Astronomy & Astrophysics

Astronomy & Astrophysics

  • Nainan Varghese added an answer:
    What is the charge of a black hole?
    What the charge of a black hole?
    Neutral? I hope not.
    Anyone know of any articles in this area?
    Nainan Varghese

    You may know certain properties of Electric charge. But, what is electric charge? See:

    Except for its excessive matter-content, a black hole is like any other macro body. It has no mysterious properties. See:

    Electric charges are related to electric fields rather than to macro bodies, which produce electric fields.


  • Nainan Varghese added an answer:
    How can I calculate the Earth's orbit, or what is the equation that enable us know its velocity vs. position at given time?


    Nainan Varghese

    Current planetary laws were derived from relative positions of sun and few planets. Hence, they can be used to predict their relative positions only. True orbital paths of planets are different from elliptical/circular paths described in text books. Please see:


  • Daniel Pfenniger added an answer:
    Can anyone help me with a question about neutrinos?

    I recently read a paper saying that, apart from those coming from stars, supenovae, cosmic rays and nuclear power plants, the majority of all the neutrinos in our universe were created at the big bang. But, considering that neutrinos are very elusive particles, that they travel almost at the speed of light and in straight lines, I think they all should be now near the boundary of the universe.

    How come that we can observe them? Is my reasoning above not right?

    Daniel Pfenniger

    Cosmologists keep saying the neutrino background has temperature T=1.9K while actually they want to say that their energy corresponds to kT, with k Boltzmann's constant.  This habit comes from the time neutrinos were commonly assumed to be massless.  In that case, like for photons, energy can be assimilated to a temperature because if they would thermalize with a thermometer a temperature T would be measured.

    But since neutrinos are massive, nowadays a substantial part of their energy is in their rest mass c^2.  A thermometer only measures the random kinetic energy part.  The  temperature that would be measured  if a huge thermometer would be brought to thermal equilibrium with the the neutrino background would be rather in the 0.001K range (depending on their still uncertain actual mass).

  • Dmitri Martila added an answer:
    Could some of the fundamental constants be functions of the gravitational potential?

    Based on several assumptions to deduce a cosmological model with three fundamental constants including the speed of light in vacuum, the Planck constant, and the gravitational constant, along with the dimensionless electroweak coupling constant turned into functions of the gravitational potential. Initial research of this model has indicated solutions to avoid the singularity in both special relativity and general relativity.

    • Source
      [Show abstract] [Hide abstract]
      ABSTRACT: Based on several assumptions to deduce a cosmological model with three fundamental constants along with the dimensionless electroweak coupling constant turned into functions of the gravitational potential. Initial research of this model has indicated solutions to avoid the singularity in both special relativity and general relativity.
      Full-text · Article · Jul 2014
    Dmitri Martila

    The varying Gravitational Constant needs the Dark Matter to satisfy the General Relativity, in the manner described in my book:

  • Dmitri Martila added an answer:
    Does inflating a Planck-scale wormhole to macroscopic size add internal space and "transit capacity", or do its internal measurements remain tiny?

    What does it actually mean when we talk about “inflating” a wormhole? If we find a Planck-scale natural wormhole, and we cram exotic matter into its two mouths to stretch it up to, say, one metre wide, then the wormhole may nominally now be a metre across … but have we actually added any additional useful space to the throat interior, or have we taken a throat that only has a fixed amount of internal space and "stretched" that fixed space, so that although it's now nominally one metre across, the internal measurement (and the wormhole's “capacity” as measured with internal rulers) might still be Planck-scale?

    Would inflation be adding more space and more useful “transit capacity” to the wormhole throat, or would we still have the original Planck-scale throat, inhabiting a distorted and stretched region of space in which everything is rescaled and magnified?

    Dmitri Martila

    Dear Baird, let solve your question  mathematically. The Ellis Wormhole is

    ds^2 = -dt^2 + dr^2/(1-m^2/r^2) + r^2 (d\theta^2+sin^2\theta d\phi^2). (1) The rescaled one (factor is n=const) has interval dS = ds/n, thus the metric

    dS^2 = (-dt^2 + dr^2/(1-m^2/r^2) + r^2 (d\theta^2+sin^2\theta d\phi^2))/n^2. (2)

    Hereby to preserve the shape of the motion of test particles, one has to write m = M n, because coordinate transformation  R= r/n, T=t/n then produces the original form of the metric dS^2 = -dT^2 + dR^2/(1-M^2/R^2) + R^2 (d\theta^2+sin^2\theta d\phi^2). (3) It is the metric in rescaled coordinates. Has it more matter than the original metric? Not, because the radius of the rescaled "throat" is R = M = m/n. Which is less, then original throat. So the making wormhole smaller means the removing of "exotic matter" (that shows the integral of T^t_t).

