%!PS-Adobe-2.0 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software %%Title: arXiv:gr-qc/0211072v1 22 Nov 2002 %%Pages: 7 %%PageOrder: Ascend %%BoundingBox: 0 0 612 792 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -R -P pk -K1 -z Cflattst.dvi -o %DVIPSParameters: dpi=600, compressed, comments removed %DVIPSSource: TeX output 2019.04.19:0752 %%BeginProcSet: texc.pro /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true 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b(along)h(the)j(axis)e(of)g(symmetry)h(is)f (considered)i(and)f(the)g(Cartan)g(torsion)328 4101 y(is)k(giv)m(en)h (in)f(terms)g(of)g(di\013eren)m(tial)f(forms)h(b)m(y)1589 4319 y Fh(T)1660 4278 y Ff(i)1715 4319 y Fl(=)c(2)p Fh(k)s(\033)t(\016) 2028 4278 y Ff(i)2024 4344 y Fk(0)2063 4319 y Fh(\022)2111 4278 y Fk(1)2151 4319 y Fg(^)p Fh(\022)2265 4278 y Fk(2)3441 4319 y Fl(\(8\))328 4538 y(where)e Fh(\033)k Fl(is)24 b(a)h(constan)m(t)h(spin)f(densit)m(y)-8 b(.)42 b(F)-8 b(or)25 b(computational)d(con)m(v)m(enience)27 b(w)m(e)g(addopt)328 4658 y(Soleng's)32 b(de\014nition)g([3)p (#reference.3) [[212 158 217 170] [1 1 1 [3 3]] [0 0 1]] pdfm (])g (for)g(the)h(R)m(C)h(rotation)c(\012)1596 4930 y(\012)e(:=)g Fg(\000)1912 4862 y Fl(1)p 1912 4906 49 4 v 1912 4998 a(2)1971 4930 y Fh(\033)e Fl(+)2160 4862 y Fh(M)2264 4826 y Fe(0)p 2160 4906 129 4 v 2176 4998 a Fl(2)p Fh(r)3441 4930 y Fl(\(9\))1922 5214 y(2)p eop %%Page: 3 3 3 2 bop 328 631 a Fl(where)34 b(\012)f(is)f(the)h(cylinder)f(R)m(C)h(v) m(orticit)m(y)-8 b(.)43 b(Cartan's)33 b(\014rst)g(structure)h(equation) e(is)1562 851 y Fh(T)1633 810 y Ff(i)1689 851 y Fl(=)27 b Fh(d\022)1891 810 y Ff(i)1941 851 y Fl(+)22 b Fh(!)2104 810 y Ff(i)2132 866 y(k)2174 851 y Fg(^)q Fh(\022)2289 810 y Ff(k)3392 851 y Fl(\(10\))328 1071 y(and)33 b(determines)h(the)g (connection)f(forms)g Fh(!)2005 1035 y Ff(i)2032 1086 y(j)2069 1071 y Fl(.The)h(conection)g(one-forms)e(are)i(giv)m(en)328 1191 y(b)m(y)1704 1312 y Fh(!)1769 1271 y Fk(0)1765 1336 y(1)1835 1312 y Fl(=)28 b Fg(\000)p Fl(\012)p Fh(!)2151 1271 y Fk(2)3392 1312 y Fl(\(11\))1742 1486 y Fh(!)1807 1445 y Fk(0)1803 1511 y(2)1874 1486 y Fl(=)f(\012)p Fh(!)2112 1445 y Fk(1)3392 1486 y Fl(\(12\))1805 1660 y Fh(!)1870 1619 y Fk(0)1866 1685 y(3)1936 1660 y Fl(=)h(0)1303 b(\(13\))1518 1879 y Fh(!)1583 1838 y Fk(1)1579 1904 y(2)1650 1879 y Fl(=)27 b