Relativistic stellar clustersG.S.Bisnovatyi-Kogan (IKI, Moscow),

ГАИШ, пятница, 21 марта 2014

Вскоре после открытия квазаров с большим красным смещением:

=1 was considered by Zeldovich and Podurets (1965)

Star Clusters with Cutoff

Comments on Astrophysics 1, 134, 1969

GR5: Tbilisi, 9-13 September 1968Proceedings: None.Abstracts: GR5, abstracts of the 5th international conference on gravitation and the theory of relativity, ed. V.A. Fock et al. Tbilisi University Press (1968).

MODELS OF CLUSTERS OF POINT MASSES WITH LARGE CENTRAL REDSHIFTS

G. S. Bisnovatyi-Kogan and Ya. B. Zel'dovich

Astrofizika, Vot. 5, No. 2, pp. 223-234, 1969

=2/a

0.006

r(g)/r=const~a

Isothermal star cluster in Newtonian limit

Variational principle

Relative binding energy E(b)/M is better for

stability analysis than M

Publications:

Earlier publications

Isolated cluster

is the kinetic energy cutoff.

In the Newtonian limit, formally reduces to

Similarity between clusters in the box and clusters with cutoff

Newtonian cluster in box GR cluster with cutoff

E(b)/N

W(0)=const, each extremum gives birth to new dynamically

unstable mode . At W(0)> 15.8 all models are stable.

Dynamic stability against perturbations with constant adiabatic invariants.

Equivalent to constant entropy for stability of gaseous star

Thermodynamic stability include processes leading to thermal equilibrium, smoothing temperature over the newtonian

cluster or star

Clusters with cutoff : ApJ (1998), 500, 217

Large central density (central redshift) regime loss of dynamic stability at T=0.06

DU T U

S S

DS TUDU T U

S S

DS TU

Astro-ph 1403.3985

Interpretation: GW from the inflation (Linde)

A simplified model of the formation of structures in dark matterand a background of very long gravitational waves

G. S. Bisnovatyi-Kogan1,2

1Space Research Institute, Moscow, Russia, Profsoyuznaya 84/32, Moscow 117997, Russia

2Theoretical Astrophysics Center, Juliane Maries Vej 30, Dk-2100 Copenhagen Ø, Denmark

Mon. Not. R. Astron. Soc. 347, 163–172 (2004)