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ENERGY–MOMENTUM DISTRIBUTION: SOME EXAMPLES

M. SHARIF

Department of Mathematics, University of Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan

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and

M. AZAM

Department of Mathematics, University of Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan

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https://doi.org/10.1142/S0217751X0703515XCited by:20 (Source: Crossref)

Abstract

In this paper, we elaborate the problem of energy–momentum in General Relativity with the help of some well-known solutions. In this connection, we use the prescriptions of Einstein, Landau–Lifshitz, Papapetrou and Möller to compute the energy–momentum densities for four exact solutions of the Einstein field equations. We take the gravitational waves, special class of Ferrari–Ibanez degenerate solution, Senovilla–Vera dust solution and Wainwright–Marshman solution. It turns out that these prescriptions do provide consistent results for special class of Ferrari–Ibanez degenerate solution and Wainwright–Marshman solution but inconsistent results for gravitational waves and Senovilla–Vera dust solution.

Keywords:

Energy–momentum distribution

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References

C. Möller , The Theory of Relativity ( Oxford University Press , 1957 ) . Google Scholar
C. W. Misner, K. S. Thorne and J. A. Wheeler, Gravitation (W. H. Freeman and Co., New York, 1973) p. 603. Google Scholar
F. I. Cooperstock and R. S. Sarracino, J. Phys. A: Math. Gen. 11, 877 (1978), DOI: 10.1088/0305-4470/11/5/018. Crossref, ADS, Google Scholar
A. Trautman , Gravitation: An Introduction to Current Research , ed. L. Written ( Wiley , New York , 1962 ) . Google Scholar
R. C. Tolman , Relativity, Thermodynamics and Cosmology ( Oxford University Press , London , 1934 ) . Google Scholar
L. D. Landau and E. M. Lifshitz , The Classical Theory of Fields ( Pergamon , Oxford , 1980 ) . Google Scholar
A. Papapetrou, Proc. R. Irish Acad. A 52, 11 (1948). Google Scholar
P. G. Bergmann and R. Thompson, Phys. Rev. 89, 400 (1953), DOI: 10.1103/PhysRev.89.400. Crossref, Web of Science, ADS, Google Scholar
S. Weinberg , Gravitation and Cosmology ( Wiley , New York , 1972 ) . Google Scholar
H. Bondi, Proc. R. Soc. London, Ser. A 427, 249 (1990). Crossref, Web of Science, ADS, Google Scholar
R. Penrose, Proc. R. Soc. London, Ser. A 388, 457 (1982). Web of Science, Google Scholar
R. Penrose, Proc. 10th Int. Conf. on General Relativity and Gravitation (GR10)1, eds. B. Bertotti, F. de Felice and A. Pascolini (Consiglio Nazionale della Ricerche, Roma, 1983) p. 607. Google Scholar
J. D. Brown and J. W. York Jr., Phys. Rev. D 47, 1407 (1993), DOI: 10.1103/PhysRevD.47.1407. Crossref, Web of Science, ADS, Google Scholar
S. A. Hayward, Phys. Rev. D 497, 831 (1994), DOI: 10.1103/PhysRevD.49.831. Google Scholar
G. Berqvist, Class. Quantum Grav. 9, 1753 (1992), DOI: 10.1088/0264-9381/9/7/009. Crossref, Web of Science, ADS, Google Scholar
C. C. Chang, J. M. Nester and C. Chen, Phys. Rev. Lett. 83, 1897 (1999), DOI: 10.1103/PhysRevLett.83.1897. Crossref, Web of Science, Google Scholar
C. Möller, Ann. Phys. (N.Y.) 4, 347 (1958), DOI: 10.1016/0003-4916(58)90053-8. Crossref, Web of Science, ADS, Google Scholar
C. Möller, Ann. Phys. (N.Y.) 12, 118 (1961), DOI: 10.1016/0003-4916(61)90148-8. Crossref, Web of Science, ADS, Google Scholar
G. Lessner, Gen. Relativ. Gravit. 28, 527 (1996), DOI: 10.1007/BF02105063. Crossref, Web of Science, ADS, Google Scholar
D. Kovacs, Gen. Relativ. Gravit. 17, 927 (1985), DOI: 10.1007/BF00773830. Crossref, Web of Science, ADS, Google Scholar