Fg(\000)p Fl(\012)p Fh(!)1965 1838 y Fk(0)2027 1879 y Fg(\000)c Fl(\()2175 1812 y(1)p 2175 1856 49 4 v 2176 1948 a Fh(r)2234 1879 y Fl(\))p Fh(!)2337 1838 y Fk(2)3392 1879 y Fl(\(14\))328 2079 y(while)32 b(others)h(v)-5 b(anish.)43 b(F)-8 b(rom)31 b(the)i(Cartan's)g(second)h(structure)g (equation)1489 2299 y Fh(R)1564 2258 y Ff(i)1592 2314 y(j)1656 2299 y Fl(=)28 b Fh(d!)1876 2258 y Ff(i)1903 2314 y(j)1962 2299 y Fl(+)22 b Fh(!)2125 2258 y Ff(i)2152 2314 y(k)2195 2299 y Fg(^)p Fh(!)2326 2258 y Ff(k)2368 2314 y(j)3392 2299 y Fl(\(15\))328 2519 y(where)38 b(the)e(curv)-5 b(ature)38 b(R)m(C)e(forms)g Fh(R)1749 2483 y Ff(i)1777 2534 y(j)1848 2519 y Fl(=)e Fh(R)2033 2483 y Ff(i)2061 2534 y(j)t(k)r(l)2158 2519 y Fh(\022)2206 2483 y Ff(k)2249 2519 y Fg(^)p Fh(\022)2363 2483 y Ff(l)2426 2519 y Fl(where)k Fh(R)2787 2483 y Ff(i)2815 2534 y(j)t(k)r(l)2948 2519 y Fl(is)e(the)h(R)m(C)g(cur-)328 2639 y(v)-5 b(ature)31 b(tensor.)43 b(This)31 b(is)f(accomplished)g(b)m(y)i(computing)d(the)j (R)m(C)f(curv)-5 b(ature)31 b(comp)s(o-)328 2760 y(nen)m(ts)j(from)d (the)i(Cartan)g(structure)h(equations)e(as)1695 2980 y Fh(R)1769 2995 y Fk(0101)1942 2980 y Fl(=)27 b(\012)2115 2939 y Fk(2)2155 2980 y Fh(;)1210 b Fl(\(16\))1703 3200 y Fh(R)1777 3215 y Fk(0112)1950 3200 y Fl(=)28 b(\012)2124 3159 y Fe(0)2147 3200 y Fh(;)1218 b Fl(\(17\))1695 3374 y Fh(R)1769 3389 y Fk(0202)1942 3374 y Fl(=)27 b(\012)2115 3333 y Fk(2)2155 3374 y Fh(;)1210 b Fl(\(18\))1703 3548 y Fh(R)1777 3563 y Fk(1201)1950 3548 y Fl(=)28 b(\012)2124 3507 y Fe(0)2147 3548 y Fh(;)1218 b Fl(\(19\))1523 3723 y Fh(R)1597 3738 y Fk(1212)1770 3723 y Fl(=)28 b(3\012)1993 3682 y Fk(2)2055 3723 y Fg(\000)22 b Fl(2\012)p Fh(\033)n(;)1039 b Fl(\(20\))328 3897 y(others)38 b(zero.)57 b(The)38 b(dash)g(here)f(represen)m(ts)j(the)d(deriv)-5 b(ativ)m(e)37 b Fh(w)s(:r)m(:t)g Fl(to)g(the)g(radial)e(co-)328 4018 y(ordinate)g Fh(r)s Fl(.)51 b(F)-8 b(rom)34 b(the)i(curv)-5 b(ature)36 b(expressions)i(ab)s(o)m(v)m(e)e(it)e(is)h(p)s(ossible)g(to) g(built)f(the)328 4138 y(ECM)g(\014eld)e(equations)h(as)1710 4258 y Fh(G)1787 4217 y Ff(i)1815 4273 y(k)1885 4258 y Fl(=)28 b Fh(k)s(T)2114 4217 y Ff(i)2142 4273 y(k)3392 4258 y Fl(\(21\))328 4433 y(where)23 b Fh(G)676 4397 y Ff(i)704 4448 y(k)768 4433 y Fl(is)f(the)g(Einstein-Cartan)f(tensor)h (and)g Fh(T)2246 4397 y Ff(i)2274 4448 y(k)2338 4433 