We here present a
relativistic model for a spherically symmetric anisotropic fluid to study the
various factors of physical and thermal phenomenon during the evolution of a
collapsing star dissipating energy in the form of radial heat flow. We also
proposed a table of some new parametric class of solutions which will be useful
for constructing the new compact star models. The constructed algorithm obeys
all the relevant requirements of a realistic model and matched with Vaidya
exterior metric over the boundary. At the initial stage the interior solutions
represent a static configuration of perfect fluid which then gradually starts
evolving into radiating collapse. The apparent luminosity as observed by the
distant observer at rest at infinity and the effective surface temperature are
zero in remote past at the instant when collapse begins and at the stage when
collapsing configuration reaches the horizon of the black hole.
References
[1]
Joshi, P.S. and Malafarina, D. (2011) Recent Developments in Gravitational Collapse and Spacetime Singularities. International Journal of Modern Physics D, 20, 2641-2729. http://dx.doi.org/10.1142/S0218271811020792
[2]
Penrose, R. (1969) Gravitational Collapse: The Role of General Relativity. La Rivista del Nuovo Cimento, 1, 252-276.
[3]
Virbhadra, K.S. (2009) Relativistic Images of Schwarzschild Black Hole Lensing. Physical Review D, 79, 083004. http://dx.doi.org/10.1103/PhysRevD.79.083004
[4]
Oppenheimer, J.R. and Snyder, H. (1939) Continued Gravitational Contraction. Physical Review, 56, 455. http://dx.doi.org/10.1103/PhysRev.56.455
[5]
Vaidya, P.C. (1951) The Gravitational Field of a Radiating Star. Proceedings of the National Academy of Sciences, India, Section A: Physical Sciences, 33, 264-276.
[6]
Vaidya, P.C. (1953) Newtonian Time in General Relativity. Nature, 171, 260-261. http://dx.doi.org/10.1038/171260a0
[7]
Santos, N.O. (1985) Non-Adiabatic Radiating Collapse. Monthly Notices of the Royal Astronomical Society, 216, 403-410. http://dx.doi.org/10.1093/mnras/216.2.403
[8]
Herrera, L. and Santos, N.O. (2004) Dynamics of Dissipative Gravitational Collapse. Physical Review D, 70, 084004. http://dx.doi.org/10.1103/PhysRevD.70.084004
[9]
Mitra, A. (2006) Why Gravitational Contraction Must Be Accompanied by Emission of Radiation Both in Newtonian and Einstein Gravity. Physical Review D, 74, 024010. http://dx.doi.org/10.1103/PhysRevD.74.024010
[10]
Tewari, B.C. (1988) Radiating Fluid Spheres in General Relativity. Astrophysics and Space Science, 149, 233-239. http://dx.doi.org/10.1007/BF00639793
[11]
Tewari, B.C. (1994) Relativistic Radiating Fluid Distribution. Indian Journal of Pure and Applied Physics, 32, 504.
[12]
Tewari, B.C. (2006) Relativistic Model for Radiating Star. Astrophysics and Space Science, 306, 273-277. http://dx.doi.org/10.1007/s10509-006-9273-y
[13]
Tewari, B.C. (2010) Radiating Fluid Balls in General Relativity. VDM Verlag, Saarbrucken.
[14]
de Oliveira, A.K.G., Santos, N.O. and Kolassis, C.A. (1985) Collapse of a Radiating Star. Monthly Notices of the Royal Astronomical Society, 216, 1001-1011. http://dx.doi.org/10.1093/mnras/216.4.1001
[15]
Bonnor W. B., de Oliveira, A.K.G. and Santos, N.O. (1989) Radiating Spherical Collapse. Physical Review Letters, 181, 269-326. http://dx.doi.org/10.1016/0370-1573(89)90069-0
[16]
Herrera, L., Di Prisco, A., Ospino, J., Fuenmayor, E. and Triconis, O. (2009) Structure and Evolution of Self-Gravi-tating Objects and the Orthogonal Splitting of the Riemann Tensor. Physical Review D, 79, Article ID: 064025. http://dx.doi.org/10.1103/PhysRevD.79.064025
[17]
Maharaj, S.D. and Govender, M. (2005) Radiating Collapse with Vanishing Weyl Stresses. International Journal of Modern Physics D, 14, 667-676. http://dx.doi.org/10.1142/S0218271805006584
[18]
Ivanov, B.V. (2012) Collapsing Shear-Free Perfect Fluid Spheres with Heat Flow. General Relativity and Gravitation, 44, 1835-1855. http://dx.doi.org/10.1007/s10714-012-1370-3
[19]
Tewari, B.C. (2012) Relativistic Collapsing Radiating Stars. Astrophysics and Space Science, 342, 73-77. http://dx.doi.org/10.1007/s10509-012-1141-3
[20]
Tewari, B.C. (2013) Collapsing Shear-Free Radiating Fluid Spheres. General Relativity and Gravitation, 45, 1547-1558. http://dx.doi.org/10.1007/s10714-013-1545-6
