Energy Transfer and Fluid Flow around a Massive Astrophysical Object

Abstract:

Article Preview

In this work it is presented the modeling and simulation of energy transfer and fluid flow of a stationary spherical arrangement of particles surrounding a gravitational body such as an astrophysical object that carries the curvature of space-time continuum in general relativity, taking into account the thermodynamics of the second law. This model also predicts the drag of space and time around an astrophysical object as it rotates, with results close to the experimental data reported by other authors. To model the energy transfer of the mass and the fluid flow in the space-time, it is used a 4-dimensional system. In order to make measurements of entropy in the arrow of time (past-present), tensors in General Relativity were used to calculate this thermodynamic quantity and with this, the big bang ́s low entropy condition in phase space of coarse graining (Hawking ́s box), according to Weyl curvature hypothesis (WCH) of Roger Penrose. Contribution of this paper is presented by tensors which carry information that has to do with something as non-distortion effect in fluid flow around the astrophysical object and the low entropy condition that is believed to exist in the past, in the big bang; what leads us to search for a new physical-mathematical science to continue. At this point, the Einstein field equations are out of context, which leads us to conclude that it is necessary a mathematical science that allows us to make calculations to rescue lost information due to collapse of matter to a black hole. This math should allow us to clear up physical phenomena (like origin of the universe) and their relationship, with the objective of unifying theories that lead to a physical science without uncertainties, as at the present time. In this regard, we propose a metric in hyperbolic coodinates to build a physical wormhole shaped object where gravitational bodies can be housed that allow us to link the past entropy with the present entropy according to the second law of thermodynamics, as a kind of mathematical space or alternative model to compensate in some way, the link between WCH and the phase space volume of the Hawking's box, and the link between WCH and the quantum-mechanical state-vector reduction, , proposed by Penrose which still have not been determined by any author. Nomenclature

Info:

Periodical:

Edited by:

Antonio F. Miguel, Luiz Rocha and Andreas Öchsner

Pages:

189-215

Citation:

R. L. Corral Bustamante et al., "Energy Transfer and Fluid Flow around a Massive Astrophysical Object", Defect and Diffusion Forum, Vol. 348, pp. 189-215, 2014

Online since:

January 2014

Export:

Price:

$38.00

[1] J.A. Isenberg, Wheeler–Einstein–Mach spacetimes,  Phys. Rev. D 24 (1981) 251–256.

DOI: https://doi.org/10.1103/physrevd.24.251

[2] R. Penrose, Twistor theory - Its aims and achievements in: Quantum gravity; Proceedings of the Oxford Symposium, Harwell, Berks., England, February 15, 16, 1974. (A76-11051 01-90) Oxford, Clarendon Press, 1975, pp.268-407.

[3] Information on http: /www. nasa. gov/vision/earth/lookingatearth/earth_drag. html.

[4] J.H. Heinbockel, Introduction to Tensor Calculus and Continuum Mechanics, Trafford Publishing, Canada, (2001).

[5] K. Sfetsos, K. Skenderis, Microscopic derivation of the Bekenstein-Hawking entropy formula for non-extremal black holes, Nucl. Phys. B 517 (1998) 179-204.

DOI: https://doi.org/10.1016/s0550-3213(98)00023-6

[6] J.D. Bekenstein, Information in the Holographic Universe, Sci. American, 17 (2007) 66-73.

[7] J.D. Bekenstein, M. Schiffer, Quantum limitations on the storage and transmission of information, Int. J. of Mod. Phys. 1 (1990) 355-422.

[8] J.D. Bekenstein, Entropy content and information flow in systems with limited energy, Phys. Rev. D 30 (1984) 1669–1679.

DOI: https://doi.org/10.1103/physrevd.30.1669

[9] J.D. Bekenstein, Communication and energy. Phys. Rev A 37 (1988) 3437-3449.

[10] J.D. Bekenstein, Black holes and everyday physics, Gen. Relativ. and Gravit. 14 (1982) 355-359.

DOI: https://doi.org/10.1007/bf00756269

[11] C.K. Zachos, A classical bound on quantum entropy, J. Phys. A: Math. Theor. 40 (2007), F407-F412.

DOI: https://doi.org/10.1088/1751-8113/40/21/f02

[12] R. Penrose, The Emperor's New Mind, Oxford University Press, Great Britain, (1989).

[13] B. Chow, D. Knopf, The Ricci Flow: an introduction, American Mathematical Society, USA (2004).

