Astrophysical Consequences of Horava Gravity: Black Holes and

Stars

Mini-Workshop in 2010 Int. School on NR and GW (28 July 2010, APCTP, Pohang)

Mu-In ParkChunbuk Nat’al Univ.

Based on arXiv:0905.4480 [JHEP], work in progress,

Plan

I. Motivations.

II. Stars and Black Holes in GR.

III. Black Holes and Stars in HoravaGravity.

I. Motivations.Theoretical Aspects:1) Horava gravity is proposed as a

“quantum gravity” : Power-countingrenormalizable without ghost problem.

2) Black Hole Solutions in Horava gravity would be more realistic than that those of GR. And several exact black hole solution have been found [Spherically symmetric sols: Lu,Mei,Pope; Kehagias-Sfetsos; MIP; Kiritisis-Kofinas, … ]

Motivations-Continued3) But the corresponding Star solutions,

whose gravitational collapse would produce the black holes, have not been studied yet.

Cf. There are some (disagreeing) works on stars in “projectable” Horava gravity [Mukohyama; Greenwald,Papazoglou,Wang]. But this is questionable in black hole (star) physics which needs non-projectability, in general.

Motivations-ContinuedExperimental Aspects:1) Horava gravity has smaller gravity in short distance than GR: There is “repulsive” (anti-) gravity due to the higher-(spatial) derivatives.2) This is the origin of

a) Inner horizon without hairs.b) Bouncing cosmology without matters.c) Accelerating universe, i.e, dark energy.

Motivations-Continued3) What are the consequences of the repulsive gravity in the interior of stars ?

Can this explain the Supernova Explosions,which is puzzling(?) in GR ?

What is its effect in the stellar evolution. Is there any new possibility in the evolution ?

II. Stars and Black Holes in GR

Schwarzschild Solution, Kerr Solution

R

Interior Solutions for given equations of state

• Interior Solution : For spherically symmetric, perfect fluid stars, the ansatz is given by

with

• rr (Einsetin) Eq. :

• (Continuity Eq.):

Tolman-Oppenheimer-Volkoff (TOV) Eq.

• Uniform Density (i.e., incompressible)Model: A simple and semi-realistic model.

• Solving TOV Eq. gives ( p(R)=0 )

• Solving rr Einstein Eq. gives

Remarks• P(r) is monotonically decreasing function

of r: P(r)>0.

• P(0) becomes infinity for GM=(4/9)R: No static solutions above this mass for a radius R. In other words, we have maximum GM/R ratio,

for static sols: Collapsing beyond this and forming a black hole with

III. Black Holes and Stars in Horava Gravity.

• IR modified Horava gravity:

• It is found that there does exit the black hole which converges to the usual Schwarzschild solution in Minkowski limit, i.e., for (s.t. Einstein-Hilbert in IR) (Kehagias, Sfetsos) .

IR modification term

• For , KS got the asymptotically flat solution

• For IR regime, one gets the usual Sch. Black hole behavior

with the two horizons ( )

Remarks• The higher-derivative term produces the

inner horizon. This is a generic feature of higher derivative gravities: The higher derivative term contributes as a matter in the Einstein’s equation.

• For more general spacetime with , but with , I can obtain

• For , this reduces to LMP’s solution (with )

• For , this reduces to KS’s solution (with )

• So, I obtained the general solution for .

(LMP’s solution)

ParkKS

Remarks

• There are more general solutions with arbitrary which reduce to LMP’s solution for . But, there is no “explicit”, analytic solution but only in “implicit” forms. (See Kiritisis-Kofinas)

Interior Sol. in IR-modified Horava Gravity

• For spherically symmetric, perfect fluid stars, the ansatz is given by

• with

• rr Eq.:

• (Continuity Eq.) :

Tolman-Oppenheimer-Volkoff (TOV) Eq.

• Uniform Density (i.e., incompressible)Model: A simple and semi-realistic model.

• Solving TOV Eq. gives ( p(R)=0 )

Stars in Minkowski space•

• There are two branches depending on b:

• I. b<0:

P(r) is monotonically decreasing function of r: P(r)>0.

P(0) becomes infinity for: No static solutions above this mass for

a radius R and Collapsing beyond this.

• II. b>0:

P(r) is monotonically increasingfunction of r: P(r)<0.

Non-static for any P(r) >0 !! : Gravity is repulsive in this case; Explosion !!

Q: Can this effect be another engine ofSupernova explosion ?

* Rough Estimation of

• Gravitational Potential has two competating parts:

Newtonian: attractive

Horava correction: repulsive