Essay Abstract

General Relativity predicts the existence of black-holes. Access to the complete space-time manifold is required to describe black-holes. This strange feature necessitates that black-hole dynamics is specified by future or teleological boundary condition. Here we demonstrate that the statistical mechanical description of black-holes, as required by the laws of black-hole thermodynamics, also requires teleological boundary condition. It is known for three decades that the Einstein's equations when projected on space-time horizons resemble Navier-Stokes equation of a fluid. Within this paradigm, we show that the specific heat and the coefficient of bulk viscosity of the horizon-fluid are negative only if the teleological boundary condition is taken into account. We argue that in quantum theory of gravity, the future boundary condition plays a crucial role and discuss its implications.

Author Bio

Shankaranarayanan obtained his Ph.D. in 2002 from IUCAA, Pune, India. After postdoctoral work at the University of Azores, ICTP-Trieste, Italy and Albert Einstein Institute-Golm, Germany; he was a Marie Curie Fellow at the ICG, Portsmouth, UK. Since 2009, he is a faculty at ISER-Thiruvananthapuram and heads Max Planck Partner Group on Cosmology and Gravity. His interests is Early-Universe Cosmology and Gravity. Bhattacharya did his PhD from TIFR, Mumbai, India. His current research interests are understanding the physics of black holes and exploring the challenges in putting together the Quantum theory and Gravity. Currently he is a postdoctoral fellow at IISER-Thiruvananthapuram.

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Dear Swastik Bhattacharya and S. Shankaranarayanan,

Your essay is well-written and very interesting. The fluid approach to the black hole thermodynamics has relevant implications, not only to the problem itself, but also to the utility of future boundary conditions. Indeed, it appears that not only the definition of the horizon requires such a view, but also the statistical descriptions of black hole entropy and temperature. I think your approach and the corresponding paradigm which relates the projection of Einstein equation on the horizon to the Navier-Stokes equation of a fluid is very promising to say the least, since it allows the study of the black hole thermodynamics without having to assume much about the quantum gravity level and the Plank scale. So whatever these may be, I think some of the fundamental properties can already be captured in this method.

Best regards,

Cristi Stoica

The Tablet of the Metalaw

    I read your interesting article, but it seems to me one of two things occurred. You cut it to fit the FQXi page requirements and that made it hard to read, or you wrote it for a very specific audience that is understanding of the finer points you bring up. To give you and example. You give a bunch of equations, but most do not include definitions of the variables. On page 9 of your article you give the equation P = nk_BT n = N/V. I'm guessing k_B is Boltzmann's constant, T is temperature, but I'm not sure about N and V. If you have a longer version of this article somewhere on the web I might be interested in reading it to see the finer points that I am missing in this article.

    Anyway, good luck in the contest.

    Jim Akerlund

      Dear Dr. Akerlund,

      Thanks for the comments. Sorry for being brief with the defintions. You guess about $k_B$, $T$ is correct. $N$ is the number of particles and $V$ is the volume.

      You can look our earlier works that are in the arxiv:

      https://arxiv.org/abs/1702.03682

      https://arxiv.org/abs/1607.06222

      https://arxiv.org/abs/1512.03680

      Thanks, once again, for your comments.

      Best,

      Shanki

      Hello to both of you,

      I liked a lot your papper and how you analyse these BHs and the horizons.The BEC also seems very relevant.I consider that dark matter, gravitation and BHs are in the cold.This zero absolute seems very relevant considering the equilibrium between gravity and electromagntism.Thanks for sharing your works and good luck in this contest.You are going to be well ranked.

      Regards

        Nice essay Bhattacharya, Shankaranarayanan ,

        Your essay is basically about Blackholes, Bigbang and CMB etc... As for Bigbang and Blackholes are mathematical singularities. As for CMB, they have not accounted for the microwave radiation emitted from Galaxies, Globular clusters and stars etc... see the essay on CMB in previous FQXi... There was no provision to eliminate this radiation in the WMAP satellite. See my essay...

        http://fqxi.org/community/forum/topic/1607

        No Bigbang generated CMB detected; You can see Branko's( another author in this contest) solution here. http://vixra.org/abs/1602.0095

        I have another objection, you are considering this whole universe as expanding universe only. You are not considering 60 percent of Galaxies like blue shifted Galaxies and Quasars etc... Do you feel it is correct...

        Even though Bigbang is popular, it is failing at experimental evidences....

        For your information Dynamic Universe model is totally based on experimental results. Here in Dynamic Universe Model Space is Space and time is time in cosmology level or in any level. In the classical general relativity, space and time are convertible in to each other.