    Therefore, to inflate the Planck wormhole one requires the "exotic matter". Therefore the inflated and not inflated wormholes are not equivalent.

    However, the Schwarzschild Wormhole ds^2 = -dt^2 + dr^2/(1-2m/r) + r^2 (d\theta^2+sin^2\theta d\phi^2) has T^t_t = 0. So indeed, the size of the throat is not directly linked to the amount of exotic matter for such wormhole (4) and your theory may hold. However, I have the book (look my profile), which tells, that hypothetical "exotic matter" is not matter.

  • Biplob Sarkar added an answer:
    Are jets in AGNs or X-ray binaries leptonic e- - e+, or they can they be also baryonic?

    In the literature we find that relativistic e- - e+ jets are not possible. For truly relativistic jests, we need to have e- - p pairs.

    Biplob Sarkar

    Thanks Bothun and Rajiv for your answers.

  • John Wyndham added an answer:
    Has the important astronomical event, supernova 1054 in constellation Taurus, played any role in the discovery of pulsars?
    I know that the development of radio astronomy was the most crucial step in the discovery, but still I am convinced that the supernova 1054 may have had some inspiring role in the discovery of pulsars.
    John Wyndham

    About myself:

    I have not worked in the field of Radio Astronomy since leaving Caltech in 1967.

    My purpose in joining ResearchGate was to feature my recent researches into the Science of 9/11.  A paper presented at the 2014 IEEE International Conference on Ethics in Science, Engineering etc (May 23-26, 2014, Chicago) is awaiting publication in the IEEE proceedings for this conference. The title of the paper is "Ethics and the Official Reports about the Destruction of the World Trade Center Twin Towers (WTC1 and WTC2) on 9/11: A Case Study" by John D. Wyndham, Wayne H. Coste, and Michael R. Smith.

  • Navtej Singh added an answer:
    Which of the following is better at plotting 3D graphs, Vectors and Contours, for astrophysical systems, Matlab, Surfer, SuperMongo or Gnuplot?

    It would be helpful if the explanations are given for 3 categories:

    1. Beginners using GUI

    2. Wannabes using both GUI and TUI

    3. Experts using TUI

    Navtej Singh

    If you go the python way then another excellent library for scientific 3D plotting and visualization is Mayavi from Enthought.

    It can be installed as part of Enthought's Canopy IDE, which is free for academic use.

  • Ken Schatten added an answer:
    How can you get the temperature of a sunspot?

    Hello, im working on a research regarding the correlation of the magnetic flux and different sunspot properties. And so far, there is no archive that has the data I need, is there an archive you could recommend that has the temperature for all sunspots which appeared from 2000-2005? or any equation that can give an approximation of a sunspot's temperature? 

    Ken Schatten

    To me , the interesting thing is the Energy flux in sunspots, and how it radiates, and

    the various energy transport mechanisms into and out of, the Sunspot..

    I think the sigma T^4 formula is not bad for just trying to get some idea of a rough

    temperature.. As Roger says, of course, there are complexitites involving the complex matter of light flowing into the sunspot, and all the "lines" in the atmosphere inside the spot, so , it is a very complex problem... To me, one can get totally overwhelmed by the complexity of nature, so perhaps some simple flat bottom to the sunspot, and a kind of chromospheric atmosphere above it, in a plane parallel approximation would do

    well, to make some kind of associattion of temperature and radiated flux, etc...

    There are many interesting variations, i think, in sunspots, as to whether they are growing, or shrinking too. as well as the various complexities as to whether one can view them as a bunch of field lines that inhibit the radiation into the spot, and that is why they are cold (Biermann), or that the convective energy transport and the downflows below the spot cool it, by taking neutral hydrogen from the photosphere to cool the energy transport into the spot... The dynamical approach is one that Gene Parker developed, and the equivalent "ion hurricane" approach one that i and my colleague Hans Mayr used in a simple analogy with our terrestrial atmospheric  situation... 

