11 research outputs found
Information Geometry on the Space of Equilibrium States of Black Holes in Higher Derivative Theories
We study the information-geometric properties of the Deser-Sarioglu-Tekin
black hole, which is a higher derivative gravity solution with contributions
from a non-polynomial term of the Weyl tensor to the Einstein-Hilbert
Lagrangian. Our investigation is focused on deriving the relevant information
metrics and their scalar curvatures on the space of equilibrium states. The
analysis is conducted within the framework of thermodynamic information
geometry and shows highly non-trivial statistical behavior. Furthermore, the
quasilocal formalism, developed by Brown and York, was successfully implemented
in order to derive the mass of the Deser-Sarioglu-Tekin black hole.Comment: 18 pages, 2 figure
Sum of Three Cubes via Optimisation
By first solving the equation with fixed for and then
considering the distance to the nearest integer function of the result, we turn
the sum of three cubes problem into an optimisation one. We then apply three
stochastic optimisation algorithms to this function in the case with ,
where there are many known solutions. The goal is to test the effectiveness of
the method in searching for integer solutions. The algorithms are a
modification of particle swarm optimisation and two implementations of
simulated annealing. We want to compare their effectiveness as measured by the
running times of the algorithms. To this end, we model the time data by
assuming two underlying probability distributions -- exponential and
log-normal, and calculate some numerical characteristics for them. Finally, we
evaluate the statistical distinguishability of our models with respect to the
geodesic distance in the manifold with the corresponding Fisher information
metric.Comment: 21 pages without the appendices. Any comments will be greatly
appreciated
Entanglement of higher-derivative oscillators in holographic systems
We study the quantum entanglement of coupled Pais-Uhlenbeck oscillators using
the formalism of thermo-field dynamics. The entanglement entropy is computed
for the specific cases of two and a ring of coupled Pais-Uhlenbeck
oscillators of fourth order. It is shown that the entanglement entropy depends
on the temperatures, frequencies and coupling parameters of the different
degrees of freedom corresponding to harmonic oscillators. We also make remarks
on the appearance of instabilities of higher-derivative oscillators in the
context of AdS/CFT correspondence. Finally, we advert to the information
geometry theory by calculating the Fisher information metric for the considered
system of coupled oscillators.Comment: 20 pages, 1 figure; v2: new section added highlighting the appearance
of higher-derivative oscillators in holographic systems; v3: an additional
example of holographic system added and title change
Observational signatures of strongly naked singularities: image of the thin accretion disk
We study the optical appearance of a thin accretion disk around the strongly
naked static Janis-Newman-Winicour singularity. The solution does not possess a
photon sphere, which results in the formation of a complex structure of bright
rings in the central region of the disk image. Such structure is absent in the
case of the Schwarzschild black hole with a thin accretion disk, where instead
of the image we observe the black hole shadow. Some of the rings emit with the
maximal observable radiation flux from the accretion disk, and should be
experimentally detectable. Thus, this qualitatively new feature can be used to
distinguish observationally black holes from naked singularities. We elucidate
the appearance of the ring structure by revealing the physical mechanism of its
formation, and explaining the nature of each of the ring images. We make the
conjecture that a similar structure would also appear for other solutions
without a photon sphere and it can serve as a general observational signature
for distinguishing compact objects possessing no photon sphere from black
holes.Comment: 30 page
Numerical Solution of Maxwell Equations for S-Wave Superconductors
The present paper is a sequel to the paper by Karchev (Condensed Matter 20 February 2017). We report the numerical solutions of the system of equations, which describes the electrodynamics of s-wave superconductors without normal quasi-particles for time-independent fields and half-plane superconductor geometry. The results are: (i) the applied magnetic field increases the Ginzburg–Landau (GL) coherence length and suppresses the superconductivity; (ii) the applied electric field decreases GL coherence length and supports the superconductivity; (iii) if the applied magnetic field is fixed and the applied electric field increases, the London penetration depth of the magnetic field decreases. The main conclusion is that by applying electric field at very low temperature where there are no normal quasi-particles one increases the critical magnetic field. This result is experimentally testable
Image of the thin accretion disk around compact objects in the Einstein-Gauss-Bonnet gravity
We study the optical appearance of a thin accretion disk around compact
objects within the Einstein-Gauss-Bonnet gravity. Considering static
spherically symmetric black holes and naked singularities we search for
characteristic signatures which can arise in the observable images due to the
modification of general relativity. While the images of the Gauss-Bonnet black
holes closely resemble the Schwarzschild black hole, naked singularities
possess a distinctive feature. A series of bright rings are formed in the
central part of the images with observable radiation times larger than
the rest of the flux making them observationally significant. We elucidate the
physical mechanism, which causes the appearance of the central rings, showing
that the image is determined by the light ring structure of the spacetime. In a
certain region of the parametric space the Gauss-Bonnet naked singularities
possess a stable and an unstable light ring. In addition the gravitational
field becomes repulsive in a certain neighbourhood of the singularity. This
combination of features leads to the formation of the central rings implying
that the effect is not specific for the Einstein-Gauss-Bonnet gravity but would
also appear for any other compact object with the same characteristics of the
photon dynamics.Comment: 16 pages, 8 figure