        Many papers and books on Dynamic Universe Model were published by the author on unsolved problems of present day Physics, for example 'Absolute Rest frame of reference is not necessary' (1994) , 'Multiple bending of light ray can create many images for one Galaxy: in our dynamic universe', About "SITA" simulations, 'Missing mass in Galaxy is NOT required', "New mathematics tensors without Differential and Integral equations", "Information, Reality and Relics of Cosmic Microwave Background", "Dynamic Universe Model explains the Discrepancies of Very-Long-Baseline Interferometry Observations.", in 2015 'Explaining Formation of Astronomical Jets Using Dynamic Universe Model, 'Explaining Pioneer anomaly', 'Explaining Near luminal velocities in Astronomical jets', 'Observation of super luminal neutrinos', 'Process of quenching in Galaxies due to formation of hole at the center of Galaxy, as its central densemass dries up', "Dynamic Universe Model Predicts the Trajectory of New Horizons Satellite Going to Pluto" etc., are some more papers from the Dynamic Universe model. Four Books also were published. Book1 shows Dynamic Universe Model is singularity free and body to collision free, Book 2, and Book 3 are explanation of equations of Dynamic Universe model. Book 4 deals about prediction and finding of Blue shifted Galaxies in the universe.

        With axioms like... No Isotropy; No Homogeneity; No Space-time continuum; Non-uniform density of matter(Universe is lumpy); No singularities; No collisions between bodies; No Blackholes; No warm holes; No Bigbang; No repulsion between distant Galaxies; Non-empty Universe; No imaginary or negative time axis; No imaginary X, Y, Z axes; No differential and Integral Equations mathematically; No General Relativity and Model does not reduce to General Relativity on any condition; No Creation of matter like Bigbang or steady-state models; No many mini Bigbangs; No Missing Mass; No Dark matter; No Dark energy; No Bigbang generated CMB detected; No Multi-verses etc.

        Many predictions of Dynamic Universe Model came true, like Blue shifted Galaxies and no dark matter. Dynamic Universe Model gave many results otherwise difficult to explain

        Have a look at my essay on Dynamic Universe Model and its blog also where all my books and papers are available for free downloading...

        http://vaksdynamicuniversemodel.blogspot.in/

        Best wishes to your essay.

        For your blessings please................

        =snp. gupta

        Dear Swastik Bhattacharya and S. Shankaranarayanan,

        Please excuse me for I have no intention of disparaging in any way any part of your essay.

        I merely wish to point out that "Everything should be made as simple as possible, but not simpler." Albert Einstein (1879 - 1955) Physicist & Nobel Laureate.

        Only nature could produce a reality so simple, a single cell amoeba could deal with it.

        The real Universe must consist only of one unified visible infinite physical surface occurring in one infinite dimension, that am always illuminated by infinite non-surface light.

        A more detailed explanation of natural reality can be found in my essay, SCORE ONE FOR SIMPLICITY. I do hope that you will read my essay and perhaps comment on its merit.

        P.S. My essay, THE SIMPLEST UNIVERSE was sent out for review by the editor of the Indian Institute Journal of Current Science on December 28, 2016. The email address for inquiries at the site cannot be accessed by my rr email server. Could you possibly advise me as to how I might find out about the delay?

        Joe Fisher, Realist

          21 days later

          Shankaranarayanan S and Swastik Bhattacharya:

          I can't pretend to understand esoteric BH concepts, but gather that temperature and viscosity differentials are driving factors in the mysteriously inscrutable black hole environment. Does the Navier-Stokes equation of a fluid relate to "fluid in a universe modeling:

          https://www.quantamagazine.org/20140212-big-bang-secrets-swirling-in-a-fluid-universe/? -- Something I reference in my essay. Does your "future influencing the present" relate to lookback time?

          Hope you get a chance to comment on my essay as well.

          Regards,

          Jim Hoover

            6 days later

            Dear Sirs!

            Physics of Descartes, which existed prior to the physics of Newton returned as the New Cartesian Physic and promises to be a theory of everything. To tell you this good news I use «spam».

            New Cartesian Physic based on the identity of space and matter. It showed that the formula of mass-energy equivalence comes from the pressure of the Universe, the flow of force which on the corpuscle is equal to the product of Planck's constant to the speed of light.

            New Cartesian Physic has great potential for understanding the world. To show it, I ventured to give "materialistic explanations of the paranormal and supernatural" is the title of my essay.

            Visit my essay, you will find there the New Cartesian Physic and make a short entry: "I believe that space is a matter" I will answer you in return. Can put me 1.

            Sincerely,

            Dizhechko Boris