20 research outputs found
Holography in Action
Einstein-Hilbert action and its natural generalizations to higher dimensions
(like the Lanczos-Lovelock action) have certain peculiar features. All of them
can be separated into a bulk and a surface term, with a specific
("holographic") relationship between the two, so that either term can be used
to extract information about the other. Further, the surface term leads to
entropy of the horizons on-shell. It has been argued in the past that these
features are impossible to understand in the conventional approach but find a
natural explanation if we consider gravity as an emergent phenomenon. We
provide further support for this point of view in this paper. We describe an
alternative decomposition of the Einstein-Hilbert action and Lanczos-Lovelock
action into a new pair of surface and bulk terms, such that the surface term
becomes Wald entropy on a horizon and the bulk term is the energy density
(which is the ADM Hamiltonian density for Einstein gravity). We show that this
new pair also obeys a holographic relationship and give a thermodynamic
interpretation to this relation in this context. Since the bulk and surface
terms, in this decomposition, are related to energy and entropy, the
holographic condition can be thought of as analogous to inverting the
expression for entropy given as a function of energy S = S(E,V) to obtain the
energy E = E(S,V) in terms of the entropy in a normal thermodynamic system.
Thus the holographic nature of the action allows us to relate the descriptions
of the same system in terms of two different thermodynamic potentials. Some
further possible generalizations and implications are discussed.Comment: 12 page
Drift, Drag and Brownian motion in the Davies-Unruh bath
An interesting feature of the Davies-Unruh effect is that an uniformly
accelerated observer sees an isotropic thermal spectrum of particles even
though there is a preferred direction in this context, determined by the
direction of the acceleration g. We investigate the thermal fluctuations in the
Unruh bath by studying the Brownian motion of particles in the bath, especially
as regards to isotropy. We find that the thermal fluctuations are anisotropic
and induce different frictional drag forces on the Brownian particle depending
on whether it has a drift velocity along the direction of acceleration g or in
a direction transverse to it. Using the fluctuation-dissipation theorem, we
argue that this anisotropy arises due to quantum correlations in the
fluctuations at large correlation time scales.Comment: v1: 5 pages, no figures, v2: some discussion added, matches published
versio
Mean field dynamo action in renovating shearing flows
We study mean field dynamo action in renovating flows with finite and non
zero correlation time () in the presence of shear. Previous results
obtained when shear was absent are generalized to the case with shear. The
question of whether the mean magnetic field can grow in the presence of shear
and non helical turbulence, as seen in numerical simulations, is examined. We
show in a general manner that, if the motions are strictly non helical, then
such mean field dynamo action is not possible. This result is not limited to
low (fluid or magnetic) Reynolds numbers nor does it use any closure
approximation; it only assumes that the flow renovates itself after each time
interval . Specifying to a particular form of the renovating flow with
helicity, we recover the standard dispersion relation of the
dynamo, in the small or large wavelength limit. Thus mean fields grow
even in the presence of rapidly growing fluctuations, surprisingly, in a manner
predicted by the standard quasilinear closure, even though such a closure is
not strictly justified. Our work also suggests the possibility of obtaining
mean field dynamo growth in the presence of helicity fluctuations, although
having a coherent helicity will be more efficient.Comment: 16 pages, 1 figur
Two Aspects of Black hole entropy in Lanczos-Lovelock models of gravity
We consider two specific approaches to evaluate the black hole entropy which
are known to produce correct results in the case of Einstein's theory and
generalize them to Lanczos-Lovelock models. In the first approach (which could
be called extrinsic) we use a procedure motivated by earlier work by Pretorius,
Vollick and Israel, and by Oppenheim, and evaluate the entropy of a
configuration of densely packed gravitating shells on the verge of forming a
black hole in Lanczos-Lovelock theories of gravity. We find that this matter
entropy is not equal to (it is less than) Wald entropy, except in the case of
Einstein theory, where they are equal. The matter entropy is proportional to
the Wald entropy if we consider a specific m-th order Lanczos-Lovelock model,
with the proportionality constant depending on the spacetime dimensions D and
the order m of the Lanczos-Lovelock theory as (D-2m)/(D-2). Since the
proportionality constant depends on m, the proportionality between matter
entropy and Wald entropy breaks down when we consider a sum of Lanczos-Lovelock
actions involving different m. In the second approach (which could be called
intrinsic) we generalize a procedure, previously introduced by Padmanabhan in
the context of GR, to study off-shell entropy of a class of metrics with
horizon using a path integral method. We consider the Euclidean action of
Lanczos-Lovelock models for a class of metrics off-shell and interpret it as a
partition function. We show that in the case of spherically symmetric metrics,
one can interpret the Euclidean action as the free energy and read off both the
entropy and energy of a black hole spacetime. Surprisingly enough, this leads
to exactly the Wald entropy and the energy of the spacetime in Lanczos-Lovelock
models obtained by other methods. We comment on possible implications of the
result.Comment: v1: 20 pages, no figures v2: added some discussion, to appear in
Phys. Rev.
Black hole shadow and acceleration bounds for spherically symmetric spacetimes
We explore an interesting connection between black hole shadow parameters and
the acceleration bounds for radial linear uniformly accelerated (LUA)
trajectories in static spherically symmetric black hole spacetime geometries of
the Schwarzschild type. For an incoming radial LUA trajectory to escape back to
infinity, there exists a bound on its magnitude of acceleration and the
distance of closest approach from the event horizon of the black hole. We
calculate these bounds and the shadow parameters, namely the photon sphere
radius and the shadow radius, explicitly for specific black hole solutions in
-dimensional Einstein's theory of gravity, in pure Lovelock theory of
gravity and in the theory of gravity. We find that for a
particular boundary data, the photon sphere radius is equal to the
bound on radius of closest approach of the incoming radial LUA trajectory
while the shadow radius is equal to the inverse magnitude of the
acceleration bound for the LUA trajectory to turn back to infinity.
Using the effective potential technique, we further show that the same
relations are valid in any theory of gravity for static spherically symmetric
black hole geometries of the Schwarzschild type. Investigating the trajectories
in a more general class of static spherically symmetric black hole spacetimes,
we find that the two relations are valid separately for two different choices
of boundary data.Comment: 27 pages, no figures, new section added, Accepted for publication in
PR
Action principle for the fluid-gravity correspondence and emergent gravity
It has been known for a long time that Einstein’s field equations when projected onto a black hole horizon look very similar to a Navier-Stokes equation in suitable variables. More recently, it was shown that the projection of Einstein’s equation onto any null surface in any spacetime reduces exactly to the Navier-Stokes form when viewed in the freely falling frame. We develop an action principle, the extremization of which leads to the above result, in an arbitrary spacetime. The degrees of freedom varied in the action principle are the null vectors in the spacetime and not the metric tensor. The same action principle was introduced earlier in the context of the emergent gravity paradigm wherein it was shown that the corresponding Lagrangian can be interpreted as the entropy density of spacetime. The current analysis strengthens this interpretation and reinforces the idea that field equations in gravity can be thought of as emergent. We also find that the degrees of freedom on the null surface are equivalent to a fluid with equation of state PA=TS. We demonstrate that the same relation arises in the context of a spherical shell collapsing to form a horizon