3,614 research outputs found
Noether Current, Horizon Virasoro Algebra and Entropy
We provide a simple and straightforward procedure for defining a Virasoro
algebra based on the diffeomorphisms near a null surface in a spacetime and
obtain the entropy density of the null surface from its central charge. We use
the off-shell Noether current corresponding to the diffeomorphism invariance of
a gravitational Lagrangian and define the Virasoro algebra
from its variation. This allows us to identify the central charge and the zero
mode eigenvalue using which we obtain the entropy density of the Killing
horizon. Our approach works for all Lanczos-Lovelock models and reproduces the
correct Wald entropy. The entire analysis is done off-shell without using the
field equations and allows us to define an entropy density for any null surface
which acts as a local Rindler horizon for a particular class of observers.Comment: V2: to appear in Phys. Rev.
Gravity: A New Holographic Perspective
A general paradigm for describing classical (and semiclassical) gravity is
presented. This approach brings to the centre-stage a holographic relationship
between the bulk and surface terms in a general class of action functionals and
provides a deeper insight into several aspects of classical gravity which have
no explanation in the conventional approach. After highlighting a series of
unresolved issues in the conventional approach to gravity, I show that (i)
principle of equivalence, (ii) general covariance and (iii)a reasonable
condition on the variation of the action functional, suggest a generic
Lagrangian for semiclassical gravity of the form with
. The expansion of in terms of the
derivatives of the metric tensor determines the structure of the theory
uniquely. The zeroth order term gives the Einstein-Hilbert action and the first
order correction is given by the Gauss-Bonnet action. Any such Lagrangian can
be decomposed into a surface and bulk terms which are related holographically.
The equations of motion can be obtained purely from a surface term in the
gravity sector. Hence the field equations are invariant under the
transformation and gravity does not
respond to the changes in the bulk vacuum energy density. The cosmological
constant arises as an integration constant in this approach. The implications
are discussed.Comment: Plenary talk at the International Conference on Einstein's Legacy in
the New Millennium, December 15 - 22, 2005, Puri, India; to appear in the
Proceedings to be published in IJMPD; 16 pages; no figure
Combining general relativity and quantum theory: points of conflict and contact
The issues related to bringing together the principles of general relativity
and quantum theory are discussed. After briefly summarising the points of
conflict between the two formalisms I focus on four specific themes in which
some contact has been established in the past between GR and quantum field
theory: (i) The role of planck length in the microstructure of spacetime (ii)
The role of quantum effects in cosmology and origin of the universe (iii) The
thermodynamics of spacetimes with horizons and especially the concept of
entropy related to spacetime geometry (iv) The problem of the cosmological
constant.Comment: Invited Talk at "The Early Universe and Cosmological Observations: a
Critical Review", UCT, Cape Town, 23-25 July,2001; to appear in
Class.Quan.Gra
A new perspective on Gravity and the dynamics of Spacetime
The Einstein-Hilbert action has a bulk term and a surface term (which arises
from integrating a four divergence). I show that one can obtain Einstein's
equations from the surface term alone. This leads to: (i) a novel, completely
self contained, perspective on gravity and (ii) a concrete mathematical
framework in which the description of spacetime dynamics by Einstein's
equations is similar to the description of a continuum solid in the
thermodynamic limit.Comment: Based on the Essay selected for Honorable Mention in the Gravity
Research Foundation Essay Contest, 2005; to appear in the special issue of
IJMP
Surface Density of Spacetime Degrees of Freedom from Equipartition Law in theories of Gravity
I show that the principle of equipartition, applied to area elements of a
surface which are in equilibrium at the local Davies-Unruh temperature, allows
one to determine the surface number density of the microscopic spacetime
degrees of freedom in any diffeomorphism invariant theory of gravity. The
entropy associated with these degrees of freedom matches with the Wald entropy
for the theory. This result also allows one to attribute an entropy density to
the spacetime in a natural manner. The field equations of the theory can then
be obtained by extremising this entropy. Moreover, when the microscopic degrees
of freedom are in local thermal equilibrium, the spacetime entropy of a bulk
region resides on its boundary.Comment: v1: 20 pages; no figures. v2: Sec 4 added; 23 page
Vacuum Fluctuations of Energy Density can lead to the observed Cosmological Constant
The energy density associated with Planck length is while the energy density associated with the Hubble length is
where . The observed value of the dark
energy density is quite different from {\it either} of these and is close to
the geometric mean of the two: .
