# Conformal Killing vectors in Robertson-Walker spacetimes

Research output: Contribution to journal › Article

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**Conformal Killing vectors in Robertson-Walker spacetimes.** / Maartens, R.; Maharaj, S. D.

Research output: Contribution to journal › Article

### Harvard

*Classical and Quantum Gravity*, vol. 3, no. 5, 027, pp. 1005-1011. https://doi.org/10.1088/0264-9381/3/5/027

### APA

*Classical and Quantum Gravity*,

*3*(5), 1005-1011. [027]. https://doi.org/10.1088/0264-9381/3/5/027

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TY - JOUR

T1 - Conformal Killing vectors in Robertson-Walker spacetimes

AU - Maartens, R.

AU - Maharaj, S. D.

PY - 1986/12/1

Y1 - 1986/12/1

N2 - It is well known that Robertson-Walker spacetimes admit a conformal Killing vector normal to the spacelike homogeneous hypersurfaces. Because these spacetimes are conformally flat, there are a further eight conformal Killing vectors, which are neither normal nor tangent to the homogeneous hypersurfaces. The authors find these further conformal Killing vectors and the Lie algebra of the full G15 of conformal motions. Conditions on the metric scale factor are determined which reduce some of the conformal Killing vectors to homothetic Killing vectors or Killing vectors, allowing the authors to regain in a unified way the known special geometries. The non-normal conformal Killing vectors provide a counter-example to show that conformal motions do not, in general, map a fluid flow conformally. They also use these non-normal vectors to find the general solution of the null geodesic equation and photon Liouville equation.

AB - It is well known that Robertson-Walker spacetimes admit a conformal Killing vector normal to the spacelike homogeneous hypersurfaces. Because these spacetimes are conformally flat, there are a further eight conformal Killing vectors, which are neither normal nor tangent to the homogeneous hypersurfaces. The authors find these further conformal Killing vectors and the Lie algebra of the full G15 of conformal motions. Conditions on the metric scale factor are determined which reduce some of the conformal Killing vectors to homothetic Killing vectors or Killing vectors, allowing the authors to regain in a unified way the known special geometries. The non-normal conformal Killing vectors provide a counter-example to show that conformal motions do not, in general, map a fluid flow conformally. They also use these non-normal vectors to find the general solution of the null geodesic equation and photon Liouville equation.

UR - http://www.scopus.com/inward/record.url?scp=0001463208&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/3/5/027

DO - 10.1088/0264-9381/3/5/027

M3 - Article

AN - SCOPUS:0001463208

VL - 3

SP - 1005

EP - 1011

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 5

M1 - 027

ER -

ID: 11642106