y Fl(is)f(the)i(total)d(energy-momen)m(tum)328 4553 y(tensor)38 b(comp)s(osed)g(of)g(the)g(\015uid)f(tensor)i Fh(T)1966 4517 y Ff(i)1993 4568 y(k)2073 4553 y Fl(=)d(\()p Fh(\032;)17 b(p)2366 4568 y Ff(r)2404 4553 y Fh(;)g Fl(0)p Fh(;)g(p)2590 4568 y Ff(z)2629 4553 y Fl(\))38 b(and)f(the)i(electromag-)328 4673 y(netic)32 b(\014eld)h(tensor)1297 4813 y Fh(t)1332 4772 y Ff(i)1361 4828 y(k)1431 4813 y Fl(=)27 b(\()p Fh(F)1649 4772 y Ff(i)1677 4828 y(l)1703 4813 y Fh(F)1780 4772 y Ff(l)1806 4828 y(k)1871 4813 y Fg(\000)1980 4746 y Fl(1)p 1980 4790 V 1980 4882 a(2)2039 4813 y Fh(\016)2086 4772 y Ff(i)2082 4838 y(k)2125 4813 y Fl(\()p Fh(E)2241 4772 y Fk(2)2303 4813 y Fg(\000)22 b Fh(B)2481 4772 y Fk(2)2521 4813 y Fl(\)\))795 b(\(22\))1922 5214 y(3)p eop %%Page: 4 4 4 3 bop 328 631 a Fl(where)43 b Fh(F)682 646 y Fk(0)p Ff(\015)804 631 y Fl(corresp)s(ond)g(to)e(the)i(electric)e(\014eld)2197 606 y Fh(~)2182 631 y(E)48 b Fl(while)41 b Fh(F)2629 646 y Ff(\013\014)2763 631 y Fl(comp)s(onen)m(ts)i(of)e(the)328 763 y(Maxw)m(ell)24 b(tensor)h(\014eld)f Fh(F)1258 778 y Ff(ij)1343 763 y Fl(corresp)s(ond)h(to)f(the)h(magnetic)e(\014eld) 2730 738 y Fh(~)2714 763 y(B)5 b Fl(.)41 b(Here)25 b(w)m(e)g(consider) 328 884 y(that)35 b(the)g(electric)f(\014eld)h(v)-5 b(anishes)36 b(along)d(the)i(cylinder,)h(and)f Fh(\013)28 b Fl(=)g(1)p Fh(;)17 b Fl(2)p Fh(;)g Fl(3)n(.)51 b(Th)m(us)36 b(the)328 1004 y(natural)42 b(notation)g Fh(E)1159 968 y Fk(2)1245 1004 y Fl(=)k(\()1420 979 y Fh(~)1405 1004 y(E)6 b Fl(\))1521 968 y Fk(2)1603 1004 y Fl(and)44 b(the)g(same)f(is)g(v)-5 b(alid)41 b(for)i(the)h(magnetic)e(\014eld.)328 1124 y(Th)m(us)34 b(explicitly)d(the)i(ECM)h(equations)e(read)1382 1378 y Fg(\000)22 b Fl(3\012)1600 1337 y Fk(2)1662 1378 y Fg(\000)h Fh(\033)t Fl(\012)28 b(=)f Fg(\000)p Fh(k)s Fl(\()p Fh(\032)c Fl(+)2372 1311 y Fh(B)2446 1326 y Ff(z)p 2372 1355 114 4 v 2405 1446 a Fl(2)2496 1378 y(\))858 b(\(23\))1590 1681 y(\012)1660 1640 y Fk(2)1728 1681 y Fl(=)27 b Fh(k)s Fl(\()p Fh(p)1972 1696 y Ff(r)2032 1681 y Fg(\000)2142 1613 y Fh(B)2216 1628 y Ff(z)p 2142 1657 V 2174 1749 a Fl(2)2266 1681 y(\))1088 b(\(24\))1810 1885 y(\012)1880 1844 y Fe(0)1931 1885 y Fl(=)28 b(0)1308 b(\(25\))1426 2104 y(\012)1496 2063 y Fk(2)1558 2104 y Fl(+)22 b Fh(\033)t Fl(\012)29 b(=)e Fg(\000)p Fh(k)s Fl(\()p Fh(p)2135 2119 y Ff(z)2198 2104 y Fl(+)2306 