3,433 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
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
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
Effective mass suppression upon complete spin-polarization in an isotropic two-dimensional electron system
We measure the effective mass (m*) of interacting two-dimensional electrons
confined to a 4.5 nm-wide AlAs quantum well. The electrons in this well occupy
a single out-of-plane conduction band valley with an isotropic in-plane Fermi
contour. When the electrons are partially spin polarized, m* is larger than its
band value and increases as the density is reduced. However, as the system is
driven to full spin-polarization via the application of a strong parallel
magnetic field, m* is suppressed down to values near or even below the band
mass. Our results are consistent with the previously reported measurements on
wide AlAs quantum wells where the electrons occupy an in-plane valley with an
anisotropic Fermi contour and effective mass, and suggest that the effective
mass suppression upon complete spin polarization is a genuine property of
interacting two-dimensional electrons.Comment: 6 pages, 7 figures, accepted for publication in Phys. Rev.
Holography of Gravitational Action Functionals
Einstein-Hilbert (EH) action can be separated into a bulk and a surface term,
with a specific ("holographic") relationship between the two, so that either
can be used to extract information about the other. The surface term can also
be interpreted as the entropy of the horizon in a wide class of spacetimes.
Since EH action is likely to just the first term in the derivative expansion of
an effective theory, it is interesting to ask whether these features continue
to hold for more general gravitational actions. We provide a comprehensive
analysis of lagrangians of the form L=Q_a^{bcd}R^a_{bcd}, in which Q_a^{bcd} is
a tensor with the symmetries of the curvature tensor, made from metric and
curvature tensor and satisfies the condition \nabla_cQ^{abcd}=0, and show that
they share these features. The Lanczos-Lovelock lagrangians are a subset of
these in which Q^{abcd} is a homogeneous function of the curvature tensor. They
are all holographic, in a specific sense of the term, and -- in all these cases
-- the surface term can be interpreted as the horizon entropy. The
thermodynamics route to gravity, in which the field equations are interpreted
as TdS=dE+pdV, seems to have greater degree of validity than the field
equations of Einstein gravity itself. The results suggest that the holographic
feature of EH action could also serve as a new symmetry principle in
constraining the semiclassical corrections to Einstein gravity. The
implications are discussed.Comment: revtex 4; 17 pages; no figure
511 KeV Photons From Color Superconducting Dark Matter
We discuss the possibility that the recent detection of 511 keV gamma rays
from the galactic bulge, as observed by INTEGRAL, can be naturally explained by
the supermassive very dense droplets (strangelets) of dark matter. These
droplets are assumed to be made of ordinary light quarks (or antiquarks)
condensed in non-hadronic color superconducting phase. The droplets can carry
electrons (or positrons) in the bulk or/and on the surface. The e^+e^-
annihilation events take place due to the collisions of electrons from the
visible matter with positrons from dark matter droplets which may result in the
bright 511 KeV gamma-ray line from the bulge of the Galaxy.Comment: Final version to appear in PRL. Added: estimation of the width, 3Ke
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