    Anyway, they give us various questions to ponder that allow distractions from Earth.

  • Igor Piskarev added an answer:
    Is there a reasonable alternative to the theory of the expanding universe?
    We know that our star, the Sun loses about 10^-14 of its mass per year as a result of electromagnetic radiation and particle emission. That reduction in mass should show up as a decreasing gravitational red shift. Same thing should happen to entire galaxies. But isn't it true that the galaxies we observe that are farther from Earth are also the younger we see (because light has taken millions of years more to come to us) and, as a consequence the more massive when we consider entire galaxies? (Because we cannot possibly see them as they are, but as they were millions of years ago.) Shouldn't we expect, correspondingly that the gravitational red shift of an observed galaxy will increase with its distance to Earth?
    Igor Piskarev

    Red shift may be not Doppler's red shift at all, but absorbtion im matter, as vacuum is relict radiation (some kind of matter)

  • R. Teixeira added an answer:
    What is currently the most accurate star catalogue to use for astrometric purposes?
    There are many star catalogues available, which star catalogue is currently the most accurate (maybe the USNO CCD Astrograph Catalog, UCAC4)?
    R. Teixeira

    In Ducourant et al. 2014 we have looked for the consensual proper motion and was just this that allows us to obtain a convergence in our trace back and so the kinematic age. 

  • Daniel Baldomir added an answer:
    Why are there no stable states with more than three or less than two quarks?

    It is known that hadrons can be divided in baryons (fermions of three quarks) and mesons (bosons of two quarks). The sum of their electric charge is always an integer number, e.g. the proton is one and the neutron is zero. What is the reason that we have not found one particle with, say, five or seven quarks?

    Daniel Baldomir


    Thank you very much for your answer and sorry for my delay in responding. The application to cosmology is not obvious at all, but it seems that in the first moments previous to the hadron formation, around 10^(-35) seconds, i.e. in the inflationary age, it seems that the implications of having so massive particles could change the application of theorems as the of Borde-Vilenkin-Guth for singularities. I know that this far of my original question but it could help to understand a little better hypothesis as the dark matter, what do you think about?

  • Edgars Alksnis added an answer:
    How are the space and time related to biocentrism?
    Robert Lanza’s Biocentrism Theory
    Edgars Alksnis

    Space is as per Descartes/Newton; with time is a bit more complicated- but, believe, not in Your case.

  • G. Bothun added an answer:
    How is the tagging of photons from astronomical sources, done?

    How are the photons from different astronomical sources, which lie in the same solid angle from an observer, emitting in the same energy (i.e frequency or wavelength) region, tagged as coming from different sources? Does the Doppler shift play a vital role here? Or other techniques come in handy?

    G. Bothun

    If you just have fluxes through bandpass filters, the separation is difficult and model dependent as discussed.  If you can do integrated spectroscopy (often difficult) over the solid angle in question, you an do much better at resolving the individual components of the emission.

  • Russell Jurek added an answer:
    What is the limiting magnitude for detecting a galaxy in the SDSS image?

    See above

    Russell Jurek

    It's complicated by the fact that SDSS uses "luptitudes", instead of standard Pogson magnitudes. SDSS Luptitudes are designed to asymptote to fixed magnitude values. This avoids the weird magnitudes that you would otherwise get when you integrate noise.

  • Viacheslav Zgonnik added an answer:
    Looking for an advise on nebulae (molecular clouds, globules, protoplanetary disks)?

    Our group of geochemists, geologists and chemists is looking for a astrophysicists or astronomer who will be interested to participate in our research. We discovered the correlation between ionization potential of elements and their abundance in planets and other bodies. This correlation could be explained by a simple termochemical equation. Predictions by this equation correlate impressively well with observed chemical composition of surface of planets. We propose a theoretical process which could explain observed facts. Details of our work are described in this document
    We are looking for a person who could help us (in collaboration way) to improve and connect our theoretical model with observations of nebulae.

    Viacheslav Zgonnik

    It is correct. In our work we tested it on new data from space probes then interpreted the observed correlation as a Boltzmann distribution depending on the distance from the Sun. We tested our model on factual data for Moon, Mars, Venus and Meteorites. We find that predictions force of the model is excellent. Then, we made surface-to-volume analysis for elements. We find periodical trends, related with affinity of elements to hydrogen and with their mass. This suggests that radial differentiation of elements inside the planet was chemically- and gravity-driven. We have far more interesting results, which are out of scope of this paper.

