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### Mohajan, Haradhan Kumar

- Upper Limit of the Age of the Universe with Cosmological Constant

Abstract Views :233 |
PDF Views:89

1 Premier University, Chittagong, BD

#### Authors

**Affiliations**

1 Premier University, Chittagong, BD

#### Source

International Journal of Reciprocal Symmetry and Theoretical Physics, Vol 1, No 1 (2014), Pagination: 43-68#### Abstract

The Friedmann, Robertson-Walker universe is based on the assumption that the universe is exactly homogeneous and isotropic. This model expresses that there is an all encompassing big bang singularity in the past as the origin from which the universe emerges in a very hot phase and continues its expansion as it cools. Here homogeneous and isotropic assumptions of the observed universe are not strictly followed to calculate the present age of the universe. Einstein equation plays an important role in cosmology to determine the present age of the universe. The determination of present age and density of the universe are two very important issues in cosmology, as they determine the future evolution and the nature of the universe. An attempt has been taken here to find the upper limit of the age of the universe with cosmological constant.#### Keywords

Einstein Equation, Geodesic, Hubble Constant, Spacetime Manifold, Universe- The Number of Vector Partitions of
*n* (Counted According to the Weight) with the Crank *m*

*n*(Counted According to the Weight) with the Crank*m*
Abstract Views :131 |
PDF Views:27

1 Department of Mathematics, Raozan University College, BD

2 Premier University, BD

#### Authors

**Affiliations**

1 Department of Mathematics, Raozan University College, BD

2 Premier University, BD

#### Source

International Journal of Reciprocal Symmetry and Theoretical Physics, Vol 1, No 2 (2014), Pagination: 91-105#### Abstract

This article shows how to find all vector partitions of any positive integral values of*n*, but only all vector partitions of 4, 5 and 6 are shown by algebraically. These must be satisfied by the definitions of crank of vector partitions.

#### Keywords

Vector Partitions, Crank, Congruences, Modulo.#### References

- Andrews G.E. (1985), The Theory of Partitions, Encyclopedia of Mathematics and its Application, vol. 2 (G-c, Rotaed) Addison-Wesley, Reading, mass, 1976 (Reissued, Cambridge University, Press, London and New York 1985).
- Andrews G.E. and Garvan F.G. (1988), Dyson’s Crank of a Partition, Bulletin (New series) of the American Mathematical Society, 18(2): 167–171.
- Atkin, A.O.L. and Swinnerton-Dyer, P. (1954), Some Properties of Partitions, Proc. London Math. Soc. 3(4): 84–106.
- Das S. 2014. Congruence Properties of Andrews’ SPT- Function ABC Journal of Advanced Research, 3, 47-56.
- Mohajan HK. Upper Limit of the Age of the Universe with Cosmological Constant International Journal of Reciprocal Symmetry and Theoretical Physics. 2014;1(1):43-68.

- Gravitational Collapse of a Massive Star and Black Hole Formation

Abstract Views :105 |
PDF Views:47

1 Premier University, Chittagong, BD

#### Authors

**Affiliations**

1 Premier University, Chittagong, BD

#### Source

International Journal of Reciprocal Symmetry and Theoretical Physics, Vol 1, No 2 (2014), Pagination: 125-140#### Abstract

This paper discusses the final fate of a gravitationally collapse of a massive star and the black hole formation. If the mass of a star exceeds Chandrasekhar limit then it must undergo gravitational collapse. This happens when the star has exhausted its nuclear fuel. As a result a space-time singularity is formed. It is conjectured that singularities must be hidden behind the black hole region which is called the cosmic censorship hypothesis. It has not been possible, to obtain a proof despite many attempts to establish the validity of cosmic censorship and it remains an open problem. An attempt has been taken here to describe causes of black hole formation and nature of singularities therein with easier mathematical calculations.#### Keywords

Black Hole, Chandrasekhar Limit, Gravitational Collapse, Singularity.#### References

- Arnett, W.D. and Bowers, R.L. (1977), A Microscopic Interpretation of Neutron Star St ructure, The Astrophysical Journal Supplement Series: 33: 415–436.
- Boyer, R.H. and Lindquist, R.W. (1967), Maximal Analytic Extension of Kerr Met ric, Journal of Mathematical Physics, 8(2): 265–281.
- Chandrasekhar, S. (1983), Mathematical Theory of Black Holes, Clarendon Press, Oxford.
- Hawking, S.W. and Ellis, G.F.R. (1973), The Large Scale Structure of Space-time, Cambridge University Press, Cambridge.
- Joshi, P.S. (1996), Global Aspects in Gravitation and Cosmology, 2
^{nd}ed., Clarendon Press, Oxford. - Joshi P.S. (2013), Spacetime Singularities, arXiv:1311.0449v1 [gr-qc] 3 Nov 2013.
- Kruskal, M.D. (1960), Maximal Extension of Schwarzschild Met ric, Physical Review, 119(5): 1743–1745.
- Lipschutz, S. (1965), Theory and Problems of General Topology, Schaum’s Outline Series, McGraw-Hill Book Company, Singapore.
- Mohajan, H.K. (2013a), Singularity Theorems in General Relativity, M. Phil. Dissertation, Lambert Academic Publishing, Germany.
- Mohajan, H.K. (2013b), Friedmann, Robertson-Walker (FRW) Models in Cosmology, Journal of Environmental Treatment Techniques, 1(3): 158–164.
- Mohajan, H.K. (2013c), Schwarzschild Geomet ry of Exact Solution of Einstein Equation in Cosmology, Journal of Environmental Treatment Techniques, 1(2): 69–75.
- Mohajan, H.K. (2014a), General Upper Limit of the Age of the Univers e, ARPN Journal of Science and Technology, 4(1): 4–12.
- Mohajan, H.K. (2014b), Upper Limit of the Age of the Universe with Cosmological Constant, International Journal of Reciprocal Symmetry and Theoretical Physics, 1(1): 43–68.
- Stephani, H.; Kramer, D.; MacCallum, M.; Hoens elaers, C.; Hertl, E. (2003), Exact Solutions to Einstein' s Field Equations (2
^{nd}ed.), Cambridge: Cambridge University Press. - Szekeres, G. (1960), On the Singularities of a Riemannian Manifold, Publicationes Mathematicae, Debrecen, 7: 285–301.