2037 y Fh(B)2380 2052 y Ff(z)p 2306 2081 V 2338 2172 a Fl(2)2429 2104 y(\))925 b(\(26\))328 2306 y(Note)51 b(that)h(equation)f(\(25)p (#equation.25) [[224 440 236 452] [1 1 1 [3 3]] [0 0 1]] pdfm (\))f (is)h(the)h(simplest)e(to)h(solv)m(e)h(and)g(yields)f(\012)60 b(=)f(\012)3390 2321 y Fk(0)3490 2306 y Fl(=)328 2426 y Fh(constant)p Fl(.)80 b(Therefore)46 b(so)e(far)g(just)h(from)e(the)i (ECM)h(\014eld)e(equations)h(w)m(e)h(cannot)328 2546 y(sa)m(y)36 b(that)f(the)h(cylinder)e(is)h(static.)51 b(Before)35 b(pro)s(ceed)h(therefore)g(it)e(is)h(useful)g(to)g(sho)m(w) 328 2667 y(that)43 b(this)h(results)g(from)e(the)j(Arkuszewski-Kop)s (czynski-P)m(onomariev)g(\(AKP\))f([6)p (#reference.6) [[491 397 497 409] [1 1 1 [3 3]] [0 0 1]] pdfm (])328 2787 y(junction)35 b(conditions)f(for)h(Einstein-Cartan)f(gra)m(vit)m (y)h(whic)m(h)h(matc)m(h)f(an)g(in)m(terior)f(so-)328 2907 y(lution)g(of)h(ECM)h(\014eld)g(equations)f(to)h(the)g(exterior)f (v)-5 b(acuum)35 b(solution)f(giv)m(en)i(b)m(y)g(the)328 3028 y(geometry)c(giv)m(en)h(b)m(y)h(expression)f(\(3)p (#equation.3) [[270 354 276 366] [1 1 1 [3 3]] [0 0 1]] pdfm (\).)44 b(The)33 b(AKP)g(conditions)f(are)1436 3239 y Fh(g)1483 3254 y Ff(ij;r)1593 3239 y Fg(j)1621 3254 y Fk(+)1708 3239 y Fl(=)27 b Fh(g)1858 3254 y Ff(ij;r)1968 3239 y Fg(j)1996 3254 y Fe(\000)2077 3239 y Fg(\000)22 b Fl(2)p Fh(K)2308 3254 y Ff(r)r Fk(\()p Ff(ij)t Fk(\))3392 3239 y Fl(\(27\))328 3450 y(for)32 b(\()p Fh(i;)17 b(j)6 b Fl(\))32 b(distinct)g(from)f(the)i(r)g(co)s(ordinate,)f(where)h(the)g (con)m(tortion)f(tensor)h(is)1363 3705 y Fh(K)1446 3720 y Ff(ij)t(k)1572 3705 y Fl(=)1686 3637 y(1)p 1686 3682 49 4 v 1686 3773 a(2)1745 3705 y(\()p Fh(T)1840 3720 y Ff(j)t(ik)1961 3705 y Fl(+)22 b Fh(T)2116 3720 y Ff(j)t(k)r(i)2237 3705 y Fg(\000)h Fh(T)2394 3720 y Ff(ij)t(k)2493 3705 y Fl(\))861 b(\(28\))328 3941 y(where)34 b Fh(T)667 3956 y Ff(j)t(ik)800 3941 y Fl(is)f(the)h(Cartan)f(torsion.)45 b(The)34 b(plus)f(and)h(min)m(us)f(signs)g(here)h(corresp)s(ond)328 4061 y(resp)s(ectiv)m(ely)h(to)e(the)h(exterior)g(and)g(in)m(terior)e (spacetimes)i(resp)s(ectiv)m(ely)-8 b(.)48 b(The)35 b(others)328 4182 y(AKP)26 b(conditions)f(state)h(that)f(the)h(\015uid)g(elemen)m (ts)g(do)f(not)h(mo)m(v)m(e)g(across)g(the)g(junction)328 4302 y(surface,)33 b(the)g(stress)i(normal)30 b(to)i(the)h(junction)g (surface)g(v)-5 b(anishes)33 b(and)g(that)1687 4513 y Fh(g)1734 4528 y Ff(ij)1795 4513 y Fg(j)1823 4528 y Fk(+)1909 4513 y Fl(=)27 b Fh(g)2059 4528 y Ff(ij)2120 4513 y Fg(j)2148 4528 y Fe(\000)3392 4513 y Fl(\(29\))328 4724 y(whic)m(h)39 b(is)f(the)h(general)f(relativistic)e(Lic)m(hnero)m(wicz)k(condition.) 