  • Joseph L Alvarez added an answer:
    Radiation can lose energy by collisions with other particles. Does all radiation tend to end up being infrared radiation?
    The loss of energy results in an increase in wavelength for radiation. If the time this progress takes is infinitely long, could all radiation (gamma, x, UV, etc.) finish with a larger wavelength.
    Joseph L Alvarez

    Your question depends upon infinitely long. How and when we introduce infinity changes the results of a calculation. The result is a paradox if infinity is not properly introduced. A popular concept of entropy is that the entropy of a system increases. A closed, insulated system has constant entropy. When is it proper to introduce infinity in a closed system? Is the universe a closed system?

    Suppose we begin with the most intense gamma ray burst attainable. The gamma rays will lose energy with each interaction with matter or other photons (except for some exceptions noted in other answers). Nevertheless, if this gamma ray burst occurred at the beginning of the universe, at the current age of the universe, we still have a probability that some of the initial gammas have not interacted. Is this a case of improper use of infinity, even if the probability is ridiculously small?

    All the photons from the initial burst will have lost energy until some final gasp when that energy is absorbed in some process. We can say that the energy of the photons goes asymptotically to zero. So the answer to your question is that the photons degrade until they quietly absorb. That is the effect of carrying the equations to infinity.

    If the universe is a closed system and the entropy does not increase, do we require continuous bursts of intense gamma rays? Will the universe finally degrade to the average with a small distribution in energy? I do not believe there is an equation that will answer these questions, but there is an equation that says a burst of gamma rays will asymptotically degrade to zero.

  • Josep M. Trigo-Rodríguez added an answer:
    What is the source of neutral sodium in comets?

    Various authors have suggested sources in the dust tail, near the nucleus, in the plasma tail or some combination of all three (that might even turn off and on depending on what comet you are looking at at what time).

    Josep M. Trigo-Rodríguez

    The two previous readings suggested are excellent as they review nicely our knowledge on Na in comets. Let me point out that if the general scenario of comet formation is correct we should expect the accretion of significant amounts of Na in these bodies, perhaps in neutral form forming part of the interstitial matrix (also in ices?). Its presence could fit our detected overabundance of Na in cometary meteoroids that could be consequence of extensive Na depletion of the inner disk during the early solar system stage. See e.g. our paper:

  • Akira Kanda added an answer:
    Can accelerated expansion of galaxies be explained as an expanding wave?

    In PNAS, August 25, 2009 edition, Blake and Smoller argued that perhaps the standard terminologies of dark energy and cosmological constant are not required for explaining the accelerated expansion of galaxies. According to them, the key to solve that puzzle is to find expanding wave solutions of the Einstein's equations.

    So do you think it is possible to use expanding wave solutions of the Einstein's equations to solve accelerated expansion of galaxies? Your comments are welcome.

    + 1 more attachment

  • Victor Christianto added an answer:
    Do Einstein's equations correspond to solutions of Klein-Fock-Gordon equation?

    I read somewhere that Einstein's equations may be expressed in terms of Klein-Fock-Gordon equation, but i am not sure yet how to do that.

    In a paper, Fiziev and Shirkov discuss solutions of Klein-Fock-Gordon equation and its implications to Einstein's equations. In effect, this may imply that Einstein's equations have wave-type solutions.

    What do you think? Your comments are welcome.

    Victor Christianto

    Thank you Stam, for your answer. Best wishes

  • Issam Sinjab added an answer:
    What is the origin of the magnetic field of a neutron star?
    After surpassing electron degeneracy and supported by quantum degeneracy pressure, these kind of stars are composed mainly by neutrons, particles without electic charge. They posses nevertheless very strong magnetic fields. So, if they are composed mainly from electrically neutral particles, what is the origin of their strong magnetic fields?
    Issam Sinjab

    Dear Marek Wojciech Gutowski 

    Sorry for my late reply as I am on holiday and I should explain better my earlier post and point out some of the difficulties that come with the conservation of magnetic flux assumption especially in connection with magnetars.