[14] A. Moroianu, Lectures on Kähler geometry, Cambridge University Press, United Kingdom, (2007).

[15] L.A. Sidorov, Ricci tensor, in: Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, (2001).

[16] R. Penrose, Singularities and time-asymmetry. In General Relativity an Einstein Centenary Survey, edited by Hawking, S.W. and Israel, W., Cambridge University Press, UK, (1979).

[17] A. Borel, J. Lizhen,  Compactifications of symmetric and locally symmetric spaces, Birkhäuser, Boston, (2006).

[18] S. Chandrasekhar, An Introduction to the Study of Stellar Structure, Dover, New York, (2005).

[19] A. Ashtekar, New variables for classical and quantum gravity. Phys. Rev. Lett 57 (1986) 2244–2247.

DOI: https://doi.org/10.1103/physrevlett.57.2244

[20] A. DeBenedictis, A. Das, On a General Class of Wormhole Geometries. Class. Quant. Grav. 18 (2001) 1187-1204.

DOI: https://doi.org/10.1088/0264-9381/18/7/304

[21] M. Morris, K. Thorne, U. Yurtsever, Wormholes, Time Machines, and the Weak Energy Condition. Phys. Rev. Lett. 61 (1988) 1446–1449.

DOI: https://doi.org/10.1103/physrevlett.61.1446

[22] M.S. Morris, K.S. Thorne, Wormholes in spacetime and their use for interstellar travel: A tool for teaching general relativity. Am. J. Phys. 56 (1988) 395-412.

[23] K. Nakamura, (Particle Data Group): The Review of Particle Physics. J. Phys. G: Nucl. Part. Phys. 37 (2010) 1-1422.

[24] R.L. Corral-Bustamante, A.R. Rodríguez-Corral, T.J. Amador-Parra, E. Martínez-Loera, and G. Irigoyen-Chávez, Modeling of Virtual Particles of the Big Bang. Comput. Therm. Sci. 4 (2012) 1-13.

DOI: https://doi.org/10.1615/computthermalscien.2012003938

[25] R.L. Corral-Bustamante, A.R. Rodríguez-Corral, Transport Phenomena in an Evaporated Black Hole. In: A. Öchsner, L.F.M. Da Silva, H. Altenbach (Eds. ), Materials with Complex Behaviour II, Springer, Heidelberg, 2012, pp.469-482.

DOI: https://doi.org/10.1007/978-3-642-22700-4_29

[26] R.M. Wald, General Relativity, The University of Chicago, USA, (1984).

[27] N. Radicella, D. Pavon, The generalized second law in universes with quantum corrected entropy relations, Phys. Lett. B 691 (2010) 121-126.

[28] H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, E. Herlt, Exact Solutions of Einstein's Field Equations, Cambridge University Press, Cambridge, (2009).

DOI: https://doi.org/10.1017/cbo9780511535185

[29] S.M. Carroll, Spacetime and Geometry: An Introduction to General Relativity, Addison-Wesley, San Francisco, USA, (2004).

[30] J.B. Hartle, Gravity: an Introduction to Einstein's General Relativity, Addison-Wesley, San Francisco, USA, (2003).

[31] G.S. Hall, D.P. Lonie, On the compatibility of Lorentz metrics with linear connections on four-dimensional manifolds, J. Phys. A: Math. Gen. 39 (2006) 2995-3010.

DOI: https://doi.org/10.1088/0305-4470/39/12/009

[32] H.A. Lorentz, Considerations on Gravitation. Proc. Acad. Science Amsterdam 2 (1900) 559–574.

[33] H.A. Lorentz, Lectures on Theoretical Physics, Macmillan & Co., New York (1927-1931).

[34] M.D. Roberts, Imploding Scalar Fields, J. Math. Phys. 37 (1996) 4557-4573.

[35] Information on http: /es. scribd. com/doc/21984643/Astronautics-and-Aeronautics.

[36] J. M. Martin-Garcia, D. Yllanes and R. Portugal, Comp. Phys. Commun. 179 (2008), 586-590.

[37] W. Rindler, Relativity: Special, General, and Cosmological, Oxford University Press, New York, (2001).

[38] A.S. Eddington, Mathematical Theory of Relativity, Cambridge University Press, London, (1922).

[39] R. Penrose, On Schwarzschild Causality – A Problem for Lorentz Covariant, General Relativity, in Essays in General Relativity, Academic Press, New York, (1980).

DOI: https://doi.org/10.1016/b978-0-12-691380-4.50007-1