60 b(F)-8 b(rom)37 b(the)i(cylinder)328 4844 y(geometry)32 b(one)h(obtains)1676 4965 y Fh(g)1723 4980 y Ff(t\036)1795 4965 y Fg(j)1823 4980 y Fk(+)1909 4965 y Fl(=)27 b Fh(g)2059 4980 y Ff(t\036)2131 4965 y Fg(j)2159 4980 y Fe(\000)3392 4965 y Fl(\(30\))1922 5214 y(4)p eop %%Page: 5 5 5 4 bop 1660 631 a Fh(g)1707 646 y Ff(\036\036)1795 631 y Fg(j)1823 646 y Fk(+)1909 631 y Fl(=)27 b Fh(g)2059 646 y Ff(\036\036)2147 631 y Fg(j)2175 646 y Fe(\000)3392 631 y Fl(\(31\))1481 803 y Fh(g)1528 818 y Ff(t\036;r)1652 803 y Fg(j)1680 818 y Fk(+)1767 803 y Fl(=)g Fh(g)1917 818 y Ff(t\036;r)2042 803 y Fg(j)2070 818 y Fe(\000)2151 803 y Fg(\000)22 b Fh(T)2307 818 y Ff(tr)r(\036)3392 803 y Fl(\(32\))1432 974 y Fh(g)1479 989 y Ff(\036\036;r)1620 974 y Fg(j)1648 989 y Fk(+)1734 974 y Fl(=)28 b Fh(g)1885 989 y Ff(\036\036;r)2026 974 y Fg(j)2054 989 y Fe(\000)2135 974 y Fg(\000)22 b Fl(2)p Fh(T)2340 989 y Ff(\036r)r(\036)3392 974 y Fl(\(33\))328 1146 y(whic)m(h)41 b(for)f(the)h(exrerior)f(and)g (in)m(terior)f(of)h(the)h(cylinder)f(matc)m(hing)f(at)h Fh(r)k Fl(=)d Fh(R)g Fl(one)328 1266 y(obtains)1728 1386 y Fh(a)28 b Fl(=)f Fh(M)10 b Fl(\()p Fh(R)q Fl(\))1227 b(\(34\))1435 1558 y Fh(B)1514 1517 y Fk(2)1553 1558 y Fl(\()p Fh(R)23 b Fl(+)f Fh(r)1830 1573 y Fk(0)1870 1558 y Fl(\))1908 1517 y Fk(2)1975 1558 y Fl(=)27 b Fh(R)2153 1517 y Fk(2)2215 1558 y Fg(\000)c Fh(M)2419 1517 y Fk(2)3392 1558 y Fl(\(35\))1572 1783 y(\012)1642 1798 y Fk(0)1709 1783 y Fl(=)28 b Fg(\000)1900 1715 y Fl(1)p 1900 1759 49 4 v 1900 1851 a(2)1959 1783 y Fh(\033)2014 1798 y Fk(0)2076 1783 y Fl(+)2184 1715 y Fh(M)2288 1679 y Fe(0)p 2184 1759 129 4 v 2186 1851 a Fl(2)p Fh(R)3392 1783 y Fl(\(36\))1647 1989 y(0)f(=)h Fh(\033)1882 2004 y Fk(0)1922 1989 y Fh(R)23 b Fg(\000)g Fh(M)2223 1947 y Fe(0)3392 1989 y Fl(\(37\))1232 2160 y Fh(B)1311 2119 y Fk(2)1351 2160 y Fl(\()p Fh(R)g Fl(+)f Fh(r)1628 2175 y Fk(0)1668 2160 y Fl(\))27 b(=)h Fh(R)23 b Fg(\000)g Fh(M)10 b(M)2242 2119 y Fe(0)2289 2160 y Fl(+)22 b Fh(M)10 b(R)q(\033)2621 2175 y Fk(0)3392 2160 y Fl(\(38\))328 2332 