Mètrica d'Alcubierre: diferència entre les revisions
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Pàgina nova, amb el contingut: «Fitxer:Alcubierre.png|thumbnail|350px|right|Gràfic de la impulsió d'Alcubierre, mostrant les regions oposades, contreta i estesa, de l'espai-temps que fa...». |
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Línia 68:
<math>ds^2 = -\left(\alpha^2- \beta_i \beta^i\right)\,dt^2+2 \beta_i \,dx^i\, dt+ \gamma_{ij}\,dx^i\,dx^j</math>
On <math>\alpha</math> és la funció que per defecte aporta l'interval de temps convenient entre les hipersuperfícies veïnes, <math>\beta ^i</math> és el [[Vector (física)|vector]] connector que relaciona els sistemes espacials coordenats en les diverses hipersuperficies i sent <math>\ Gamma_ {ij}</math> una [[mètrica]] positivament definida en cadascuna de les hipersuperfícies. La forma particular que Alcubierre va estudiar el 1994 és definida per:
:<math>\alpha=1\,</math>
Línia 85:
:<math>r_s(t)=[(x-x_s(t))^2+y^2+z^2]^{\frac{1}{2}}</math>
i
:<math>f(r_s)=\frac{\tanh(\sigma (r_s + R))-\tanh(\sigma (r_s - R))}{2 \tanh(\sigma R)}</math>
Línia 96:
:<math>-\frac{c^4}{8 \pi G} \frac{v_s^2 (x^2+y^2)}{4 g^2 r_s ^2} \left(\frac{df}{dr_s}\right)^2</math>
D <math>g</math> is the determinant of the metric [[tensor]]. Thus, as the energy density is negative, one needs [[exotic matter]] to travel faster than the speed of light'.<ref name="Christopher Pike" /> The existence of exotic matter is not theoretically ruled out, the [[Casimir effect]] and the [[Accelerating Universe]] both lends support to the proposed existence of such matter. However, generating enough exotic matter and sustaining it to perform feats such as faster-than-light travel (and also to keep open the 'throat' of a [[wormhole]]) is thought to be impractical. Low has argued that within the context of general relativity, it is impossible to construct a warp drive in the absence of exotic matter.<ref>{{cite journal | autor=Low, Robert J. | title=Speed Limits in General Relativity | pub-periódica=Class. Quant. Grav. | año=1999 | volumen=16 | páginas=543-549}} See also the {{Cita web | title=eprint version | work=arXiv | url=http://www.arxiv.org/abs/gr-qc/9812067 | accessmonthday=30 June | añoacceso=2005}}</ref> It is generally believed that a consistent theory of [[quantum gravity]] will resolve such issues once and for all.
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