[21]
Pinheiro, G. and Chan, R. (2013) Radiating Shear-Free Gravitational Collapse with Charge. General Relativity and Gravitation, 45, 243-261. http://dx.doi.org/10.1007/s10714-012-1468-7
[22]
Tewari, B.C. and Charan, K. (2014) Radiating Star, Shear-Free Gravitational Collapse without Horizon. Astrophysics and Space Science, 351, 613-617. http://dx.doi.org/10.1007/s10509-014-1851-9
[23]
Tewari, B.C. and Charan, K. (2015) Dissipative Spherical Gravitational Collapse of Isotropic Fluid. Journal of Modern Physics, 6, 453-462. http://dx.doi.org/10.4236/jmp.2015.64049
[24]
Sharif, M. and Iftikhar, S. (2015) Charged Dissipative Collapse of Shearing Viscous Star. Astrophysics and Space Science, 357, 79. http://dx.doi.org/10.1007/s10509-015-2246-2
[25]
Bowers, R.L. and Liang, E.P.T. (1974) Anisotropic Spheres in General Relativity. Astrophysical Journal, 188, 657-665. http://dx.doi.org/10.1086/152760
[26]
Herrera, L. and Santos, N.O. (1997) Local Anisotropy in Self-Gravitating Systems. Physics Reports, 286, 53-130. http://dx.doi.org/10.1016/S0370-1573(96)00042-7
[27]
Herrera, L., Di Prisco, A., Hernandez-Pastoraand, J.L. and Santos, N.O. (1998) On the Role of Density Inhomogeneity and Local Anisotropy in the Fate of Spherical Collapse. Physics Letters A, 237, 113-118. http://dx.doi.org/10.1016/S0375-9601(97)00874-8
[28]
Ivanov, B.V. (2010) Evolving Spheres of Shear-Free Anisotropic Fluid. International Journal of Modern Physics A, 25, 3975-3991. http://dx.doi.org/10.1142/S0217751X10050202
[29]
Ivanov, B.V. (2011) Self-Gravitating Spheres of Anisotropic Fluid in Geodesic Flow. International Journal of Modern Physics D, 20, 319-334. http://dx.doi.org/10.1142/S0218271811018858
[30]
Reddy, K.P., Govender, M. and Maharaj, S.D. (2015) Impact of Anisotropic Stresses during Dissipative Gravitational Collapse. General Relativity and Gravitation, 47, 35. http://dx.doi.org/10.1007/s10714-015-1880-x
[31]
Tewari, B.C. and Charan, K. (2015) Horizon Free Eternally Collapsing Anisotropic Radiating Star. Astrophysics and Space Science, 357, 107. http://dx.doi.org/10.1007/s10509-015-2335-2
[32]
Tewari, B.C. and Charan, K. (2015) Gravitational Collapse, Shear-Free Anisotropic Radiating Star. arxiv:1503.02165
[33]
Govender, M., Bogadi, R.S., Lortan, D.B. and Maharaj, S.D. (2016) Radiating Collapse in the Presence of Anisotropic Stresses. International Journal of Modern Physics D, 25, Article ID: 1650037. http://dx.doi.org/10.1142/S0218271816500371
[34]
Ivanov, B.V. (2016) All Solutions for Geodesic Anisotropic Soherical Collapse with Shear and Heat Flow. Astrophysics and Space Science, 361, 18. http://dx.doi.org/10.1007/s10509-015-2603-1
[35]
Ivanov, B.V. (2016) A Different Approach to Anisotropic Spherical Collapse with Shear and Heat Radiation. International Journal of Modern Physics D, 25, Article ID: 1650049. http://dx.doi.org/10.1142/S0218271816500498
[36]
Cahill, M.E. and McVittie, G.C. (1970) Spherical Symmetry and Mass Energy in General Relativity I. General Theory. Journal of Mathematical Physics, 11, 1382-1391. http://dx.doi.org/10.1063/1.1665273
[37]
Misner, C.W. and Sharp, D.H. (1964) Relativistic Equations for Adiabatic Spherically Symmetric Gravitational Collapse. Physical Review B, 136, 571-576. http://dx.doi.org/10.1103/PhysRev.136.B571
[38]
Banerjee, A., Chatterjee, S. and Dadhich, N. (2002) Spherical Collapse with Heat Flow and without Horizon. Modern Physics Letters A, 17, 2335-2339. http://dx.doi.org/10.1142/S0217732302008320
[39]
Israel, W. and Stewart, J. (1979) Transient Relativistic Thermodynamics and Kinetic Theory. Annals of Physics, 118, 341-372. http://dx.doi.org/10.1016/0003-4916(79)90130-1
[40]
Maartens, R. (1995) Dissipative Cosmology. Classical and Quantum Gravity, 12, 1455-1465. http://dx.doi.org/10.1088/0264-9381/12/6/011
[41]
Martinez, J. (1996) Transport Processes in the Gravitational Collapse of an Anisotropic Fluid. Physical Review D, 53, 6921-6940. http://dx.doi.org/10.1103/PhysRevD.53.6921
[42]
Schwarzschild, M. (1958) Structure and Evolution of stars. Dover, New York.
[43]
Misner, C.W. and Sharp, D.H. (1965) Spherical Gravitational Collapse with Energy Transport by Radiative Diffusion. Physics Letters, 15, 279-281. http://dx.doi.org/10.1016/0031-9163(65)91247-3