y(Substitution)35 b(of)g Fh(M)1108 2296 y Fe(0)1168 2332 y Fl(ab)s(o)m(v)m(e)h(in)m(to)f (expression)i(\(36)p (#equation.36) [[331 437 343 449] [1 1 1 [3 3]] [0 0 1]] pdfm (\))e (yields)g(the)h(desired)g(result)g(that)328 2452 y(the)27 b(Riemann-Cartan)e(rotation)g(\012)i(v)-5 b(anishes.)42 b(The)27 b(remaining)e(junction)h(conditions)328 2572 y([7)p (#reference.7) [[115 408 120 420] [1 1 1 [3 3]] [0 0 1]] pdfm (])32 b(yield)1635 2741 y Fh(B)1714 2700 y Fk(2)1781 2741 y Fl(=)2034 2674 y Fh(R)p 1895 2718 355 4 v 1895 2809 a Fl(\()p Fh(R)23 b Fl(+)f Fh(r)2172 2824 y Fk(0)2211 2809 y Fl(\))3392 2741 y(\(39\))1525 3029 y Fh(\033)1580 3044 y Fk(0)1647 3029 y Fl(=)1774 2962 y(4)p 1761 3006 76 4 v 1761 3098 a Fh(R)1846 3029 y Fl([1)g Fg(\000)2053 2962 y Fh(R)i Fl(+)e Fh(r)2293 2977 y Fk(0)p 2053 3006 279 4 v 2155 3098 a Fh(R)2342 3029 y Fl(])1023 b(\(40\))328 3226 y(Substitution)47 b(of)h(these)i(results)e(in)m(to)g(the)h (exterior)f(metric)f(yields)h(the)g(follo)m(wing)328 3347 y(exterior)32 b(spacetime)h(for)f(the)h(spin)f(p)s(olarised)f (cylinder)492 3614 y Fh(ds)589 3573 y Fk(2)656 3614 y Fl(=)c Fg(\000)p Fh(dt)922 3573 y Fk(2)984 3614 y Fg(\000)c Fl(2)p Fh(\033)1188 3629 y Fk(0)1228 3614 y Fh(R)1303 3573 y Fk(2)1342 3614 y Fh(dtd\036)f Fl(+)g Fh(dr)1755 3573 y Fk(2)1815 3614 y Fl(+)g Fh(R)q Fl(\()2036 3546 y(\()p Fh(r)j Fl(+)d Fh(r)2285 3561 y Fk(0)2325 3546 y Fl(\))2363 3510 y Fk(2)p 2036 3591 366 4 v 2080 3682 a Fh(R)h Fl(+)f Fh(r)2319 3697 y Fk(0)2434 3614 y Fg(\000)h Fh(\033)2589 3629 y Fk(0)2629 3573 y(2)2668 3614 y Fh(R)2743 3573 y Fk(3)2783 3614 y Fl(\))p Fh(d\036)2930 3573 y Fk(2)2990 3614 y Fl(+)f Fh(dz)3188 3573 y Fk(2)3392 3614 y Fl(\(41\))328 3868 y(No)m(w)33 b(going)e(bac)m(k)j(to)e(the)h(ECM)h (equations)f(w)m(e)g(obtain)f(the)h(follo)m(wing)d(constrain)m(ts)1789 4124 y Fh(\032)e Fl(=)1981 4056 y Fh(B)2055 4071 y Ff(z)p 1981 4101 114 4 v 2013 4192 a Fl(2)3392 4124 y(\(42\))328 4363 y(whic)m(h)41 b(states)g(that)f(the)g(energy)h(densit)m(y)g(is)f (purely)g(of)g(magnetic)f(origin.)64 b(Besides)328 4483 y(to)34 b(k)m(eep)j(the)e(stabilit)m(y)e(of)i(the)g(spin)g(p)s (olarised)e(cylinder)i(and)g(its)f(static)g(nature)h(one)328 4604 y(obtains)28 b(that)g(the)h(radial)e(pressure)j Fh(p)1735 4619 y Ff(r)1801 4604 y Fh(>)d Fl(0)h(while)g(the)h(axial)e (pressure)j(is)e(negativ)m(e)h(or)328 4724 y Fh(p)377 4739 y