Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Linearization stability results and active measurements for the
  Einstein-scalar field equations   We study the Einstein equations coupled with the scalar field equations,
$\hbox{Ein}(g)=T$, $T=T(g,\phi)+F^1$, and $\square_g\phi^\ell-m^2\phi^\ell=
F^2$, where the sources $F=(F^1, F^2)$ correspond to perturbations of the
physical fields which we control. Here $\phi=(\phi^\ell)_{\ell=1}^L$ and
$(M,g)$ is a 4-dimensional globally hyperbolic Lorentzian manifold. The sources
$F$ need to be such that the fields $(g,\phi,F)$ satisfy the conservation law
$\hbox{div}_g(T)=0$. If $(g_\epsilon,\phi_\epsilon)$ solves the above
equations, $\dot g=\partial_\epsilon g_\epsilon|_{\epsilon=0}$,
$\dot\phi=\phi_\epsilon|_{\epsilon=0}$, and $f=(f^1,f^2)= \partial_\epsilon
F_\epsilon|_{\epsilon=0}$ solve the linearized Einstein equations and the
linearized conservation law $$ \frac 12 \hat g^{pk}\hat \nabla_p f^1_{kj}+
\sum_{\ell=1}^L f^2_\ell \, \partial_j\hat\phi_\ell=0, $$ where $\hat g=
g_\epsilon|_{\epsilon=0}$ and $\hat \phi= \phi_\epsilon|_{\epsilon=0}$. Then
$(\hat g,\hat \phi)$ and $f$ have the linearization stability property. Here
ask the converse: If $\dot g$, $\dot \phi$, and $f$ solve the linearized
Einstein equations and the linearized conservation law, are there
$F_\epsilon=(F^1_\epsilon,F^2_\epsilon)$ and $(g_\epsilon,\phi_\epsilon)$
depending on $\epsilon\in [0,\epsilon_0)$, $\epsilon_0>0$, such that
$(g_\epsilon,\phi_\epsilon)$ solves the Einstein-scalar field equations and the
conservation law. When $\hat g$ and $\hat \phi$ vary enough and $L\geq 5$, we
prove a microlocal version of this: When $Y\subset M$ is a 2-surface and
$(y,\eta)\in N^*Y$, there is $f$ that is a conormal distibutions wrt. the
surface $Y$ with a given principal symbol at $(y,\eta)$ such that $(\hat g,\hat
\phi)$ and $f$ have the linearization stability property.

29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: econ
3
The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph