2 2 ( ) 2 2 ( ) 2 2 2 22= sinr rds e dt e dr r d dψ λ θ θ ϕ − + + +

( )p p ρ=

(0) (1)=g g gµ ν µ ν µ ν+(0) (1)=T T Tµ ν µ ν µ ν+

24dM

rdr

π ρ=3(4 )( )

( 2 )

dp r p M p

dr r M r

π ρ+ +=−

1

( )

d dp

dr p dr

υρ

−=+

2

2*

( ) 0lm

l lmd ZV r Z

drω + − =

23

3( ) ( 1) 4 ( ) 6l e

V r l l r r p Mr

υ

π ρ = + + + −

2

2*

( ) 0lm

l lmd ZV r Z

drω + − =

( ) ( )

2 3 2 2 2 34 2

2( 2 )( ) ( 1) 3 9 9

( 3 )

1 2

2

l r MV r n n r Mn r M nr M

r nr M

l ln

− = + + + + +− −

=

{ }( 1 ), , ,lm lm lm lmV H K W

*

*

lim

lim

i rout

r

i rin

r

Z e

Z e

ω

ω

−

→ ∞

→ ∞

:

:

* * * /lim Ri r i r routr

Z e e eω ω τ− −

→ ∞=:

'Zg

Z=

2 22

2 4

2 ( 1) 60

(2 2 ) ( 2 ) ( 2 )r

r M l l r Mg g g

M r r M r r M

ω + −∂ + + − =− − −

i r i r

i r i r

Ae Beg i

Ae Be

ω ω

ω ωω−

−

−+

:

g iω: g iω−:

ir a ye α−= +

sin cos 0R Iω α ω α+ >

g iω−: g iω:

Axial fundamental wI mode: Hyperon matter

( ) ( )M

kHz R Km A BR

ω = +

Axial fundamental wI mode: Hybrid – quark matter

1( )

( )

MkHz A B

R Km Rω = + ÷

Axial fundamental wI mode: Hyperon matter2310

( )( )

M MM M a b c

s R Rτ µ = + + ÷ ÷ e

Axial fundamental wI mode: Hybrid – quark matter

2310( )

( )

M MM M a b c

s R Rτ µ = + + ÷ ÷ e

Polar fundamental wI mode: Hyperon matter

( ) ( )M

kHz R Km A BR

ω = +

Polar fundamental wI mode: Hybrid – quark matter

( ) ( )M

kHz R Km A BR

ω = +

Polar fundamental wI mode: Hyperon matter

2310( )

( )

M MM M a b c

s R Rτ µ = + + ÷ ÷ e

Polar fundamental wI mode: Hybrid – quark matter

2310( )

( )

M MM M a b c

s R Rτ µ = + + ÷ ÷ e

Axial fundamental wII mode: Hyperon matter

2 ( )( ) ( ) RkHz M M A Be λω = +e

Axial fundamental wII mode: Hybrid – quark matter

2 ( )( ) ( ) RkHz M M A Be λω = +e

Polar f mode: Hyperon matter

3( )

MkHz A B

Rω = +

Polar f mode: Hybrid – quark matter

3( )

MkHz A B

Rω = +

Polar f mode: Hyperon matter

3

4 ( )

cM Mu v

R s Rτ = + ÷

Polar f mode: Hybrid – quark matter

3

4 ( )

cM Mu v

R s Rτ = + ÷

Polar fundamental p mode: Hyperon matter

( ) ( )M

kHz M Km A BR

ω = +

Polar fundamental p mode: Hybrid – quark matter

( ) ( )M

kHz M Km A BR

ω = +

Axial modes: scaling in units of the central pressure

Similar por Polar wI0 modes: scaling in units of the central pressure

Axial fundamental wI modes

Polar fundamental wI modes

Polar f modes: scaling in units of Mass / Radius respectively