Ff(z)444 4724 y Fh(<)f Fl(0.)42 b(Indeed)31 b(from)d(the)i (\014eld)f(equations)h(w)m(e)h(obtain)d Fh(p)2504 4739 y Ff(z)2571 4724 y Fl(=)g Fg(\000)2762 4685 y Ff(B)2815 4693 y Fd(z)2851 4660 y Fc(2)p 2762 4701 124 4 v 2807 4758 a Fk(2)2925 4724 y Fl(while)h Fh(p)3226 4739 y Ff(r)3292 4724 y Fl(=)3405 4685 y Ff(B)3458 4693 y Fd(z)3494 4660 y Fc(2)p 3405 4701 V 3449 4758 a Fk(2)3539 4724 y Fl(.)328 4844 y(Ph)m(ysically)36 b(this)f(is)h(in)f(accordance)i(with)f(the)g (fact)g(that)g(the)h(radial)d(stresses)k(,)f(here)328 4965 y(including)31 b(the)j(magnetic)e(stress)j(\()p Fh(T)1715 4929 y Fk(1)1701 4989 y(1)1754 4965 y Fl(\))e(m)m(ust)g(v)-5 b(anish)33 b(at)g(the)h(cylinder)f(surface.)46 b(The)1922 5214 y(5)p eop %%Page: 6 6 6 5 bop 328 631 a Fl(heat)27 b(\015o)m(w)g(also)e(v)-5 b(anishes)28 b(whic)m(h)f(in)e(the)i(ECM)h(\014eld)e(equations)h (implies)d(that)i(the)h(R)m(C)328 751 y(rotation)37 b(m)m(ust)j(b)s(e)f (in)f(principle)g(constan)m(t.)63 b(Ph)m(ysical)39 b(applications)e(of) i(the)g(mo)s(del)328 872 y(discuss)33 b(here)h(ma)m(y)e(b)s(e)g(in)g (the)h(in)m(v)m(estigation)e(of)g(the)i(gra)m(vitational)c(extra)k (e\013ects)h(on)328 992 y(the)42 b(w)m(ell-kno)m(wn)h(Einstein-de)e (Haas)h(e\013ect)h(due)g(to)f(the)g(non-Riemannian)d(e\013ects)328 1112 y(from)34 b(the)i(spin)f(densit)m(y)-8 b(.)53 b(Unfortunatly)35 b(due)h(to)f(the)h(fact)f(that)g(the)h(magnetic)e(\014eld)328 1233 y(is)39 b(strong)h(for)e(the)i(most)f(kno)m(wn)i(ferrimagnetic)d (comp)s(ounds)h(on)h(Earth)f(lab)s(orato-)328 1353 y(ries,suc)m(h)h(as) f(HoF)-8 b(e)38 b([8)p (#reference.8) [[209 555 215 567] [1 1 1 [3 3]] [0 0 1]] pdfm (])h(w)m (e)h(w)m(ould)e(ha)m(v)m(e)i(to)e(shield)h(some)f(magnetic)f(e\013ects) j(in)e(the)328 1474 y(cylinder)30 b(to)h(b)s(e)g(able)f(to)h(detect)h (torsion)e(e\013ects)i(on)e(a)h(torsion)f(balance)g(exp)s(erimen)m(t.) 328 1594 y(Ho)m(w)m(ev)m(er)36 b(since)e(the)g(presence)h(of)e (magnetic)g(\014elds)h(w)m(ould)f(b)s(e)h(alw)m(a)m(ys)g(presen)m(t)h (ev)m(en)328 1714 y(for)27 b(some)h(sup)s(erconductors)i(our)e(mo)s (del)f(seems)i(to)e(b)s(e)i(a)f(more)f(realistic)f(geometrical)328 1835 y(mo)s(del)d(that)i(could)g(b)s(e)h(used)g(in)e(the)i(LAB.)f (Another)h(p)s(ossibilit)m(y)d(is)i(to)f(use)j(this)d(mo)s(del)328 1955 y(to)31 b(in)m(v)m(estigate)h(mo)s(dels)f(of)g(spinning)g(strings) h(in)f(sup)s(er\015uids)h(and)g(\014nding)g(solutions)328 