Hyperscaling-violating Lifshitz solutions in cubic gravity

Considering the cubic theory of gravity which has been constructed in R. C. Myers and B. Robinson, J. High Energy Phys. 08 (2010); 067R. C. Myers and A. Sinha, Phys. Rev. D 82, 046006 (2010); R. C. Myers and A. Sinha, J. High Energy Phys. 01 (2011) 125, we study the existence of Lifshitz and hyperscaling-violating Lifshitz solutions. We first extend the black hole solution of R. C. Myers and B. Robinson, J. High Energy Phys. 08 (2010); 067R. C. Myers and A. Sinha, Phys. Rev. D 82, 046006 (2010); R. C. Myers and A. Sinha, J. High Energy Phys. 01 (2011) 125 and find that such extended solutions are valid for any value of dynamical exponent z. Next, we examine the existence of the AdS black hole solution with nonzero hyperscaling-violating exponent. and general dynamical exponent z. We find that the solutions do exist only for theta = 0, 2 in four dimensions and theta = 0, 3 in five dimensions. In particular, when theta = 2(3) in four (five) dimensions, we have Lifshitz and Schwarzschild-AdS black hole solutions for z = {0, 1}.