of the second order it's 8 mu nu minus h mu nu.

plus h mu alpha,

h alpha nu.

Also modulus of g at this order

is approximately 1+h

Plus one half H squared minus

one half H nu nu, H nu mu.

All in all, we can do, well,

this is the second order Now one can find also g,

the Ricci scalar, or Ricci tensor,

Ricci tensor in this approximation,

and the second order, to the second order,

looks quite tedious but it is like this,

it's one half H row sigma d mu d nu

h row sigma minus h row sigma d row d mu.

H nu alpha and symmetrized over the indices mu and nu.

Plus one quarter

of d mu h rho sigma d

nu h rho sigma plus

remaining terms also

quite tedious.

And hope we will fit into the board.

So, it's a d

sigma h rho mu

times d rho h g

sigma h rho mu.

And to symmetries over

this synthesis.Plus

one-half d sigma

(h rho sigma d rho h mu

nu)- one quarter

d rho H mu nu gyro of H,

and finally minus

D sigma H ro Sigma

minus one half zero

of h times d nu h nu

row zenith rise.

So, this is the Rehman Ritchie Scaler At the second

order to find these terms one has to day mind that

these terms are approximately the falling.

So, reach it turns to the second order

minus one half at the menu times r to

the second minus One half h mu nu times

a scaler to the first order.

After straight forward calculation one can.

Find that this quantity coincides

with models with 16 pi kappa times t mu nu.

As calculated from the expression that we have written for this for

quantity before in this lecture we have the next expression for this quantity.

If we substitute into that expression, this and

do the calculation of the second order, this will conside with this expression.

With the second order.

Here with the second order in h squared here.

So the meaning of this quantity is actually that it is nonlinear part,

if we consider linearized perturbations and

expand in powers of h, this is nonlinear part in h, so

it can be attributed to the right hand side Of the Einstein equations.

So now, one can easily understand the reason

why this quantity cannot be made tensorial.

You see, in the gravity, to specify what means energy flux, so

the flux through some distance surface we have to, first fix this surface.

To fix this surface we have to fix a background, so

we have to have a background and consider perturbations over this

background which carry the flux through that surface.

So we have to consider background and perturbations But

this separation on what means background and

what means preservation changes.

If we have caught in a transformation, this terms mix on the arbitrary.

Non infant decimal caught in it not necessary, non linearized.

Not such transformation, but Genetic.

We make an observation.

Then we have to separate again what means background and what means perturbations.

And this separation is ambiguous and

that's the reason this quantity it doesn't have tensorial properties.

And finally, one can see that under these transformations Under this transformations

this quantity transforms as a tanser under such linearized transformations.

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