2076 y(of)i(Einstein-Cartan)f(theory)i(for)f(neutron)h(stars)g(with)f (sup)s(er\015uid)h(mo)s(dels.)48 b(P)m(art)34 b(of)328 2196 y(this)g(pro)5 b(ject)35 b(ha)m(v)m(e)g(already)f(b)s(egun)h(with) f(the)h(in)m(v)m(estigation)e(of)g(phonon)i(scattering)328 2316 y(in)d(sup)s(er\015uids)h([9)p (#reference.9) [[187 439 193 451] [1 1 1 [3 3]] [0 0 1]] pdfm (])g(in) f(torsioned)g(spacetime)g(where)i(holonom)m(y)d(w)m(as)j(computed.)328 2520 y Fb(Ac)m(kno)m(wledgemen)m(ts)328 2723 y Fl(I)c(w)m(ould)f(lik)m (e)g(to)h(thank)g(Professors)h(H.Soleng)e(and)h(P)-8 b(.S.Letelier)30 b(for)f(helpful)f(discus-)328 2844 y(sions)34 b(on)h(the)g(sub)5 b(ject)36 b(of)e(this)h(pap)s(er.I)g(also)e(thank)i (m)m(y)g(daugh)m(ter)g(Maria)f(Carolina)328 2964 y(Pires)29 b(de)h(Andrade)g(for)e(her)i(patience)f(while)f(this)h(w)m(ork)h(w)m (as)g(carried)e(out.)43 b(Financial)328 3084 y(supp)s(ort)33 b(from)e(CNPq.)45 b(and)33 b(UERJ)g(\()p Fh(P)14 b(r)s(ociencia)p Fl(\))32 b(is)g(gratefully)f(ac)m(kno)m(wledged.)1922 5214 y(6)p eop %%Page: 7 7 7 6 bop 328 631 a Fa(References)328 850 y Fl([1])49 b(L.C.Garcia)31 b(de)i(Andrade,Class.)h(Quan)m(tum)e(Gra)m(vit)m(y)h(\(2001\))e (18,3097.)328 1053 y([2])49 b(M.L.Bedran)24 b(and)g(L.C.Garcia)f(de)h (Andrade,Prog.Theor.Ph)m(ys.\(1983\)12,1583.)328 1257 y([3])49 b(H.Soleng,Class.)32 b(and)h(Quan)m(t.)g(Gra)m(vit)m(y)f (7,\(1990\),999.)328 1460 y([4])49 b(C.L\177)-49 b(ammerzahl,Ph)m (ys.Lett.)33 b(A)g(228)f(\(1997\)223.)328 1664 y([5])49 b(H.)32 b(Soleng,)g(Gen.)h(Rel.)f(and)h(Gra)m(vitation)d(\(1992\))i (24,1,111.)328 1867 y([6])49 b(W.)40 b(Arkuszewski,)45 b(W.)c(Kop)s(czynski)h(and)e(V.N.)h(P)m(onomariev,)h(Comm.)d(Math.)480 1987 y(Ph)m(ys.\(1975\)45,183.)328 2191 y([7])49 b(A.)32 b(Beessange,Class.)j(and)e(Quan)m(tum)f(Gra)m(vit)m(y)h(\(2000\))e (17,2509.)328 2394 y([8])49 b(Li-Shing)24 b(Hou)i(and)h(W)-8 b(ei-tou)25 b(Ni,Rotatable)g(torsion)g(balance)h(equiv)-5 b(alence)27 b(prin-)480 2515 y(ciple)k(exp)s(erimen)m(t)i(for)f(spin-p) s(olarised,Mo)s(d.)f(Ph)m(ys.)j(Lett.)f(A)g(\(2000\).)328 2718 y([9])49 b(C.)31 b(F)-8 b(urtado,)31 b(Garcia)f(de)i(Andrade,)g (A.)g(M.)f(Carv)-5 b(alho)31 b(and)g(F.)g(Moraes,)h(Phonon)480 2838 y(scattering)g(in)g(sup)s(er\015uids,)h(in)f(preparation.)1922 5214 y(7)p eop %%Trailer end end userdict /end-hook known{end-hook}if %%EOF