Abstract: The unbounded center-of-mass (CM) energy of colliding particles near horizon of a black hole emerges even in 1+ 1-dimensional Horava-Lifshitz gravity. The latter has imprints of renormalizable quantum gravity characteristics in accordance with simple power counting. The result obtained is valid also for a 1-dimensional Compton process between a massive/massless Hawking photon emaneting from the black hole and an in falling massless/massive particle.

1. Particle Collision near 1+1-D
Horava-Lifshitz Black Holes
M. Halilsoy & A. Ovgun
Eastern Mediterranean University (EMU)
arXiv:1504.03840 [gr-qc]
QDIS14 Famagusta, Northern Cyprus
2 May 2015
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]

2. Outline
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]
 MOTIVATION
 1+1-D HL BLACK HOLES
 CM ENERGY OF PARTICLE COLLISION NEAR THE
HORIZON OFTHE 1+1 -D HL BLACK HOLE
 SOME EXAMPLES
 HAWKING PHOTONVERSUS AN INFALLING
PARTICLE
 CONCLUSION

3. Motivation
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]
Banados, Silk, West (BSW Effect),
Phys. Rev. Lett. 103, 111102 (2009).

4. Motivation
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]
Is it also valid for near horizon of a black
hole emerges even in 1+1- dimensional
Hořava-Lifshitz gravity ?
Banados, Silk, West (BSW Effect),
Phys. Rev. Lett. 103, 111102 (2009).

5. M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]
1+1-D HL BLACK HOLES
 The line element is
where a general class of solutions is obtained as follows
 In the case of and , it
gives a Schwarzschild-like solution;

6. 1+1-D HL BLACK HOLES
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]
 On the other hand, the choice of the parameters, for ,
 gives a Reissner--Nordström-like solution.
 The new black hole solution which is derived by Bazeia
et. al. is found by taking


7. 1+1-D HL BLACK HOLES
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]
 This solution develops the following horizons
 As they degenerate, i.e.
 The Hawking temperature is given in terms of the outer
horizon as follows

8. 1+1-D HL BLACK HOLES
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]
 For the special case
the horizons are independent of the mass :
The temperature is then given simply by
This is a typical relation between the Hawking temperature
and the mass of black holes in dimensions

9. CM ENERGY OF PARTICLE COLLISION NEAR THE
HORIZON OF THE 1+1 -D HL BLACK HOLE
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]

10. CM ENERGY OF PARTICLE COLLISION NEAR THE
HORIZON OF THE 1+1 -D HL BLACK HOLE
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]
 Lagrangian equation
 The canonical momenta calculated as
 Hence,
 and by using the normalization
condition for time-like particles
t
E

11. CM ENERGY OF PARTICLE COLLISION NEAR THE
HORIZON OF THE 1+1 -D HL BLACK HOLE
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]
 The two-velocities can be written as,
 The CM energy is given by
t
E

12. CM ENERGY OF PARTICLE COLLISION NEAR THE
HORIZON OF THE 1+1 -D HL BLACK HOLE
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]
 The lowest order term gives the CM energy of two
particles as
 There are two cases for this CM energy, when 0 ,
the CM energy is reduced to
which is unbounded for
 when
t
E

13. SOME EXAMPLES
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]
 Schwarzchild-like Solution:
 Reissner-Nordstrom-like solution:
When the location of particle 1 which has positive energy
approachs the horizon , on the other hand the particle 2
escaping from the horizon with negative energy might give
us the BSW effect
t
E

14. SOME EXAMPLES
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]
 The Non-Black Hole case:
 The Extremal case of the Reissner-Nordstrom like black
hole:
 Specific New Black Hole Case:
t
E

15. HAWKING PHOTON VERSUS AN INFALLING PARTICLE
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]
 The massless photon of such an emission can naturally scatter an infalling
particle or vice versa.This phenomenou is analogous to a Compton
scattering taking place in 1+1-dimensions. Null-geodesics for a photon can
be described simply by
 The center-of-mass energy of a Hawking photon and the infalling particle
can be taken now as
t
E

16. HAWKING PHOTON VERSUS AN INFALLING PARTICLE
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]
 The center-of-mass energy of a Hawking photon and the infalling particle
can be taken now as
 In the near horizon limit this reduces to

 Note that for we have
 which is finite and therefore is not of interest. On the other hand for
we obtain an unbounded one.
t
E

17. CONCLUSION
M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]
 Our aim is to show that the BSW effect which arises in
higher dimensional black holes applies also in the 1+1- D.
 In other words the strong gravity near the event horizon
effects the collision process with unlimeted source to
turn it into a natural accelerator.
 Key property: presence of event horizon plus critical
 particle
 Finally, we must admit that absence of rotational effects in
1+1- D confines the problem to the level of a toy model.

18. M.Halilsoy,A.Ovgun Particle Collision near 1+1-D Horava-Lifshitz Black Holes arXiv:1504.03840 [gr-qc]