Τομέας Αστροφυσικής, Αστρονομίας και Μηχανικής
Library of the School of Science

2011-06-23

2011

Γιαννοπούλου Μαρία

Θεοχάρης Αποστολάτος, Θεοδόσιος Χριστοδουλάκης, Μιχαήλ Τσαμπαρλής.

Επέκταση του Θεωρήματος Birkhoff σε θεωρίες βαρύτητας f(R) και διερεύνηση λύσεων.

Greek

We consider the more general spherically symmetric metric:

(*)


We have the Einstein-Hilbert action . If this become static, we derive the
Einstein equations .

We consider now the general action . When this becomes static, derives the
following equations of motion:


or



where we see that the second member of the equation is not necesserily
diagonal. I general the components are not zero.

Birkhoff’ s theorem says that if we impose the Einstein equations at a general
spherically symmetric metric like (*), then the metric becomes static. That is
to say that depends only from distance.

We are trying now to develop the Birkhoff’ s theorem at a more general gravity
theories . We have to find under which conditions the metric becomes static.

At first, we have to diagonalize the equations of motion. This happens when
and or .

If we choose or -so that - the equations of motion become diagonal and the metric becomes
static.


That is to say that the metric may become static whitout necessarily the
equations of motion being satisfying.


The natural solutions (that make the metric Minkowski at infinity) are:

, where και:

- For , must be .

- For must be .
When , we get the Schwarzschild solution.

Birkoff's theorem, f(R) gravity theories

No

0

No

2

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