761 research outputs found
Conservation laws for self-adjoint first order evolution equations
In this work we consider the problem on group classification and conservation
laws of the general first order evolution equations. We obtain the subclasses
of these general equations which are quasi-self-adjoint and self-adjoint. By
using the recent Ibragimov's Theorem on conservation laws, we establish the
conservation laws of the equations admiting self-adjoint equations. We
illustrate our results applying them to the inviscid Burgers' equation. In
particular an infinite number of new symmetries of these equations are found
and their corresponding conservation laws are established.Comment: This manuscript has been accepted for publication in Journal of
Nonlinear Mathematical Physic
Accretion Processes for General Spherically Symmetric Compact Objects
We investigate the accretion process for different spherically symmetric
space-time geometries for a static fluid. We analyse this procedure using the
most general black hole metric ansatz. After that, we examine the accretion
process for specific spherically symmetric metrics obtaining the velocity of
the sound during the process and the critical speed of the flow of the fluid
around the black hole. In addition, we study the behaviour of the rate of
change of the mass for each chosen metric for a barotropic fluid.Comment: 10 pages, 15 figures, v2 accepted for publication in 'European
Physical Journal C
Fast Scramblers Of Small Size
We investigate various geometrical aspects of the notion of `optical depth'
in the thermal atmosphere of black hole horizons. Optical depth has been
proposed as a measure of fast-crambling times in such black hole systems, and
the associated optical metric suggests that classical chaos plays a leading
role in the actual scrambling mechanism. We study the behavior of the optical
depth with the size of the system and find that AdS/CFT phase transitions with
topology change occur naturally as the scrambler becomes smaller than its
thermal length. In the context of detailed AdS/CFT models based on D-branes,
T-duality implies that small scramblers are described in terms of matrix
quantum mechanics.Comment: 14 pages, 3 figures. Added reference
Higher Dimensional Cylindrical or Kasner Type Electrovacuum Solutions
We consider a D dimensional Kasner type diagonal spacetime where metric
functions depend only on a single coordinate and electromagnetic field shares
the symmetries of spacetime. These solutions can describe static cylindrical or
cosmological Einstein-Maxwell vacuum spacetimes. We mainly focus on
electrovacuum solutions and four different types of solutions are obtained in
which one of them has no four dimensional counterpart. We also consider the
properties of the general solution corresponding to the exterior field of a
charged line mass and discuss its several properties. Although it resembles the
same form with four dimensional one, there is a difference on the range of the
solutions for fixed signs of the parameters. General magnetic field vacuum
solution are also briefly discussed, which reduces to Bonnor-Melvin magnetic
universe for a special choice of the parameters. The Kasner forms of the
general solution are also presented for the cylindrical or cosmological cases.Comment: 16 pages, Revtex. Text and references are extended, Published versio
Fast Scramblers, Horizons and Expander Graphs
We propose that local quantum systems defined on expander graphs provide a
simple microscopic model for thermalization on quantum horizons. Such systems
are automatically fast scramblers and are motivated from the membrane paradigm
by a conformal transformation to the so-called optical metric.Comment: 22 pages, 2 figures. Added further discussion in section 3. Added
reference
Surfaces away from horizons are not thermodynamic
Since the 1970s, it has been known that black-hole (and other) horizons are truly thermodynamic. More generally, surfaces which are not horizons have also been conjectured to behave thermodynamically. Initially, for surfaces microscopically expanded from a horizon to so-called stretched horizons, and more recently, for more general ordinary surfaces in the emergent gravity program. To test these conjectures we ask whether such surfaces satisfy an analogue to the first law of thermodynamics (as do horizons). For static asymptotically flat spacetimes we find that such a first law holds on horizons. We prove that this law remains an excellent approximation for stretched horizons, but counter-intuitively this result illustrates the insufficiency of the laws of black-hole mechanics alone from implying truly thermodynamic behavior. For surfaces away from horizons in the emergent gravity program the first law fails (except for spherically symmetric scenarios), thus undermining the key thermodynamic assumption of this program
From the Bloch sphere to phase space representations with the Gottesman-Kitaev-Preskill encoding
In this work, we study the Wigner phase-space representation of qubit states
encoded in continuous variables (CV) by using the Gottesman-Kitaev-Preskill
(GKP) mapping. We explore a possible connection between resources for universal
quantum computation in discrete-variable (DV) systems, i.e. non-stabilizer
states, and negativity of the Wigner function in CV architectures, which is a
necessary requirement for quantum advantage. In particular, we show that the
lowest Wigner logarithmic negativity of qubit states encoded in CV with the GKP
mapping corresponds to encoded stabilizer states, while the maximum negativity
is associated with the most non-stabilizer states, H-type and T-type quantum
states.Comment: (v1) Accepted for publication in the Springer's "Mathematics for
Industry" series. (v2) Typo in the abstract fixed; URL of the conference
where the paper has been presented added: International Symposium on
Mathematics, Quantum Theory, and Cryptography (MQC), held in September 2019
in Fukuoka, Japan (https://www.mqc2019.org/mqc2019/program
Logarithmic Corrections to Schwarzschild and Other Non-extremal Black Hole Entropy in Different Dimensions
Euclidean gravity method has been successful in computing logarithmic
corrections to extremal black hole entropy in terms of low energy data, and
gives results in perfect agreement with the microscopic results in string
theory. Motivated by this success we apply Euclidean gravity to compute
logarithmic corrections to the entropy of various non-extremal black holes in
different dimensions, taking special care of integration over the zero modes
and keeping track of the ensemble in which the computation is done. These
results provide strong constraint on any ultraviolet completion of the theory
if the latter is able to give an independent computation of the entropy of
non-extremal black holes from microscopic description. For Schwarzschild black
holes in four space-time dimensions the macroscopic result seems to disagree
with the existing result in loop quantum gravity.Comment: LaTeX, 40 pages; corrected small typos and added reference
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