    You asked:

    "Where from did you get "the conservation of magnetic flux"? "

    Well, it was first suggested by Manchester & Taylor (1977) and by Smith (1977). See for example:

    Manchester, R. N., & Taylor, J. H. 1997, Pulsars (San Francisco: Freeman, W.H. & Company).

    Also, please refer to Jeremy Heyl's post dated Dec 4 2012:

    "The electrical conductivity is very high so that over the timescale of the collapse of the star the magnetic field lines cannot move far relative to the collapsing plasma, so the magnetic flux threading the core is conserved Flux ~ B R^2 so as R decreases the field increases."

    There are however serious problems with this assumption as we shall see below.

    A large value of the magnetic field near the neutron star's surface is customarily assumed to be associated with magnetic flux conservation during gravitational collapse, also called fossil field hypothesis. The simplest and most popular hypothesis, magnetic flux conservation, is that neutron stars magnetic fields are simple remnants of their main sequence (MS) progenitors. For a star of radius R and surface magnetic field strength B, Conservation of magnetic flux in gravitational collapse require the magnetic flux BR^2=constant. Consider a star of  B=100G and R=7x 10^8 m. If a star of this surface magnetic field strength and radius collapsed to a neutron star of radius R(ns)=10 km, it would have a surface magnetic field of B(ns) equal to about 10^11 G. Admittedly, this is unrealistically optimistic estimate because the neutron star contains only some 15% of the progenitor's mass! The other major problem of course, as you rightly indicated, is that the magnetic field strength 10^11 G is at least 1-4 orders of magnitude weaker to explain magnetars with magnetic field strengths 10^12-10^15 G. The fossil hypothesis is therefore not an attractive one, at least not for magnetars.

    One could argue that some MS stars have much higher fields, the strongest fields known in MS stars are around 10^4 G. Magnetic flux conservation during gravitational collapse of these stars would imply  B(ns) equal to about 10^13. Not only is this still insufficient for magnetar but there is also a problem of statistics. Only a very small fraction of progenitors has magnetic fields as large as 10^4 G. Magnetars, on the other hand, are born frequently. Their birth rate is probably comparable to that of normal neutron stars-Woods(2008).

    One other serious problem of the magnetic flux conservation is that not only the neutron star contains only some 15% of the progenitor's mass but also the core of a typical progenitor MS star occupy only some 2-3% of the star's cross section!

    Here's a research paper that attempts to explain the phenomena using an approach for induced magnetic moments in neutron superfluids:

    The Physics of Strong Magnetic Fields in Neutron Stars:

  • Jesús Varela López added an answer:
    Is anyone interested in the full data release of the ALHAMBRA data?
    The ALHAMBRA survey ( has just published its 1st full data release.
    You can find the the data (catalogs with photo-z and synthetic F814W images) through the following links:
    * web server:
    * FTP server:
    * Spanish Virtual Observatory:
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      [Show abstract] [Hide abstract]
      ABSTRACT: The Advance Large Homogeneous Area Medium-Band Redshift Astronomical (ALHAMBRA) survey has observed eight different regions of the sky, including sections of the Cosmic Evolution Survey (COSMOS), DEEP2, European Large-Area Infrared Space Observatory Survey (ELAIS), Great Observatories Origins Deep Survey North (GOODS-N), Sloan Digital Sky Survey (SDSS) and Groth fields using a new photometric system with 20 optical, contiguous ∼300-Å filters plus the JHKs bands. The filter system is designed to optimize the effective photometric redshift depth of the survey, while having enough wavelength resolution for the identification of faint emission lines. The observations, carried out with the Calar Alto 3.5-m telescope using the wide-field optical camera Large Area Imager for Calar Alto (LAICA) and the near-infrared (NIR) instrument Omega-2000, represent a total of ∼700 h of on-target science images. Here we present multicolour point-spread function (PSF) corrected photometry and photometric redshifts for ∼438 000 galaxies, detected in synthetic F814W images. The catalogues are complete down to a magnitude I ∼ 24.5 AB and cover an effective area of 2.79 deg2. Photometric zero-points were calibrated using stellar transformation equations and refined internally, using a new technique based on the highly robust photometric redshifts measured for emission-line galaxies. We calculate Bayesian photometric redshifts with the Bayesian Photometric Redshift (bpz)2.0 code, obtaining a precision of δz/(1 + zs) = 1 per cent for I < 22.5 and δz/(1 + zs) = 1.4 per cent for 22.5 < I < 24.5. The global n(z) distribution shows a mean redshift 〈z〉 = 0.56 for I < 22.5 AB and 〈z〉 = 0.86 for I < 24.5 AB. Given its depth and small cosmic variance, ALHAMBRA is a unique data set for galaxy evolution studies.
      Full-text · Article · Jun 2013 · Monthly Notices of the Royal Astronomical Society
    Jesús Varela López

    Hi Somak,

      the description of the data in the catalogues can be found in Molino et al.(2014) paper:

      If you have doubts about the content of the catalogues, I would suggest to contact directly the first author (Dr. Alberto Molino).