It is argued that classical gravity is actually a probe of the vacuum {\it
fluctuations} of energy density, rather than the energy density itself. While
the globally defined ground state, being an eigenstate of Hamiltonian, will not
have any fluctuations, the ground state energy in the finite region of space
bounded by the cosmic horizon will exhibit fluctuations . When used as a source of gravity, this should
lead to a spacetime with a horizon size . This bootstrapping condition
leads naturally to an effective dark energy density which is precisely the observed value. The model
requires, either (i) a stochastic fluctuations of vacuum energy which is
correlated over about a Hubble time or (ii) a semi- anthropic interpretation.
The implications are discussed.Comment: r pages; revtex; comments welcom
Self-similar collapse and the structure of dark matter halos: A fluid approach
We explore the dynamical restrictions on the structure of dark matter halos
through a study of cosmological self-similar gravitational collapse solutions.
A fluid approach to the collisionless dynamics of dark matter is developed and
the resulting closed set of moment equations are solved numerically including
the effect of halo velocity dispersions (both radial and tangential), for a
range of spherically averaged initial density profiles. Our results highlight
the importance of tangential velocity dispersions to obtain density profiles
shallower than in the core regions, and for retaining a memory of the
initial density profile, in self-similar collapse. For an isotropic core
velocity dispersion only a partial memory of the initial density profile is
retained. If tangential velocity dispersions in the core are constrained to be
less than the radial dispersion, a cuspy core density profile shallower than
cannot obtain, in self-similar collapse.Comment: 25 pages, 7 figures, submitted to Ap
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
Why Does Gravity Ignore the Vacuum Energy?
The equations of motion for matter fields are invariant under the shift of
the matter lagrangian by a constant. Such a shift changes the energy momentum
tensor of matter by T^a_b --> T^a_b +\rho \delta^a_b. In the conventional
approach, gravity breaks this symmetry and the gravitational field equations
are not invariant under such a shift of the energy momentum tensor. I argue
that until this symmetry is restored, one cannot obtain a satisfactory solution
to the cosmological constant problem. I describe an alternative perspective to
gravity in which the gravitational field equations are [G_{ab} -\kappa T_{ab}]
n^an^b =0 for all null vectors n^a. This is obviously invariant under the
change T^a_b --> T^a_b +\rho \delta^a_b and restores the symmetry under
shifting the matter lagrangian by a constant. These equations are equivalent to
G_{ab} = \kappa T_{ab} + Cg_{ab} where C is now an integration constant so that
the role of the cosmological constant is very different in this approach. The
cosmological constant now arises as an integration constant, somewhat like the
mass M in the Schwarzschild metric, the value of which can be chosen depending
on the physical context. These equations can be obtained from a variational
principle which uses the null surfaces of spacetime as local Rindler horizons
and can be given a thermodynamic interpretation. This approach turns out to be
quite general and can encompass even the higher order corrections to Einstein's
gravity and suggests a principle to determine the form of these corrections in
a systematic manner.Comment: Invited Contribution to the IJMPD Special Issue on Dark Matter and
Dark Energy edited by D.Ahluwalia and D. Grumiller. Appendix clarifies
several conceptual and pedgogical aspects of surface term in Hilbert action;
ver.2: references and some clarifications adde
Event horizon - Magnifying glass for Planck length physics
An attempt is made to describe the `thermodynamics' of semiclassical
spacetime without specifying the detailed `molecular structure' of the quantum
spacetime, using the known properties of blackholes. I give detailed arguments,
essentially based on the behaviour of quantum systems near the event horizon,
which suggest that event horizon acts as a magnifying glass to probe Planck
length physics even in those contexts in which the spacetime curvature is
arbitrarily low. The quantum state describing a blackhole, in any microscopic
description of spacetime, has to possess certain universal form of density of
states which can be ascertained from general considerations. Since a blackhole
can be formed from the collapse of any physical system with a low energy
Hamiltonian H, it is suggested that when such a system collapses to form a
blackhole, it should be described by a modified Hamiltonian of the form
where .I also show
that it is possible to construct several physical systems which have the
blackhole density of states and hence will be indistinguishable from a
blackhole as far as thermodynamic interactions are concerned. In particular,
blackholes can be thought of as one-particle excitations of a class of {\it
nonlocal} field theories with the thermodynamics of blackholes arising
essentially from the asymptotic form of the dispersion relation satisfied by
these excitations. These field theoretic models have correlation functions with
a universal short distance behaviour, which translates into the generic
behaviour of semiclassical blackholes. Several implications of this paradigm
are discussed
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