content_image/413050.jpg content_image/413054.jpg content_image/413062.jpg content_image/413056.jpg content_image/413047.jpg content_image/413049.jpg content_image/413063.jpg content_image/413048.jpg content_image/413053.jpg content_image/413055.jpg
are not invariant under the coordinate transformations (3.11). In particular, under these transformations, we have 

For spherically symmetric static solutions, the extra term δR$_{ij}$ in general gives rise to an anisotropic fluid with heat flow [38], possibly subjected to some energy conditions [31]. In particular, for the LMP solutions of Eqs. (3.1) and (3.21), the energy density J $^{t}$, defined by 

is given by the Hamiltonian equation, 

<img src='content_image/413050.jpg'>

where 

<img src='content_image/413054.jpg'>

where Δ is given by Eq. (3.22), and Δ ′ ≡ d Δ /dx . The quantity v , defined by 

which is related to heat flow [38], is given by 

<img src='content_image/413062.jpg'>

On the other hand, the corresponding stress part τ ij defined by, 

[1] P. Horava, JHEP, 0903 , 020 (2009) [arXiv:0812.4287]; Phys. Rev. D 79 , 084008 (2009) [arXiv:0901.3775]; and 

<img src='content_image/413056.jpg'>

<img src='content_image/413047.jpg'>

<img src='content_image/413049.jpg'>

<img src='content_image/413063.jpg'>

can be written in the form, 

<img src='content_image/413048.jpg'>

<img src='content_image/413053.jpg'>

with 

<img src='content_image/413055.jpg'>

Clearly, to interpret the above as an anisotropic fluid with heat flow, some energy conditions [31] might need to be imposed. Since in this paper we are mainly concerned with the nature of singularities, we shall not study these conditions here. 

Phys. Rev. Lett. 102 , 161301 (2009) [arXiv:0902.3657]. 

