hole ultimately settles down to a
stationary state. This result reinforces the physical interpretation of Wald
entropy for Lanczos-Lovelock models and takes a step towards proving the
analogue of the black hole area increase-theorem in a wider class of
gravitational theories.Comment: 5 pages, no figur
Membrane Paradigm and Horizon Thermodynamics in Lanczos-Lovelock gravity
We study the membrane paradigm for horizons in Lanczos-Lovelock models of
gravity in arbitrary D dimensions and find compact expressions for the pressure
p and viscosity coefficients \eta and \zeta of the membrane fluid. We show that
the membrane pressure is intimately connected with the Noether charge entropy
S_Wald of the horizon when we consider a specific m-th order Lanczos-Lovelock
model, through the relation pA/T=(D-2m)/(D-2)S_Wald, where T is the temperature
and A is the area of the horizon. Similarly, the viscosity coefficients are
expressible in terms of entropy and quasi-local energy associated with the
horizons. The bulk and shear viscosity coefficients are found to obey the
relation \zeta=-2(D-3)/(D-2)\eta.Comment: v1: 13 pages, no figure. (v2): refs added, typos corrected, new
subsection added on the ratio \eta/s. (v3): some clarification added, typos
corrected, to appear in JHE
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
Conservative entropic forces
Entropic forces have recently attracted considerable attention as ways to
reformulate, retrodict, and perhaps even "explain'" classical Newtonian gravity
from a rather specific thermodynamic perspective. In this article I point out
that if one wishes to reformulate classical Newtonian gravity in terms of an
entropic force, then the fact that Newtonian gravity is described by a
conservative force places significant constraints on the form of the entropy
and temperature functions. (These constraints also apply to entropic
reinterpretations of electromagnetism, and indeed to any conservative force
derivable from a potential.)
The constraints I will establish are sufficient to present real and
significant problems for any reasonable variant of Verlinde's entropic gravity
proposal, though for technical reasons the constraints established herein do
not directly impact on either Jacobson's or Padmanabhan's versions of entropic
gravity. In an attempt to resolve these issues, I will extend the usual notion
of entropic force to multiple heat baths with multiple "temperatures'" and
multiple "entropies".Comment: V1: 21 pages; no figures. V2: now 24 pages. Two new sections (reduced
mass formulation, decoherence). Many small clarifying comments added
throughout the text. Several references added. V3: Three more references
added. V4: now 25 pages. Some extra discussion on the relation between
Verlinde's scenario and the Jacobson and Padmanabhan scenarios. This version
accepted for publication in JHE
Condensation of an ideal gas with intermediate statistics on the horizon
We consider a boson gas on the stretched horizon of the Schwartzschild and
Kerr black holes. It is shown that the gas is in a Bose-Einstein condensed
state with the Hawking temperature if the particle number of the
system be equal to the number of quantum bits of space-time N \simeq
{A}/{{\l_{p}}^{2}}. Entropy of the gas is proportional to the area of the
horizon by construction. For a more realistic model of quantum degrees of
freedom on the horizon, we should presumably consider interacting bosons
(gravitons). An ideal gas with intermediate statistics could be considered as
an effective theory for interacting bosons. This analysis shows that we may
obtain a correct entropy just by a suitable choice of parameter in the
intermediate statistics.Comment: 12 pages, added new sections related to an ideal gas with
intermediate statistic