J. Novotny, Gen. Relativ. Gravit. 19, 1043 (1987), DOI: 10.1007/BF00759583. Crossref, Web of Science, Google Scholar
A. Komar, Phys. Rev. 113, 934 (1959), DOI: 10.1103/PhysRev.113.934. Crossref, Web of Science, ADS, Google Scholar
A. E. Scheidegger, Rev. Mod. Phys. 25, 451 (1953), DOI: 10.1103/RevModPhys.25.451. Crossref, Web of Science, ADS, Google Scholar
N. Rosen, Helv. Phys. Acta. Suppl. 4, 171 (1956). Google Scholar
N. Rosen, Phys. Rev. 110, 291 (1958), DOI: 10.1103/PhysRev.110.291. Crossref, Web of Science, ADS, Google Scholar
N. Rosen and K. S. Virbhadra, Gen. Relativ. Gravit. 26, 429 (1993), DOI: 10.1007/BF00757123. Web of Science, Google Scholar
K. S. Virbhadra, Phys. Rev. D 41, 1086 (1990), DOI: 10.1103/PhysRevD.41.1086. Crossref, Web of Science, Google Scholar
K. S. Virbhadra, Phys. Rev. D 42, 1066 (1990), DOI: 10.1103/PhysRevD.42.1066. Crossref, Web of Science, Google Scholar
K. S. Virbhadra, Phys. Rev. D 60, 104041 (1999), DOI: 10.1103/PhysRevD.60.104041. Crossref, Web of Science, Google Scholar
K. S. Virbhadra, Phys. Rev. D 42, 2919 (1990), DOI: 10.1103/PhysRevD.42.2919. Crossref, Web of Science, Google Scholar
K. S. Virbhadra and J. C. Parikh, Phys. Lett. B 317, 312 (1993), DOI: 10.1016/0370-2693(93)91001-4. Crossref, Web of Science, ADS, Google Scholar
K. S. Virbhadra and J. C. Parikh, Phys. Lett. B 331, 302 (1994), DOI: 10.1016/0370-2693(94)91056-1. Crossref, Web of Science, ADS, Google Scholar
J. M. Aguirregabiria, A. Chamorro and K. S. Virbhadra, Gen. Relativ. Gravit. 28, 1393 (1996), DOI: 10.1007/BF02109529. Crossref, Web of Science, ADS, Google Scholar
S. S. Xulu, Int. J. Mod. Phys. A 15, 1979 (2000). Web of Science, Google Scholar
S. S. Xulu, Mod. Phys. Lett. A 15, 1151 (2000), DOI: 10.1142/S0217732300001651. Link, Web of Science, Google Scholar
S. S. Xulu, Astrophys. Space Sci. 283, 23 (2003), DOI: 10.1023/A:1021252824061. Crossref, Web of Science, ADS, Google Scholar
A. Chamorro and K. S. Virbhardra, Int. J. Mod. Phys. D 5, 251 (1994), DOI: 10.1142/S0218271896000175. Link, Web of Science, ADS, Google Scholar
S. S. Xulu, Int. J. Mod. Phys. D 7, 773 (1998), DOI: 10.1142/S0218271898000516. Link, Web of Science, ADS, Google Scholar
M. Sharif, Int. J. Mod. Phys. A 17, 1175 (2002), DOI: 10.1142/S0217751X02009655. Link, Web of Science, ADS, Google Scholar
M. Sharif, Int. J. Mod. Phys. A 18, 4361 (2003), DOI: 10.1142/S0217751X03016094. Link, Web of Science, ADS, Google Scholar
M. Sharif, Int. J. Mod. Phys. A 19, 1495 (2004), DOI: 10.1142/S0217751X04018439. Link, Web of Science, ADS, Google Scholar
M. Sharif, Int. J. Mod. Phys. D 13, 1019 (2004), DOI: 10.1142/S0218271804004700. Link, Web of Science, Google Scholar
A. Komar, Phys. Rev. 127, 1411 (1962), DOI: 10.1103/PhysRev.127.1411. Crossref, Web of Science, ADS, Google Scholar
A. Komar, Phys. Rev. 129, 1873 (1963), DOI: 10.1103/PhysRev.129.1873. Crossref, Web of Science, Google Scholar
R. Penrose, Proc. R. Soc. London, Ser. A 381, 53 (1982). Crossref, Web of Science, ADS, Google Scholar
R. Penrose , In Asymptotic Behavior of Mass and Spacetime Geometry , ed. J. F. Flaherty ( Springer , Berlin , 1984 ) . Google Scholar
A. Feinstein and J. B. Griffiths, Class. Quantum Grav. 11, L109 (1994), DOI: 10.1088/0264-9381/11/8/001. Crossref, Web of Science, Google Scholar
G. A. Alekseev and J. B. Griffiths, Class. Quantum Grav. 13, 2191 (1996), DOI: 10.1088/0264-9381/13/8/014. Crossref, Web of Science, ADS, Google Scholar
J. B. Griffiths , Colliding Plane Wave in General Relativity ( Oxford University Press , 1991 ) . Google Scholar
M. M. J. Senovilla and R. Vera, Class. Quantum Grav. 4, 3481 (1997), DOI: 10.1088/0264-9381/14/12/028. Google Scholar
J. Wainwright and J. B. Marshman, Phys. Lett. A 72, 275 (1979), DOI: 10.1016/0375-9601(79)90466-3. Crossref, Web of Science, ADS, Google Scholar