Universal temperature corrections to the free energy for the gravitational field

G. E. Volovik^{*}, A. Zelnikov^{+}

^{*}Low Temperature Laboratory, Helsinki University of Technology , FIN-02015 HUT, Finland

^{*}L. D. Landau Institute for Theoretical Physics RAS, 117334 Moscow, Russia

^{+}Theoretical Physics Institute, University of Alberta Edmonton, Alberta, Canada T6G 2J1

^{+}P. N. Lebedev Physics Institute RAS, 119991 Moscow, Russia

PACS: 04.62.+v, 05.30.-d, 67.90.+z

**Abstract**
The temperature correction to the free energy of the gravitational
field is considered which does not depend on the Planck energy physics. The
leading correction may be interpreted in terms of the temperature dependent
effective gravitational constant G_{ eff}. The temperature correction
to G_{ eff}^{-1} appears to be valid for all temperatures . It is universal since it is determined only by the number of
fermionic and
bosonic fields with masses , does not contain the Planck
energy scale E_{ Planck} which determines the gravitational constant
at T=0, and does not depend on whether or not the gravitational field
obeys the Einstein equations. That is why this universal modification of
the free energy for gravitational field can be used to study
thermodynamics of quantum systems in condensed matter (such as quantum
liquids superfluid
^{3}He and ^{4}He), where the effective gravity emerging for
fermionic and/or bosonic quasiparticles in the low-energy corner is quite
different from the Einstein gravity.