      Regarding the public images, you are right, they are indeed the synthetic F814W images reconstructed from the narrow band images. The way in which they have been constructed is also explained in Molino et al.(2014).

      Finally, with respect to the NIR images, I'll try to find out whether they will be made public.


  • Parviz Parvin added an answer:
    Why don't we consider the time before the Big Bang?
    The entire universe originated from a single point after the Big Bang. Then how can we explain the time before big bang?
    Parviz Parvin

    Model is restricting " time". The fact may be something else and time may have existed even before Big-Bang. I asked similar question posted in RG:" What was before Big-Bang?" If we accept Big-Bang theory, what has been before that? No space, no time, no mass, no energy, no momentum, no event, no sequence...??!! 

  • Victor Christianto added an answer:
    Are there wave models of planetary orbits in the solar system?
    I just found a new paper by Chaudry and Thurman, with the title "A simple planetary evolution model using the solar nebula theory." (H-SC journal, march 2014). See :

    Other papers that I know include the wave universe model by Chechelnitsky, and the fractal Schrodinger model of Laurent Nottale.

    Do you know other papers discussing planetary orbits in the solar system using the wave model? Your comments are welcome.
    Victor Christianto

    Thank you for your answer, Nainan. Best wishes

  • George E. Van Hoesen added an answer:
    Can a planet or star exist without rotating on its axis?
    Do magnetic fields exist because of the rotation of planets and stars, or do magnetic fields induce rotation in the planets and stars? Can we say a planet is dead if it does not rotate about its axis?
    George E. Van Hoesen

    I know that the actions of the down vote are anonymous..  However I would like to know why my last comment which is well within the excepted science of today, was voted down. 

    I reserve the down vote for comments that are not scientific or intellectual in nature but just stabs at others.  My concern here is that down votes should not be just because you do not like something or someone.  Have the courage to tell me I am wrong.

    If I have pointed out something outside of science or incorrect in this forum I except a rebuttal from someone that knows better than I do. 

    The down votes can be taken back as can the up votes.  This is a scientific forum not a popularity contest.

  • Allard Jan Van Marle added an answer:
    What are the main astrophysical radio wave sources?
    I have a project and I need to know the sources of electromagnetic radiation along with the processes by which they are emitted in space. Any help would be appreciated.
    Allard Jan Van Marle

    Emission from molecular electronic transitions (rotational and vibrational)

  • Thomas Ihle added an answer:
    Scaling solution to BBGKY-hierarchy in Astrophysics
    I am interested in finding closure relations for the BBGKY-equations and came across an old article ``On the integration of the BBGKY equations for the development of strongly nonlinear clustering in an expanding universe'' by M DAVIS, PJE PEEBLES, Astrophysical Journal Supplement Series, 1977. I am used to closures where the three-particle correlations are either neglected or are approximated by Kirkwood's superposition principle, which appears ad hoc to me and is inaccurate for certain applications.
    In the article by Davis and Peebles, something I haven't seen before was used, a scaling solution where n-particle correlation functions are approximated by a simple power law. It looks like this only works if the particles are far apart from each other and if there is no characteristic length scale in the particle interactions, which is the case for gravity. This made me curious: How useful did this approach become in Astrophysics simulations, is it still used or was this a dead end? If not, has there been any recent improvements on this approach?
    Has such a scaling approach to the BBGKY-hierarchy been used in other areas of physics, like plasma physics where there is also a power law (Coulomb) interaction?
    Thomas Ihle

    Thank you for your answer. If your truth would be embarrassing for me, it would also embarrass such icons of soviet physics as Bogolubov and Landau, and I'd be totally fine with being part of that axis-of-shame :-) I agree that one has to be careful with ensemble averages when talking about inhomogeneous systems, for example, when describing soliton-like waves in active matter (see my Phys. Rev. E from 2013, and the Discussion on Ohta paper in 2014)). However, I disagree that hierarchy-equations like the BBGKY-hierarchy are useless in general. In your own papers, you also use such hierarchies of equations for multi-point correlation functions. In my opinion, for the ensemble average, one just has to imagine that only  the proper microscopic members that describe a particular inhomogeneous state are part of the ensemble. For example, for a single soliton, only those microscopic states should be  included that have the same density and momentum profile (coarse-grained over small cells in phase space) at the same time. Another argument to not dismiss BBGKY-like hierarchies is to consider the extreme case of a N-particle ensemble distribution that consists of products of delta-functions at time t. That means, all ensemble members have particles at the same positions with the same momenta and the BBGKY-equations would be equivalent to the evolution of a particular real system with those initial conditions. A more pragmatic argument: I recently used the first two BBGKY equations (adopted to my system) for self-propelled particles in a weakly-correlated limit where three-particle correlations are negligible compared to two-particle ones and I found perfect quantitative agreement with particle-based direct simulations. I didn't have to explicitly select the proper members of the ensemble, I did neither use thermodynamics nor Gibbs distributions, I just solved the time-dependent hierarchy equations until  a stationary state was reached. Thus, if you have an alternative theory, I suggest testing it quantitatively with Molecular Dynamics simulations and see how it does. In contrast to experiments, simulations can be adjusted to mirror all the approximations made in a theory and thus allow ``comparing apples with apples''. In my opinion, the more serious problem with kinetic theory is the closure of the hierarchy. You mentioned in your papers that you somehow close your equations at the two-particle level but I couldn't find any details. For self-propelled particles, there is parameter ranges where the three-particle correlations are stronger than the two-particle ones and the four-particle-ones are even stronger than three-particle ones and so on. Thus, in this strongly-correlated system, some type of generating function should be found that contains correlations to all orders, at least approximately, or a systematic closure for all multi-particle correlations is needed. In your papers, you mention discrepancies between experiments and theory. Could that also be due to neglecting these higher multi-particle correlations or using an inappropriate closure ?

  • F. Leyvraz added an answer:
    Time freezes at the event of horizon therfore for observer the mass falling into it looks like it doesn't fall, so how could you get this pre and post flare?
    At the center of our Milky Way Galaxy, a mere 27,000 light-years away, lies a black hole with 4 million times the mass of the Sun. Fondly known as Sagittarius A* (pronounced A-star), the Milky Way's black hole is fortunately mild-mannered compared to the central black holes in distant active galaxies, much more calmly consuming material around it. From time to time it does flare-up, though.

    The flare sequence is illustrated in the panels at the far right. X-rays are generated in material heated to over 100 million degrees Celsius, accelerated to nearly the speed of light as it falls into the Miky Way's central black hole. The main inset X-ray image spans about 100 light-years. In it, the bright white region represents the hottest material closest to the black hole, while the pinkish cloud likely belongs to a nearby supernova remnant.

    Credit: NuSTAR project,APOD(NASA)
    F. Leyvraz

    The motion of a particle near a black hole is given by the geodesics corresponding to the metric describing the black hole. The motion can be described in various coordinate systems, but it is, of course, always the same motion. This motion has no particular singularity at the horizon, if we are talking of an ordinary Schwarzschild black hole. However distant observers will in fact see strange things as the paticle nears the horizon, but these are simply due to the fact that the coordinate system of the distant observer cannot be used to describe the neighbourhood of the horizon.

    Saying that ``time freezes'' is doubtless easier than attempting to describe in detail what a particle does when it comes near a black hole. But it is not nearly as clear, nor nearly as precise. What is the time we mean? In what sense does it ``freeze''? I do not deny that such expressions may be used to describe what happens, but it is very easy to be led to misconceptions when abstract concepts are used without reference to their concrete use and their precise definitions....

  • Mahak Singh Chauhan added an answer:
    How do I check the performance of the Genetic Algorithm in MATLAB ?
    As every time GA gives different results but how do I know which one is best ?

    Maybe it is possible to check the fitness error but I do not know how to check it

    Please add your answer.

    Thanks a lot.
    Mahak Singh Chauhan
    Thank you all !! Your answers are really helpful.

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